##
## Bibliography in BiB-TeX Format## Mladen Victor Wickerhauser |

## 2012

@InProceedings(ww:wtnnl, Author = {Zhu Wei and Mladen Victor Wickerhauser}, Title = {Wavelet Transforms by Nearest Neighbor Lifting}, Abstract = {We show that any discrete wavelet transform using finite impulse response filters may be factored into lifting steps that use only nearest-neighbor array elements. We then discuss the advantages and disadvantages of imposing this additional requirement.}, URL = {http://www.math.wustl.edu/~victor/papers/zwnnlift.pdf}, DOI = {}, BookTitle = {Excursions in Harmonic Analysis}, Editor = {Travis Andrews and Radu V. Balan and John J. Benedetto and Wojciech Czaja and Kasso Okoudjou}, Publisher = {Springer-Verlag}, Address = {New York}, Pages = {175--194}, Month = {}, Year = {2012})

## 2011

@Article(hmmwmwlw:ispdcumitn, Author = {Michael Hughes and Jon N. Marsh and John E. McCarthy and Mladen Victor Wickerhauser and Brian Maurizi and Kirk D. Wallace and Gregory M. Lanza and Samuel A. Wickline}, Title = {Improved Signal Processing to Detect Cancer by Ultrasonic Molecular Imaging of Targeted Nanoparticles}, Abstract = {In several investigations of molecular imaging of angiogenic neovasculature using a targeted contrast agent, R\'enyi entropy [If(r)] and a limiting form of R\'enyi entropy (If,infinity) exhibited significantly more sensitivity to subtle changes in scattering architecture than energy-based methods. Many of these studies required the fitting of a cubic spline to backscattered waveforms prior to calculation of entropy [either If(r) or If,infinity]. In this study, it is shown that the robustness of If,infinity may be improved by using a smoothing spline. Results are presented showing the impact of different smoothing parameters. In addition, if smoothing is preceded by low-pass filtering of the waveforms, further improvements may be obtained.}, URL = {http://link.aip.org/link/?JAS/129/3756/1}, DOI = {10.1121/1.3578459}, Journal = {Journal of the Acoustical Society of America}, Volume = {129}, Number = {6}, Pages = {3756--3767}, Month = {June}, Year = {2011}) @Article(hammmwww:ussabuwamstdm, Author = {Michael S. Hughes and Kwesi Agyem and Jon N. Marsh and John E. McCarthy and Brian N. Maurizi and M. Victor Wickerhauser and Kirk D. Wallace and Samuel A. Wickline}, Title = {Use of Smoothing Splines for Analysis of Backscattered Ultrasonic Waveforms: Application to Monitoring of Steroid Treatment of Dystrophic Mice}, Abstract = {Duchenne muscular dystrophy (DMD) is an X-linked genetic disease characterized by progressive weakness and wasting of skeletal and cardiac muscle; boys present with weakness by the age of 5 years and, if left untreated, are unable to walk without assistance by the age of 10 years. Therapy for DMD has been primarily palliative, with oral steroids emerging as a first-line approach even though this treatment has serious side-effects. Consequently, low-cost imaging technology suitable for improved diagnosis and treatment monitoring of DMD would be of great value, especially in remote and underserved areas. Previously, we reported use of the logarithm of the signal energy, log[Ef], and a new method for ultrasound signal characterization using entropy, Hf, to monitor prednisolone treatment of skeletal muscle in a dystrophin-deficient mouse model. Three groups were studied: mdx mice treated with prednisolone, a control group of mdx mice treated with saline, and a control group of wild-type mice treated with saline. It was found that both log[Ef] and Hf were required to statistically differentiate the three groups. In the current study, we show that preprocessing of the raw ultrasound using optimal smoothing splines before computation of either log[Ef] or a rapidly computable variant of Hf, denoted If,infinity, permits delineation of all three groups by either metric alone. This opens the way to the ultimate goal of this study, which is identification and implementation of new diagnostically sensitive algorithms on the new generation of low-cost hand-held clinical ultrasonic imaging systems.}, DOI = {10.1109/TUFFC.2011.2093}, URL = {http://dx.doi.org/10.1109/TUFFC.2011.2093}, Journal = {IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control}, Pages = {2361--2369}, Volume = {58}, Number = {11}, Month = {November}, Year = {2011})

## 2010

@Article(mwmwmlwh:artclfremit, Author = {Jon N. Marsh and Kirk D. Wallace and John E. McCarthy and M. Victor Wickerhauser and Brian N. Maurizi and Gregory M. Lanza and Samuel A. Wickline and Michael S. Hughes}, Title = {Application of a Real-Time, Calculable Limiting Form of the {R}{\'e}nyi Entropy for Molecular Imaging of Tumors}, Abstract = {Previously, we reported new methods for ultrasound signal characterization using entropy, Hf; a generalized entropy, the R\'enyi entropy, If(r); and a limiting form of R\'enyi entropy suitable for real-time calculation, If,infinity. All of these quantities demonstrated significantly more sensitivity to subtle changes in scattering architecture than energy-based methods in certain settings. In this study, the real-time calculable limit of the R\'enyi entropy, If,infinity, is applied for the imaging of angiogenic murine neovasculature in a breast cancer xenograft using a targeted contrast agent. It is shown that this approach may be used to reliably detect the accumulation of targeted nanoparticles at five minutes post-injection in this in vivo model.}, URL = {http://www.ncbi.nlm.nih.gov/pubmed/20679020} Journal = {IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control}, Volume = {57}, Number = {8}, Pages = {1890--1895}, Month = {August}, Year = {2010}) @InProceedings(mwlwhmw:alfremitucrp, Author = {Jon N. Marsh and Kirk D. Wallace and Gregory M. Lanza and Samuel A. Wickline and Michael S. Hughes and John E. McCarthy and M. Victor Wickerhauser}, Title = {Application of a Limiting Form of the {R}{\'e}nyi Entropy for Molecular Imaging of Tumors Using a Clinically Relevant Protocol}, Abstract = { In earlier studies we reported on the application of R\'enyi entropy, I_f(r), r<2, for the detection of precancerous lesions, by detection of subtle changes in backscattered waveforms f(t) that occured as targeted nanoparticles slowly accumulated near the lesion. In contrast, the signal energy defined as the sum of squares of the signal over the same moving window, was unable to detect this change (as was conventional B-mode imaging). Although the computational effort to obtain the result precluded its clinical application with currently available equipment, the study raised the possibility of further sensitivity improvements by using values of r closer to the limiting value of 2, where I_f(r) approaches infinity. The current study demonstrates that by extracting the asymptotic form of I_f(r) as r tends to 2 there is no loss of sensitivity. However, the resulting algorithm is must faster than previous approaches and has an operation count that is suitable for implementation in a real-time imaging system. }, DOI = {10.1109/ULTSYM.2010.5935829}, URL = {http://dx.doi.org/10.1109/ULTSYM.2010.5935829}, BookTitle = {International Ultrasonics Symposium (IUS)}, Institution = {IEEE}, Address = {San Diego, California}, Pages = {53--56}, Month = {11--14 October}, Year = {2010})

## 2009

@Article(rtrepmiutn:wmwmlwh, Author = {Kirk Wallace and John McCarthy and Victor Wickerhauser and Jon Marsh and Gregory Lanza and Samuel Wickline and Michael Hughes}, Title = {Real-Time {R}enyi Entropy Processing for Molecular Imaging Using Targeted Nanoparticles}, URL = {http://www.math.wustl.edu/~victor/papers/rtrepmiutn.pdf}, Abstract = {Previously, improvements in in vivo molecular imaging sensitivity were obtained using Renyi entropy, Ifr with values of r near 2, specifically r1.99. This result raised the possibility of further improvements in sensitivity even closer to the limit r-->2 at r2, Ifr is undefined. However, such an investigation was not feasible due to excessive computational time required to calculate Ifr near this limit. In this study, an asymptotic expression for the limiting behavior of Ifr as r-->2 is derived and used to present results analogous to those obtained with If1.99. Moreover, the limiting form, If, is computable directly from the experimentally measured waveform, ft by an algorithm suitable for real-time implementation. To test our approach, five mice were injected with 3-targeted nanoparticles, and ultrasound images obtained at 0-, 15-, 30-, and 45-min post-injection. Two control groups N5, injected with untargeted-nanoparticles, or no injection were also imaged. Renyi images were able to differentiate the groups p0.05 at 15 min post-injection. This outcome agrees with previous studies using targeted-nanoparticles and demonstrates the ability of entropy-based signal receivers when used in conjunction with targetednanoparticles to elucidate the presence of 3-integrins in primordial neovasculature, particularly in acoustically unfavorable environments.} Journal = {Journal of the Acoustical Society of America}, Volume = {126}, Number = {4}, Page = {2214}, Month = {October}, Year = {2009}) @Article(hmwmafwtsalw:rtclfreadscsa, Author = {Michael S. Hughes and John E. McCarthy and M. Victor Wickerhauser and Jon N. Marsh and Jeffery M. Arbeit and Ralph W. Fuhrhop and Kirk D. Wallace and Lewis Thomas and James Smith and Kwesi Agyem and Gregory M. Lanza and S. A. Wickline}, Title = {Real-time Calculation of a Limiting Form of the {R}enyi Entropy Applied to Detection of Subtle Changes in Scattering Architecture}, URL = {http://www.math.wustl.edu/~victor/papers/hmwmafwtsalw.pdf}, Abstract = {Previously we reported a new method for ultrasound signal characterization using entropy, $H_f$, and demonstrated that in certain settings, further improvements in signal characterization could be obtained by generalizing to Renyi Entropy-based signal characterizations, $I_f(r)$, with values of $r$ near 2 (specifically $r=1.99$). We speculated that further improvements in sensitivity might be realized at the limit $r\to 2$. At that time, such investigation was not feasible due to excessive computational time required to calculate $I_f(r)$ near this limit. In this paper, we now derive an asymptotic expression for the limiting behavior of $I_f(r)$ as $r\to 2$ and present results analogous to those obtained with $I_f(1.99)$. Morover, the limiting form, $I_{f,\infty}$, is computable directly from the experimentally measured waveform, $f(t)$, by an algorithm that is suitable for real-time calculation and implmentation. }, DOI = {10.1121/1.3224714}, Journal = {Journal of the Acoustical Society of America}, Volume = {126}, Number = {5}, Pages = {2350--2358}, Month = {November}, Year = {2009})

## 2007

@InProceedings(ow:kldmommslspp, Author = {Peter Fogh Odgaard and Mladen Victor Wickerhauser}, Title = {{K}arhunen-{L}o\'{e}ve ({PCA}) based detection of multiple oscillations in multiple measurement signals from large-scale process plants}, URL = {http://www.math.wustl.edu/~victor/papers/kloscinew.pdf}, Abstract = {In the perspective of optimizing the control and operation of large scale process plants, it is important to detect and to locate oscillations in the plants. This paper presents a scheme for detecting and localizing multiple oscillations in multiple measurements from such a large-scale power plant. The scheme is based on a Karhunen-Lo\`{e}ve analysis of the data from the plant. The proposed scheme is subsequently tested on two sets of data: a set of synthetic data and a set of data from a coal-fired power plant. In both cases the scheme detects the beginning of the oscillation within only a few samples. In addition the oscillation localization has also shown its potential by localizing the oscillations in both data sets.}, BookTitle = {Proceedings of the {A}merican {C}ontrol {C}onference 2007}, Publisher = {American Automatic Control Council ({AACC})}, Pages = {5893--5898}, Address = {New York, NY}, Month = {11--13 July}, Year = {2007})

## 2006

@Article(osawm:fbhsfcdp, Author = {Peter Fogh Odgaard and Jakob Stoustrup and Palle Andersen and Mladen Victor Wickerhauser and Henrik Fl\o e Mikkelsen}, Title = {Feature Based Handling of Surface Faults in Compact Disc Players}, URL = {http://www.math.wustl.edu/~victor/papers/osawm.pdf}, DOI = {http://dx.doi.org/10.1016/j.conengprac.2006.01.002}, Abstract = { Compact Disc Players have been on the market for more than two decades and a majority of the control problems involved have been solved. However, there are still problems with playing Compact Discs related to surface faults like scratches and fingerprints. two servo control olops are used to keep the Optical Pick-up Unit focused on the information track of the Compact Disc. The problem is to design servo controllers which are well suited for handling surface faults that disturb position measurements, yet still react sufficiently against normal disturbances like mechanical shocks. In this paper a novel method called feature based control is presented. The method is based on a fault tolerant control scheme, which uses extracted features of the surface faults to remove those from the detector signals used for control during the occurence of surface faults. The extracted features are Karhunen--Lo\`eve approximations of the surface faults. The performance of the feature based control scheme is validated by experimental work with Compact Discs having known surface defects. }, Journal = {Control Engineering Practice}, Volume = {14}, Number = {12}, Pages = {1495--1509}, Institution = {Washington University}, Address = {Saint Louis, Missouri}, Month = {December}, Year = {2006}) @InProceedings(ow:fpccdp, Author = {Peter Fogh Odgaard and Mladen Victor Wickerhauser}, Title = {Fault Predictive Control of Compact Disk Players}, URL = {http://www.math.wustl.edu/~victor/papers/fpccdp.pdf}, Abstract = {Optical disc players such as CD-players have problems playing certain discs with surface faults like scratches and fingerprints. The problem is to be found in the servo controller which positions the optical pick-up, such that the laser beam is focused on the information track. A scheme handling this problem, called feature based control, has been presented in an other publications of the first author. This scheme is based on an assumption that the surface faults do not change from encounter to encounter. This assumption is unfortunately not entirely true. This paper proposes an improvement of the feature based control scheme, such that a prediction step is included. The proposed scheme is compared with the feature based control scheme, in the perspective of handling surface faults, by simulations. These simulations show the improvements given by the proposed algorithm.}, BookTitle = {Proceedings of 6th {IFAC} Symposium on Fault Detection, Supervision and Safety of Technical Processes.}, Publisher = {IFAC}, Address = {Beijing, China}, Month = {30 August to 1 September}, Pages = {1063--1068}, Year = {2006}) @InProceedings(osw:wpbdsfcd, Author = {Peter Fogh Odgaard and Jakob Stoustrup and Mladen Victor Wickerhauser}, Title = {Wavelet Packet based Detection of Surface Faults on Compact Discs}, URL = {http://www.math.wustl.edu/~victor/papers/wpbdsfcd.pdf}, Abstract = {In this paper the detection of faults on the surface of a compact disc is addressed. Surface faults like scratches and fingerprints disturb the on-line measurement of the pick-up position relative to the track. This is critical since the pick-up is focused on and tracked at the information track based on these measurements. A precise detection of the surface fault is a prerequisite to a correct handling of the faults in order to protect the pick-up of the compact disc player from audible track losses. The actual fault handling which is addressed in other publications can be carried out by the use of dedicated filters adapted to remove the faults from the measurements. In this paper detection using wavelet packet filters is demonstrated. The filters are designed using the joint best basis method. Detection using these filters shows a distinct improvement compared to detection using ordinary threshold methods.}, BookTitle = {Proceedings of 6th {IFAC} Symposium on Fault Detection, Supervision and Safety of Technical Processes.}, Publisher = {IFAC}, Address = {Beijing, China}, Month = {30 August to 1 September}, Pages = {1165--1170}, Year = {2006})

## 2005

@Article(elnetal:cmcdcdt, Title = {A Comparison of {M}onte {C}arlo Dose Calculation Denoising Techniques}, Author = {I. El Naqa and I. Kawrakow and M. Fippel and J. V. Siebers and P. E. Lindsay and M. V. Wickerhauser and M. Vicic and K. Zakarian and N. Kauffmann and J. O. Deasy}, URL = {http://stacks.iop.org/0031-9155/50/909}, DOI = {doi:10.1088/0031-9155/50/5/014}, Abstract = {Recent studies have demonstrated that Monte Carlo (MC) denoising techniques can reduce MC radiotherapy dose computation time significantly by preferentially eliminating statistical fluctuations (`noise') through smoothing. In this study, we compare new and previously published approaches to MC denoising, including 3D wavelet threshold denoising with sub-band adaptive thresholding, content adaptive mean-median-hybrid (CAMH) filtering, locally adaptive Savitzky--Golay curve-fitting (LASG), anisotropic diffusion (AD) and an iterative reduction of noise (IRON) method formulated as an optimization problem. Several challenging phantom and computed-tomography-based MC dose distributions with varying levels of noise formed the test set. Denoising effectiveness was measured in three ways: by improvements in the mean-square-error (MSE) with respect to a reference (low noise) dose distribution; by the maximum difference from the reference distribution and by the `Van Dyk' pass/fail criteria of either adequate agreement with the reference image in low-gradient regions (within 2 percent in our case) or, in high-gradient regions, a distance-to-agreement-within-2-percent of less than 2 mm. Results varied significantly based on the dose test case: greater reductions in MSE were observed for the relatively smoother phantom-based dose distribution (up to a factor of 16 for the LASG algorithm); smaller reductions were seen for an intensity modulated radiation therapy (IMRT) head and neck case (typically, factors of 2.4). Although several algorithms reduced statistical noise for all test geometries, the LASG method had the best MSE reduction for three of the four test geometries, and performed the best for the Van Dyk criteria. However, the wavelet thresholding method performed better for the head and neck IMRT geometry and also decreased the maximum error more effectively than LASG. In almost all cases, the evaluated methods provided acceleration of MC results towards statistically more accurate results.}, Journal = {Physics in Medicine and Biology}, Volume = {50}, Year = {2005}, Pages = {909--922}) @Article(cmwj:fwewb, Author = {Elvir \v{C}au\v{s}evi\'c and Robert E. Morley and M. Victor Wickerhauser and Arnaud E. Jacquin}, Title = {Fast Wavelet Estimation of Weak Biosignals}, URL = {http://www.math.wustl.edu/~victor/papers/cmwj.pdf}, Abstract = {Wavelet based signal processing has become commonplace in the signal processing community over the past decade and wavelet based software tools and integrated circuits are now commercially available. One of the most important applications of wavelets is in removal of noise from signals, called denoising, accomplished by thresholding wavelet coefficients in order to separate signal from noise. Substantial work in this area was summarized by Donoho and colleagues at Stanford University, who developed a variety of algorithms for conventional denoising. However, conventional denoising fails for signals with low signal-to-noise ratio (SNR). Electrical signals acquired from the human body, called biosignals, commonly have below 0 dB SNR. Synchronous linear averaging of a large number of acquired data frames is universally used to increase the SNR of weak biosignals. A novel wavelet-based estimator is presented for fast estimation of such signals. The new estimation algorithm provides a faster rate of convergence to the underlying signal than linear averaging. The algorithm is implemented for processing of auditory brainstem response (ABR) and of auditory middle latency evoked potential response (AMLR) signals. Experimental results with both simulated data and human subjects demonstrate that the novel wavelet estimator achieves superior performance to that of linear averaging.}, Journal = {IEEE Transactions on Biomedical Engineering}, Month = {June}, Volume = {52}, Number = {6}, Pages = {19}, Year = {2005})

## 2004

@TechReport(gw:ptcnii, Author = {William F. Gossling and Mladen Victor Wickerhauser}, Title = {Prices, the Trade Cycle, and the Nature of Industrial Interdependence}, Abstract = {The continuance of a rise in prices in a Western economy well after a downturn in final demands, termed ``Stagflation,'' has been a puzzle to economists in the 20th century: we hope, from the results set out in this paper, that any stagflation encountered in the 21st century will have been understood and even anticipated (in the proper sense of that word) by appropriate economic policies which include the use of input-output (or interindustry) tables. In conclusion, at the end of this paper, attention is drawn to the computability of projections of industrial price-levels and rates of return: the ``duals'' to the familiar ``primal'' projections (embracing industrial outputs and growth rates) into the future. This leads one to a conjoint ``forward view'' (see Gielnik, 1980, in ``Input, Output, and Marketing,'' London, I.-O. P. C.) which should be applicable at least to most economies which have enough of the required data.}, URL = {http://www.math.wustl.edu/~victor/papers/gw.pdf}, Software = {http://www.math.wustl.edu/~victor/software/cycles/index.html}, Pages = {13}, Institution = {Washington University}, Address = {Saint Louis, Missouri}, Year = {2004}) @TechReport(osawm:smfrs, Author = {Peter Fogh Odgaard and Jakob Stoustrup and Palle Andersen and Mladen Victor Wickerhauser and Henrik Fl\o e Mikkelsen}, Title = {A Simulation Model of Focus and Radial Servos in {C}ompact {D}isc players with Disc Surface Defects}, URL = {http://www.math.wustl.edu/~victor/papers/cdsim.pdf}, Abstract = {Compact Disc players have been on the market for more than two decades, and most of the control servo problems have been solved. One large remainig problem is the handling of severe surface defects like scratches and fingerprints. This paper introduces a method for making the design of controllers handling surface defects easier: a model simulating a Compact Disc player reading a disc with surface defects. The model is based on data from discs with known surface defects. It is used to compare a high-bandwidth and a low-bandwidth controller's performance handling surface defects.}, Note = {Accepted by the {\em Proceedings of the IEEE Joint CCA, ISIC and CACSD}, September 2--4, 2004, Taipei, Taiwan.}, Pages = {8}, Institution = {Washington University}, Address = {Saint Louis, Missouri}, Year = {2003}) @Misc(w:mfmm-ex, Title = {Additional Solved Exercises from {\em {M}athematics for {M}ultimedia}}, Author = {Mladen Victor Wickerhauser}, HowPublished = {Available to instructors from Elsevier's Faculty Lounge}, Note = {236 pages}, Month = {September}, Year = {2004}) @InProceedings(wc:spie5439, Author = {Mladen Victor Wickerhauser and Wojciech Czaja}, Title = {A Simple Nonlinear Filter for Edge Detection in Images}, Abstract = {We specialize to two simple cases the algorithm for singularity detection in images from eigenvalues of the dual local autocovariance matrix. The eigenvalue difference, or ``edginess'' at a point, then reduces to a simple nonlinear function. We discuss the derivation of these functions, which provide low-complexity nonlinear edge filters with parameters for customization, and obtain formulas in the two simplest special cases. We also provide an implementation and exhibit its output on six sample images.}, URL = {http://www.math.wustl.edu/~victor/papers/mpedge.pdf}, Software = {http://www.math.wustl.edu/~victor/papers/mpedge.zip}, CrossRef = {spie5439}, Pages = {24--31}, Year = {2004}) @Proceedings(spie5439, Editor = {Harold H. Szu and Mladen V. Wickerhauser and Barak A. Pearlmutter and Wim Sweldens}, Title = {Independent Component Analyses, Wavelets, Smart Sensors, and Neural Networks {II}}, BookTitle = {Independent Component Analyses, Wavelets, Smart Sensors, and Neural Networks {II}}, Publisher = {SPIE}, Series = {SPIE Proceedings}, Volume = {5439}, Address = {Orlando, Florida}, ISBN = {0-8194-5362-5}, ISSN = {0277-786X}, Month = {14--15 April}, Year = {2004})

## 2003

@Book(w:mfmm, Author = {Mladen Victor Wickerhauser}, Title = {Mathematics for Multimedia}, URL = {http://www.math.wustl.edu/~victor/mfmm}, ISBN = {0-12-748451-5}, Abstract = {This textbook presents selected results in algebra and analysis, chosen for their usefulness in understanding and creating application software for multimedia signal processing and communication. Over one hundred exercises with complete solutions as well as example programs in Standard C are included to aid the student. The material forms the basis for a one-semester upper-level undergraduate course of Topics in Applied Mathematics at Washington University.}, Publisher = {Elsevier/Academic Press}, Address = {San Diego, California}, Pages = {xii + 302}, Month = {November}, Year = {2003}) @InCollection(w:introix, Author = {Mladen Victor Wickerhauser}, Title = {Introduction to {S}ection {IX}: Selected Applications}, URL = {http://www.math.wustl.edu/~victor/papers/introix.pdf}, Abstract = {Over the past decade, wavelet transforms have been widely applied. Good implementations of the discrete wavelet transform (DWT) were built into software systems such as Matlab and S-Plus, and DWT became a frequently-used tool for data analysis and signal processing. There are certain problems, though, on which this tool works particularly well. The most common ingredient in those problems is some complicated object that can be closely approximated by a few superposed wavelets. This compilation includes four seminal articles that introduced some of these stand-out DWT applications. I have taken a random and sparse sampling of relevant articles and books published around the same time, in order to place the results in context and illustrate their influence.}, Pages = {733--740}, BookTitle = {Fundamental Papers in Wavelet Theory}, ISBN = {cloth:0-691-11453-6,paper:0-691-12705-0}, Editor = {Christopher Heil and David Walnut}, Publisher = {Princeton University Press}, Address = {Princeton, New Jersey}, Month = {July}, Year = {2006}) @TechReport(ow:discr, Author = {Peter Fogh Odgaard and Mladen Victor Wickerhauser}, Title = {Discrimination Between Different Kinds of Surface Defects on Compact Discs}, URL = {http://www.math.wustl.edu/~victor/papers/odgaardd.pdf}, Abstract = {Compact Disc players have problems playing discs with surface defects such as scratches and finger prints. The problem is that handling normal disturbances such as mechanical shocks requires a high bandwidth of the controllers that keep the Optical Pick-Up focused and radially placed on the information track on the disc. In order for the controllers to handle the surface defects it is required that they are non-sensitive to the frequency contents of the defect, since a defect can be viewed as a disturbance on the measurements. A simple solution to this problem is to decrease the controller bandwidth during the defect. However, due to the variation of defects a more adaptive control strategy would be preferable. In this paper the defects are categorised into three groups. A discriminator is designed, based on the local most-discriminating basis vectors of the Karhunen-Lo\`eve and Haar bases as well as the mean of defect group vectors. In these bases the discrimination rule is simple. The defect in question is a member of the group it is closest to. The Karhunen-Lo\`eve basis gives a correct classification rate of more than 85.7 percent with three basis vectors and the Haar basis of more than 94.6 percent with 5 basis vectors.}, Note = {Accepted by the {\em Proceedings of IECON 2004}, Busan, Korea}, Pages = {6}, Institution = {Washington University}, Address = {Saint Louis, Missouri}, Year = {2003}) @TechReport(ow:timeloc, Author = {Peter Fogh Odgaard and Mladen Victor Wickerhauser}, Title = {Time Localisation of Surface Defects on Optical Discs}, URL = {http://www.math.wustl.edu/~victor/papers/odgaardt.pdf}, Abstract = {Many have experienced problems with their Compact Disc player when a disc with a scratch or finger print is played. One way to improve the playability of discs with such defects is to locate the defect in time and then handle it in a special way. This time localisation must be quite accurate, and Fang's algorithm for segmentation of the time axis is used because of its good performance in similar applications. For those defects where Fang's algorithm fails, the usual variance threshold method may be used as it handles eccentricity and end localisation better. }, Note = {Accepted by the {\em Proceedings of the IEEE Joint CCA, ISIC and CACSD}, September 2--4, 2004, Taipei, Taiwan.}, Pages = {6}, Institution = {Washington University}, Address = {Saint Louis, Missouri}, Year = {2003}) @Proceedings(spie5102, Editor = {Anthony J. Bell and Mladen V. Wickerhauser and Harold H. Szu}, Title = {Independent Component Analyses, Wavelets and Neural Networks}, BookTitle = {Independent Component Analyses, Wavelets and Neural Networks}, Publisher = {SPIE}, Series = {SPIE Proceedings}, Volume = {5102}, Address = {Orlando, Florida}, ISBN = {0-8194-4962-8}, ISSN = {0277-786X}, Month = {22--25 April}, Year = {2003}) @Article(w:ajse, Author = {Mladen Victor Wickerhauser}, Title = {Some Problems Related to Wavelet Packet Bases and Convergence}, URL = {http://www.math.wustl.edu/~victor/papers/ajse.pdf}, Abstract = {Wavelet packets are subsets of a multiresolution analysis and derive many of their properties therefrom. Those defined by a single filter pair have uncontrolled size and basis properties, in general. By substituting different filters at different scales according to a rule, these can be controlled. The number of orthonormal bases available in an MRA satisfies a recursion equation depending on the basis selection method, and some of these recursions have closed form solutions. Some of these orthonormal bases consist of uniformly bounded, uniformly compactly supported wavelet packets and are Schauder bases for many Banach spaces. With controlled size and support, the Carleson--Hunt theorem applies to show that a wavelet packet Fourier series of a continuous function converges pointwise almost everywhere.}, Journal = {Arabian Journal for Science and Engineering}, Volume = {28}, Number = {1C}, Pages = {45-58}, Month = {June}, Year = {2003}) @Article(w:ripples, URL = {http://www.math.wustl.edu/~victor/papers/ripples.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {Two Introductions to Wavelets}, Abstract = {Review of {\em Ripples in Mathematics: The Discrete Wavelet Transform}, by A. Jensen and A. la Cour-Harbo, ISBN 3-540-41662, and {\em A First Course in Wavelets with Fourier Analysis}, by Albert Boggess and Francis J. Narcowich, ISBN 0-13-022809-5}, Note = {Book review.}, Pages = {163--167}, Journal = {American Mathematical Monthly}, Volume = {110}, Number = {2}, Month = {February}, Year = {2003})

## 2002

@Misc(w:swaa, URL = {http://www.math.wustl.edu/~victor/talks/mvwswaa1.pdf, http://www.math.wustl.edu/~victor/talks/mvwswaa2.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {Survey of Wavelet Algorithms and Applications}, HowPublished = {SPIE Short Course Notes SC475, AeroSense 2002, Orlando, Florida}, Abstract = {DESCRIPTION: A brief description of wavelets and wavelet packets will be followed by a moderately detailed survey of fast discrete wavelet transform algorithms and implementations. Emphasis will be placed on the ``lifting'' implementation, treatment of boundaries, and wavelet and basis selection, keyed to the transforms used in the WSQ and JPEG2000 image compression algorithms. The related lapped orthogonal transforms will be discussed as well. LEARNING OUTCOMES: At the conclusion, students should have learned to: - define wavelets and wavelet packets and state their useful mathematical properties. - implement a basic wavelet transform by the lifting method; - implement one or more boundary treatments for wavelet transforms; - choose an appropriate wavelet for a given signal class; - describe the transforms used in the WSQ and JPEG2000 image compression algorithms. INTENDED AUDIENCE: The lecture will be pitched to engineers with some programming and signal processing experience, but will be understandable to anyone with a basic undergraduate mathematics, science, or engineering preparation. It will focus on the image compression example, but is intended to be useful to anyone seeking deeper understanding of the mathematical principles underlying signal analysis. }, Month = {April 4}, Year = {2002}) @Article(w:jmr, URL = {http://www.math.wustl.edu/~victor/papers/jmr.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {{\bf Wavelets: Tools for Science \& Technology}, by St\'ephane Jaffard, Yves Meyer, and Robert D. Ryan}, Abstract = {Review of {\em Wavelets: Tools for Science \& Technology}, by St\'ephane Jaffard, Yves Meyer, and Robert D. Ryan, SIAM, Philadelphia, 2001, ISBN 0-89871-448-6.}, Pages = {302--305}, Journal = {SIAM Review}, Volume = {44}, Number = {2}, Year = {2002}) @InProceedings(w:pwaa, URL = {http://www.math.wustl.edu/~victor/papers/pwaa.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {Progress in Wavelet Algorithms and Applications}, Abstract = {Wavelet and wavelet packet transforms are presently used for image compression and denoising. There has been recent progress on three fronts: implementing multiplication operations in wavelet bases, estimating compressibility by wavelet packet transform coding, and designing wavelet packets to control frequency spreading and pointwise convergence. Some open problems are mentioned.}, Editor = {Harold H. Szu}, BookTitle = {Wavelet and Independent Component Analysis Applications {IX}}, Publisher = {SPIE}, Series = {SPIE Proceedings}, Volume = {4738}, Address = {Orlando, Florida}, Month = {3--5 April}, CrossRef = {spie4738}, Pages = {157--168}, Year = {2002}) @InProceedings(w:aec, URL = {http://www.math.wustl.edu/~victor/papers/aec.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {Basis and Convergence Properties of Wavelet Packets}, Abstract = {Wavelet packets defined by a single filter pair have uncontrolled size and basis properties, in general. By substituting different filters at different scales according to a rule, these can be controlled. One can obtain Schauder bases of uniformly bounded, uniformly compactly supported wavelet packets. By controlling size and support, one can apply the Carleson--Hunt theorem to show that certain wavelet packet Fourier series of a continuous function converge almost everywhere.}, BookTitle = {Proceedings of the International Conference on Wavelet Analysis and Applications, Guangzhou, China, November, 1999}, Editor = {Donggao Deng and Daren Huang and Rong-Qing Jia and Wei Lin and Jianzhong Wang}, Publisher = {American Mathematical Society, International Press}, Address = {Providence, Rhode Island}, Series = {AMS/IP Studies in Advanced Mathematics}, Volume = {25}, Pages = {279-287}, ISBN = {0-8218-2991-2}, Year = {2002}) @InProceedings(w:awaa, URL = {http://www.math.wustl.edu/~victor/papers/awaa.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {Advances in Wavelet Algorithms and Applications}, Abstract = {Wavelet and wavelet packet transforms are presently used for image compression and denoising. There has been recent progress on three fronts: implementing multiplication operations in wavelet bases, estimating compressibility by wavelet packet transform coding, and designing wavelet packets to control frequency spreading and pointwise convergence. Some open problems are mentioned.}, BookTitle = {Wavelet Analysis: Twenty Years' Developments}, Note = {Proceedings of the International Conference on Computational Harmonic Analysis, City University of Hong Kong, 4--8 June, 2001}, Editor = {Ding-Xuan Zhou}, Publisher = {World Scientific Publishing}, Address = {Singapore}, Pages = {289-310}, ISBN = {981-238-142-2}, Year = {2002})

## 2001

@Book(twyl:waa01, Editor = {Yuan Y. Tang and Victor Wickerhauser and Pong C. Yuen and Chun-hung Li}, Title = {Wavelet Analysis and Its Applications}, Series = {Lecture Notes in Computer Science}, Volume = {2251}, Note = {Proceedings of the Second International Conference, {WAA} 2001, Hong Kong, China, December, 2001}, Publisher = {Springer-Verlag}, Address = {Berlin}, ISBN = {3-540-43034-2}, Year = {2001}) @Article(cw:sdiudla, Author = {Wojciech Kladiusz Czaja and Mladen Victor Wickerhauser}, Title = {Singularity Detection in Images Using Dual Local Autocovariance}, URL = {http://www.math.wustl.edu/~victor/papers/edges.pdf}, Software = {http://www.math.wustl.edu/~victor/software/acha/edges-c.zip}, Abstract = { We use the eigenvalues of a version of the autocovariance matrix to recognize directions at which the Fourier transform of a function is slowly decreasing, which provides us with a technique to detect singularities in images. }, Journal = {Applied and Computational Harmonic Analysis}, Volume = {13}, Number = {1}, Pages = {77--88}, Month = {July}, Year = {2002}) @Article(dwp:amcs, URL = {http://www.math.wustl.edu/~victor/papers/dwp.pdf}, Author = {Joseph O. Deasy and M. Victor Wickerhauser and Mathieu Picard}, Title = {Accelerating {M}onte {C}arlo Simulations of Radiation Therapy Dose Distributions Using Wavelet Threshold De-Noising}, Abstract = {Limit distributions approximated by long Monte Carlo simulations can also be obtained with good precision by applying wavelet threshold denoising to much shorter simulations.}, Journal = {Medical Physics}, Volume = {29}, Number = {10}, Pages = {2366--2373}, Year = {2002}) @Article(sw:icf, URL = {http://www.math.wustl.edu/~victor/papers/icf.pdf}, Author = {Hrvoje \v{S}iki\'{c} and Mladen Victor Wickerhauser}, Title = {Information Cost Functions}, Abstract = { We derive some curious inequalities for discrete probability densities by carefully examining certain Schur concave functions.}, Journal = {Applied and Computational Harmonic Analysis}, Volume = {11}, Number = {2}, Pages = {147--166}, Month = {September}, Year = {2001}) @TechReport(ww:icisp01, Author = {Eva Wesfreid and Mladen Victor Wickerhauser}, Title = {Frequency Change Function and Acoustic Signals}, Type = {Preprint}, URL = {http://www.math.wustl.edu/~victor/papers/icisp01.pdf}, Abstract = { The local cosine4 orthonormal bases are particularly well adapted for analyzing signals with piecewise time behaviour. There are many acoustic signals in music and speech processing that can be considered as a sequence of overlapping elementary structures such as phonemes in speech signals. The Best Basis algorithm computes a local spectrum defined over a dyadic segmentation, however, there is no reason for elementary structures to begin and end near dyadic points. We use Fang's algorithm which segments the time axis into intervals of arbitrary length; this algorithm constructs a frequency change function whose local maxima denote structure changes. The smooth cosine4 orthonormal basis defined over this segmentation is used to compute a local spectrum associated with elementary structures. We show that this representation compared with the Best Basis coefficients has less reconstruction distortion and better local pattern description.}, Note = {Proceedings of the First International Conference on Image and Signal Processing (ICISP 2001)}, Institution = {Ibn Zohr University}, Address = {Agadir, Morocco}, Pages = {7}, Month = {May}, Year = {2001})

## 2000

## 1999

@InCollection(pw:mswsucc, URL = {http://www.math.wustl.edu/~victor/papers/connec.pdf}, Author = {Valerie Perrier and Mladen Victor Wickerhauser}, Title = {Multiplication of Short Wavelet Series Using Connection Coefficients}, Abstract = {Given two functions approximable with short wavelet series, we wish to find the short wavelet series representing their product. This can be done by pre-calculating the {\em connection coefficients} which express the product of two wave\-lets or scaling functions as a wavelet series. We follow a method suggested by Daubechies and also used by Dahmen, {\it et al.}, to rapidly compute these coefficients as elements of a matrix which solves a fixed-point problem, and derive some of the formulas and identities satisfied by the coefficients. We estimate the complexity of the connection coefficient multiplication algorithm by counting the number of terms, and then illustrate through a series of graphs how few of these terms are non-negligible.}, BookTitle = {Advances in Wavelets}, Editor = {Ka-Sing Lau}, ISBN = {981-4021-08-3}, Publisher = {Springer-Verlag}, Address = {Singapore}, Pages = {77--101}, Year = {1999}) @InProceedings(wwc:cimaf99, URL = {http://www.math.wustl.edu/~victor/papers/cimaf99.pdf}, Author = {Eva Wesfreid and Mladen Victor Wickerhauser}, Title = {Vocal Command Signal Segmentation and Phoneme Classification}, Abstract = { We show that Xiang Fang's segmentation algorithm of nearly constant instantaneous frequency is well-adapted to some noisy vocal command signals and that the orthonormal local trigonometric transform defined over this segmentation offers an optimal, non-dyadic time-frequency tiling. We use this method to compute a local spectrum for speech processing corresponding nearly to phonemes and, in a biomedical application, to measure velopharyngeal closure timing for a swallowing sound.}, BookTitle = {Proceedings of the II Artificial Intelligence Symposium at {CIMAF} 99}, Editor = {Alberto A. Ochoa.}, Organization = {Institute of Cybernetics, Mathematics and Physics (ICIMAF), Habana, Cuba}, Pages = {10}, Year = {1999})

## 1998

@InCollection(w:wta, URL = {http://www.math.wustl.edu/~victor/papers/watc.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {Wavelet Transforms}, Abstract = { This article will present a very brief sketch of the history and theory of wavelet analysis, and then list a few applications to physical and computational chemistry.}, Volume = {5}, Pages = {3214--3222}, BookTitle = {Encyclopedia of Computational Chemistry}, Editor = {P. v. R. Schleyer and N. L. Allinger and T. Clark and J. Gasteiger and P. A. Kollman and Henry F. Schaeffer III and P. R. Schreiner}, Publisher = {John Wiley \& Sons, Limited}, Address = {Chichester, England}, ISBN = {0-471-96588-X}, Year = {1998}) @InProceedings(w:dcwpicsafsd, URL = {http://www.math.wustl.edu/~victor/papers/grossman.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {Designing a Custom Wavelet Packet Image Compression Scheme, with Applications to Fingerprints and Seismic Data}, Abstract = { No single image compression algorithm can be expected to work well for all images, and designing a transform coding image compression algorithm for a given application is itself a meta-algorithm. Sampling rates, frequency content, and pixel quantization all influence the compressibility of the original data. Subsequent machine or human analyses of the compressed data, or its presentation at various magnifications, all influence the nature and visibility of distortion and artifacts. Thus, algorithms like JPEG, established for a ``natural'' images intended to be viewed by humans, do not satisfy the requirements for compressing fingerprint images intended to be scanned by machines. In that particular example, it was necessary to develop a new algorithm {\em WSQ}. One procedure focuses on the transform portion of the compression algorithm: the {\em best basis method\/} automatically finds a transform which provides the best average compression of a representative set of images, selected from a set of ``fast'' transforms. A version of this method was used to design the WSQ fingerprint image compression algorithm, while another was used to design compression algorithms for various types of seismic exploration data.}, BookTitle = {Perspectives in Mathematical Physics: Conference in honor of Alex Grossmann}, Editor = {Matthias Holschneider and Ginette Saracco}, Publisher = {CRC Press}, Organization = {CFML}, Address = {Marseille-Luminy, France}, Pages = {5}, Month = {July}, Year = {1998}) @InProceedings(wwb, URL = {http://www.math.wustl.edu/~victor/papers/wwb.pdf}, Author = {Eva Wesfreid and Mladen Victor Wickerhauser and R. Bouguerra}, Title = {Well Adapted Non Dyadic Local Spectrum for Some Acoustic Signals}, Abstract = { We show that Fang's segmentation algorithm of nearly constant instantaneous frequency is well-adapted to some noisy vocal command signals and that the orthonormal trigonometric basis of l^2(Z) defined over this segmentation offers an optimal, non-dyadic time-frequency tiling. We use this basis in speech processing to compute a local spectrum and approximate phonemes. We also use the algorithm to measure velopharyngeal closure timings from swallowing sounds for biomedical applications.}, Pages = {223--225}, BookTitle = {Proceedings of IWC-Tangier 98, International Wavelets Conference ``Wavelets and Multiscale Methods''}, Editor = {Aline Bonami and Albert Cohen and Abdelhak Ezzine and Paolo Gon\c calv\`es and St\'ephane Jaffard and Yves Meyer}, Month = {13--17 April}, Organization = {INRIA, Rocquencourt, France}, Address = {Tangier, Morocco}, Year = {1998}) @InCollection(cw:eawdmsi, URL = {http://www.math.wustl.edu/~victor/papers/eawdmsi.pdf}, Author = {Ronald Raphael Coifman and Mladen Victor Wickerhauser}, Title = {Experiments with Adapted Wavelet De-Noising for Medical Signals and Images}, Abstract = { We first describe some new libraries of waveforms, including wavelets, wavelet packets, and local sines and cosines, which are well-adapted to representing biological and biomedical signals. By expanding a signal in a library of waveforms which are well-localized in both time and frequency, we can separate coherent structures from incoherent noise. We experiment with one implementation of adapted wavelet denoising, and compute the signal-to-noise ratio improvement obtained for certain simple signals.}, Pages = {323--346}, BookTitle = {Time-Frequency and Wavelets in Biomedical Engineering}, Editor = {Metin Akay}, Publisher = {IEEE Press}, ISBN = {0-7803-1147-7}, Address = {Piscataway, New Jersey}, Year = {1998}) @InProceedings(klgcw:wbarmdis, URL = {http://www.math.wustl.edu/~victor/papers/klgcw.pdf}, Author = {Mingqi Kong and Jean-Pierre Leduc and Bijoy K. Ghosh and Jonathan R. Corbett and Mladen Victor Wickerhauser}, Title = {Wavelet Based Analysis of Rotational Motion in Digital Image Sequences}, Abstract = { This paper addresses the problem of estimating, analyzing and tracking objects moving with spatio-temporal rotational motion (spin or orbit). It is assumed that the digital signals of interest are acquired from a camera and structured as digital image sequences. The trajectories in the signal are two-dimensional spatial projections in time of motion taking place in a three-dimensional space. The purpose of this work is to focus on the rotational motion, i.e. estimate the angular velocity. In natural scenes, rotational motion usually composes with translational or accelerated motion on a trajectory. This paper shows that trajectory parameters and rotational motion can be efficiently estimated and tracked either simultaneously or separately. The final goal of this work is to provide selective reconstructions of moving objects of interest. This paper constructs new continuous wavelet transforms that can be tuned to both translational and rotational motion. The parameters of analysis that are taken into account in these rotational wavelet transforms are space and time position, velocity, spatial scale, angular orientation and angular velocity. The continuous wavelet functions are finally discretized for signal processing. The link between rotational motion, symmetry and critical sampling is also presented. Applications are presented with tracking and estimation.}, Volume = {5}, Pages = {2777--2780}, BookTitle = {Proceedings of ICASSP-98, Seattle}, Publisher = {IEEE Press}, Organization = {IEEE}, Address = {Piscataway, New Jersey}, Month = {12--15 May}, Year = {1998}) @InProceedings(lckwg:astwt, URL = {http://www.math.wustl.edu/~victor/papers/lckwg.pdf}, Author = {Jean-Pierre Leduc and Jonathan R. Corbett and Mingqi Kong and Mladen Victor Wickerhauser and Bijoy K. Ghosh}, Title = {Accelerated Spatio-temporal Wavelet Transforms: An Iterative Trajectory Estimation}, Abstract = { We estimate and analyze accelerated motion in digital image sequences, using expansions in a new continuous wavelet transform. Our wavelets are parametrized by spatial and temporal position, velocity, and acceleration, spatial scale and spatial rotation. We can produce selective reconstructions of accelerated objects of interest.}, Volume = {5}, Pages = {2781--2784}, BookTitle = {Proceedings of ICASSP-98, Seattle}, Publisher = {IEEE Press}, Organization = {IEEE}, Address = {Piscataway, New Jersey}, Month = {12--15 May}, Year = {1998}) @InProceedings(lcw:rwtmaet, URL = {http://www.math.wustl.edu/~victor/papers/lcw.pdf}, Author = {Jean-Pierre Leduc and Jonathan R. Corbett and Mladen Victor Wickerhauser}, Title = {Rotational Wavelet Transforms for Motion Analysis, Estimation, and Tracking}, Abstract = { We estimate and analyze rotational motion in digital image sequences, using expansions in a new continuous wavelet transform. Our wavelets are parametrized by spatial and temporal position, velocity, and spatial rotation. The continuous wavelet functions are ultimately discretized for signal processing.}, BookTitle = {Proceedings of the 1998 IEEE International Conference on Image Processing (ICIP-98), Chicago, Illinois, October 4-7, 1998}, Volume = {2}, Pages = {195-199}, ISBN = {0-8186-8821-1}, Publisher = {IEEE Press}, Organization = {IEEE Computer Society}, Address = {Piscataway, New Jersey}, Year = {1998) @InProceedings(klgw:stcwtmbsris, URL = {http://www.math.wustl.edu/~victor/papers/klgw.pdf}, Author = {Mingqi Kong and Jean-Pierre Leduc and Bijoy K. Ghosh and Mladen Victor Wickerhauser}, Title = {Spatio-Temporal Continuous Wavelet Transforms for Motion-Based Segmentation in Real Image Sequences}, Abstract = { We describe an algorithm to track objects moving with spatio-temporal rotation in digital image sequences, using expansions in a new continuous wavelet transform. We show that trajectory parameters and rotational motion can be efficiently estimated and tracked. The link between rotational motion, symmetry, and critical sampling is also discussed.}, BookTitle = {Proceedings of the 1998 IEEE International Conference on Image Processing (ICIP-98), Chicago, Illinois, October 4-7, 1998}, Volume = {2}, Pages = {662-666}, ISBN = {0-8186-8821-1}, Publisher = {IEEE Press}, Organization = {IEEE Computer Society}, Address = {Piscataway, New Jersey}, Year = {1998})

## 1997

@InProceedings(vw:cwicssdc, URL = {http://www.math.wustl.edu/~victor/papers/spie3169.pdf}, Author = {Anthony Vassiliou and Mladen Victor Wickerhauser}, Title = {Comparison of Wavelet Image Coding Schemes for Seismic Data Compression}, Abstract = { Wavelet transform coding image compression is applied to two raw seismic data sets. The parameters of filter length, depth of decomposition, and quantization method are varied through 36 parameter settings and the rate-distortion relation is plotted and fitted with a line. The lines are compared to judge which parameter setting produces the highest quality for a given compression ratio on the sample data. It is found that long filters, moderate decomposition depths, and frequency-weighted, variance-adjusted quantization yield the best results.}, Editor = {Akram Aldroubi and Andrew F. Laine and Michael A. Unser}, BookTitle = {Wavelet Applications in Signal and Image Processing {V}}, Volume = {3169}, Month = {July}, Publisher = {SPIE}, Organization = {SPIE}, Pages = {9}, Year = {1997}) @InCollection(wfg:tdcst, URL = {http://www.math.wustl.edu/~victor/papers/tdcst.pdf}, Author = {Mladen Victor Wickerhauser and Marie Farge and Eric Goirand}, Title = {Theoretical Dimension and the Complexity of Simulated Turbulence}, Abstract = {A global quantity called ``theoretical dimension'' is roughly proportional to the number of coherent structures that expert observers count in simulated two-dimensional turbulent viscous flows. The quantity is computed for a few academic examples and then for a small number of flows computed from random initial vorticity fields.}, Pages = {473--492}, Editor = {Wolfgang Dahmen and Peter Oswald and Andrew J. Kurdila}, BookTitle = {Multiscale Wavlet Methods for Partial Differential Equations}, Series = {Wavelet Analysis and Applications}, Volume = {6}, Publisher = {Academic Press}, ISBN = {0-12-200675-5}, Address = {Boston}, Year = {1997})

## 1996

@Article(h-nw:wtfa, URL = {http://www.math.wustl.edu/~victor/papers/wtfa.pdf}, Author = {Nikolaj Hess-Nielsen and Mladen Victor Wickerhauser}, Title = {Wavelets and Time-Frequency Analysis}, Abstract = { We present a selective overview of time-frequency analysis and some of its key problems. In particular we motivate the introduction of wavelet and wavelet packet analysis. Different types of decompositions of an idealized time-frequency plane provide the basis for understanding the performance of the numerical algorithms and their corresponding interpretations within the continuous models. As examples we show how to control the frequency spreading of wavelet packets at high frequencies using non-stationary filtering and study some properties of periodic wavelet packets. Furthermore we derive a formula to compute the time localization of a wavelet packet from its indices which is exact for linear phase filters, and show how this estimate deteriorates with deviation from linear phase.}, Journal = {Proceedings of the IEEE}, Volume = {84}, Number = {4}, Pages = {523-540}, Note = {Special issue on wavelet applications}, Month = {April}, Year = {1996}) @InCollection(cw:wawd, URL = {http://www.math.wustl.edu/~victor/papers/eeg.pdf}, Author = {Ronald Raphael Coifman and Mladen Victor Wickerhauser}, Title = {Wavelets, Adapted Waveforms, and De-Noising}, Abstract = {This is a short summary of a talk presented by Wickerhauser at the Frontier Science in EEG Symposium, ``Continuous Waveform Analysis,'' held 9 October 1993 in New Orleans. We describe some new libraries of waveforms well-adapted to various numerical analysis and signal processing tasks. The main point is that by expanding a signal in a library of waveforms which are well-localized in both time and frequency, one can achieve both understanding of structure and efficiency in computation. We briefly cover the properties of the new ``wavelet packet'' and ``localized trigonometric'' libraries. The main focus will be applications of such libraries to the analysis of complicated transient signals: a feature extraction and data compression algorithm for speech signals which uses best-adapted time and frequency decompositions, and an adapted waveform analysis algorithm for removing fish noises from hydrophone recordings. These signals share many of the same properties as EEG traces, but with distinct features that are easier to characterize and detect.}, BookTitle = {Continuous Wave-Form Analysis}, Editor = {Richard M. Dashieff and Diana J. Vincent}, Series = {Electroencephalography and Clinical Neurophysiology, Supplement 45}, Pages = {57--78}, Publisher = {Elsevier}, Address = {New York}, Year = {1996}) @InProceedings(w:cwpicd, URL = {http://www.math.wustl.edu/~victor/papers/cwpicd.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {Custom Wavelet Packet Image Compression Design}, Abstract = {This tutorial paper presents a meta-algorithm for designing a transform coding image compression algorithm specific to a given application. The goal is to select a decorrelating transform which performs best on a given collection of data. It consists of conducting experimental trials with adapted wavelet transforms and the best basis algorithm, evaluating the basis choices made for a training set of images, then selecting a transform that, on average, delivers the best compression for the data set. A crude version of the method was used to design the WSQ fingerprint image compression algorithm.}, BookTitle = {Proceedings of the 3rd International Workshop on Image and Signal Processing, Manchester, UK, 4--7 November 1996}, Editor = {Todor Cooklev}, Publisher = {UMIST}, Organization = {UMIST}, Address = {Manchester, UK}, Pages = {7}, Year = {1996}) @InProceedings(w:bmw, URL = {http://www.math.wustl.edu/~victor/papers/bmw.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {Custom Wavelet Packet Image Compression for Multimedia}, Abstract = { We show how to design a transform coding image compression algorithm specific to a given application. A ``joint best basis'' decorrelating transform is chosen which, on average, performs best on a given collection of data. The transform always has low complexity, and is adapted to the training set used to choose it.}, BookTitle = {Tutorials of the Broadband and Multimedia Workshop, Zagreb, Croatia}, Editor = {Mladen Kos}, Publisher = {University of Zagreb}, Organization = {FER}, Address = {Zagreb, Croatia}, Pages = {7}, Month = {11--12 November}, Year = {1996})

## 1995

@Book(w:awatus, Author = {Mladen Victor Wickerhauser}, Title = {Adaptive Wavelet-Analysis, theorie und software}, Translator = {Kurt Jetter}, Publisher = {Vieweg Verlag}, Address = {Braunschweig/Wiesbaden}, ISBN = {3-528-06688-1}, Pages = {xii + 440}, Note = {German translation of ``Adapted Wavelet Analysis from Theory to Software''}, Month = {12 December}, Year = {1995}) @Article(w:mcc94, URL = {http://www.math.wustl.edu/~victor/papers/mcc94.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {Time Localization Techniques for Wavelet Transforms}, Abstract = { We consider the following pair of problems related to orthonormal compactly supported wavelet expansions: (1) Given a wavelet coefficient with its nominal scale and position indices, find the precise location of the transient signal feature which produced it; (2) Given two collections of wavelet coefficients, determine whether they arise from a periodic signal and its translate, and if so find the translation which maps one into the other. Both problems may be solved by traditional means after inverting the wavelet transform, but we propose two alternative algorithms which rely solely on the wavelet coefficients themselves.}, Note = {Proceedings of the Ninth {D}ubrovnik International Course and {M}ath-{C}hem-{C}omp 1994}, Journal = {Croatica Chemica Acta}, Volume = {68}, Number = {1}, Pages = {1--27}, Month = {April}, Year = {1995}) @TechReport(tw:rbswetd, URL = {http://www.math.wustl.edu/~victor/papers/tw.pdf}, Author = {Aurelija Trgo and Mladen Victor Wickerhauser}, Title = {A Relation between {S}hannon--{W}eaver Entropy and ``Theoretical Dimension'' for classes of Smooth functions}, Abstract = { Suppose that an infinite sequence is produced by independent trials of a random variable with a fixed distribution. The Shannon--Weaver entropy of the sequence determines the minimum bit rate needed to transmit the values of the sequence. We show that if the source distribution is highly concentrated, as is commonly observed in practice, then its entropy is equal to the logarithm of the theoretical dimension of the sequence. We conclude that the best-basis algorithm, which minimizes this theoretical dimension over a library of transformations, both chooses the transformation that yields best compression and also gives an estimate of the compression rate.}, Type = {Preprint}, Institution = {Washington University}, Address = {Saint Louis, Missouri}, Pages = {7}, Year = {1995}) @InProceedings(cmw:nha, URL = {http://www.math.wustl.edu/~victor/papers/numharan.pdf}, Author = {Ronald Raphael Coifman and Yves Meyer and Mladen Victor Wickerhauser}, Title = {Numerical Harmonic Analysis}, Abstract = { The purpose of this talk is to describe recent developments involving the numerical implementation of methods from classical harmonic analysis in signal processing and computational P.D.E.}, Pages = {162--174}, BookTitle = {Essays on {F}ourier Analysis in Honor of {E}lias {M.} {S}tein}, Editor = {Charles Fefferman and Robert Fefferman and Stephen Wainger}, ISBN = {0-691-08655-9}, Publisher = {Princeton University Press}, Address = {Princeton, New Jersey}, Note = {Proceedings of the Princeton Conference in Harmonic Analysis, held 13--17 May 1991}, Year = {1995}) @Article(cw:emb, URL = {http://www.math.wustl.edu/~victor/papers/emb.pdf}, Author = {Ronald Raphael Coifman and Mladen Victor Wickerhauser}, Title = {Adapted Waveform ``de-Noising'' for Medical Signals and Images}, Abstract = {We describe some new libraries of waveforms well-adapted to various numerical analysis and signal processing tasks. The main point is that by expanding a signal in a library of waveforms which are well-localized in both time and frequency, one can achieve both understanding of structure and efficiency in computation. We briefly cover the properties of the new ``wavelet packet'' and ``localized trigonometric'' libraries. The main focus will be applications of such libraries to the analysis of complicated transient signals: a feature extraction and data compression algorithm for speech signals which uses best-adapted time and frequency decompositions, and an adapted waveform analysis algorithm for removing fish noises from hydrophone recordings. These signals share many of the same properties as EEG traces, but with distinct features that are easier to characterize and detect.}, Journal = {IEEE Engineering in Medicine and Biology}, Volume = {14}, Number = {5}, Pages = {578--586}, Month = {September/October}, Year = {1995}) @Manual(w:awa3, URL = {http://www.math.wustl.edu/~victor/papers/www.fmah.com}, Author = {Mladen Victor Wickerhauser}, Title = {AWA 3: Adapted Wavelet Analysis Library, version 3}, Note = {Software Documentation}, Organization = {Fast Mathematical Algorithms and Hardware Corporation}, Address = {Hamden, Connecticut}, Month = {June}, Year = {1995})

## 1994

@InProceedings(w:spie2277, URL = {http://www.math.wustl.edu/~victor/papers/timeloc.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {Time Localization Techniques for Wavelet Transforms}, Abstract = { We consider the following pair of problems related to orthonormal compactly supported wavelet expansions: (1) Given a wavelet coefficient with its nominal scale and position indices, find the precise location of the transient signal feature which produced it; (2) Given two collections of wavelet coefficients, determine whether they arise from a periodic signal and its translate, and if so find the translation which maps one into the other. Both problems may be solved by traditional means after inverting the wavelet transform, but we propose two alternative algorithms which rely solely on the wavelet coefficients themselves.}, Pages = {18}, Editor = {Richard J. Mammone and J. David Murley Jr}, BookTitle = {Automatic Systems for the Identification and Inspection of Humans}, Organization = {SPIE}, Publisher = {SPIE}, Series = {SPIE Proceedings}, Volume = {2277}, Address = {San Diego, California}, Month = {24--29 July}, Year = {1994}) @InCollection(w:cpcm, URL = {http://www.math.wustl.edu/~victor/papers/taormina.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {Comparison of Picture Compression Methods: Wavelet, Wavelet Packet, and Local Cosine Transform Coding}, Abstract = { This summary describes several experiments in picture compression using wavelets and the local cosine transform of Coifman and Meyer. It describes an adaptive wavelet transform coding method and a local cosine transform algorithm based on the idea of a ``best basis,'' and provide Standard C algorithms for computing some of the described transforms.}, Pages = {585--621}, Editor = {Charles K. Chui and Laura Montefusco and Luigia Puccio}, BookTitle = {Wavelets: Theory, Algorithms, and Applications}, Series = {Proceedings of the International Conference in Taormina, Sicily, 14--20 October 1993}, Organization = {University of Messina}, Publisher = {Academic Press}, Address = {San Diego, California}, ISBN = {0-12-174575-9}, Year = {1994}) @InCollection(wfgwc:ecwpalc, URL = {http://www.math.wustl.edu/~victor/papers/taormina2.pdf}, Author = {Mladen Victor Wickerhauser and Marie Farge and Eric Goirand and Eva Wesfreid and Echeyde Cubillo}, Title = {Efficiency Comparison of Wavelet Packet and Adapted Local Cosine Bases for Compression of a Two-dimensional Turbulent Flow}, Abstract = { We compare the efficiency of two rank-reduction methods for representing the essential features of a two-dimensional turbulent vorticity field. The two methods are both projections onto the largest components, in one case onto the wavelet packet best basis, in the other case onto the best basis of adapted local cosines. We compare the two methods in three ways: for efficiency of capturing enstrophy or square-vorticity, for faithfulness to the power spectrum, and for precision in resolving coherent structures. These properties are needed for subsequent segmentation into isolated coherent structures, or for measurement of statistical quantities related to coherent structures. We find that in all three respects the wavelet packet representation is superior to the local cosine representation.}, Pages = {509--531}, Editor = {Charles K. Chui and Laura Montefusco and Luigia Puccio}, BookTitle = {Wavelets: Theory, Algorithms, and Applications}, Series = {Proceedings of the International Conference in Taormina, Sicily, 14--20 October 1993}, Organization = {University of Messina}, Publisher = {Academic Press}, Address = {San Diego, California}, ISBN = {0-12-174575-9}, Year = {1994}) @InProceedings(w:slob2, URL = {http://www.math.wustl.edu/~victor/papers/slob.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {Smooth Localized Orthonormal Bases}, Abstract = { We describe a decomposition of L^2(R) into an orthogonal direct sum of copies of L^2(T). The decomposition maps smooth functions to smooth periodic functions. It generalizes certain earlier constructions of smooth orthonormal windowed bases. In particular, it shows the existence of smooth orthonormal windowed exponential, wavelet, and wavelet packet bases for L^2(R).}, Pages = {160--173}, Editor = {Alfred Z. Msezane and Katrina L. Barnum}, BookTitle = {Proceedings of the Sixth Annual Conference of the National Alliance of Research Centers of Excellence}, Month = {17--19 March}, Year = {1994}, Address = {Clark Atlanta University, Atlanta, Georgia 30314}, Organization = {The Center for Theoretical Studies of Physical Systems}) @Article(w:waa, URL = {http://www.math.wustl.edu/~victor/papers/meyer.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {{\bf Wavelets: Algorithms and Applications} by {Y}ves {M}eyer}, Abstract = { Review of {\em Wavelets : Algorithms and Applications}, by Yves Meyer, Society for Industrial and Applied Mathematics, Philadelphia, 1993, softcover, pp. 133, \$19.50, ISBN 0-89871-309-9.}, Note = {Book review}, Pages = {526--528}, Journal = {SIAM Review}, Volume = {36}, Number = {526--528}, Month = {September}, Year = {1994}) @InProceedings(w:awfc, URL = {http://www.math.wustl.edu/~victor/papers/awfc.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {An Adapted Waveform Functional Calculus}, Abstract = { We briefly survey how to use libraries of (orthonormal) bases of well-behaved waveforms, including wavelets and lapped orthogonal transforms, so as to obtain fast numerical algorithms for the expansion of functions and operators in these bases. The most important applications are fast approximate matrix multiplication, and application of matrices to vectors.}, Pages = {418--421}, BookTitle = {Proceedings of the Cornelius Lanczos Centenary, Raleigh, North Carolina, 12--17 December 1993}, Editor = {Moody Chu and Robert Plemmons and David Brown and Donald Ellison}, Publisher = {SIAM Press}, Organization = {SIAM}, ISBN = {0-89871-339-0}, Address = {Philadelphia}, Year = {1994}) @InProceedings(ww:tpom, Author = {Eva Wesfreid and Mladen Victor Wickerhauser}, Title = {Traitement de la Parole par Ondelettes de {M}alvar}, BookTitle = {Reconnaisance Automatique de la Parole}, Editor = {J. P. Haton}, Series = {Actes du S{\'e}minaire}, Organization = {CRIN/INRIA--Nancy}, Month = {10--11 March}, Year = {1994}) @Article(cw:oe, URL = {http://www.math.wustl.edu/~victor/papers/awaatr.pdf}, Author = {Ronald Raphael Coifman and Mladen Victor Wickerhauser}, Title = {Adapted Waveform Analysis as a Tool for Modeling, Feature Extraction, and Denoising}, Abstract = { We describe the development of Adapted Waveform Analysis (AWA) as a tool for fast processing of the various identification tasks involved in medical diagnostics and Automatic Target Recognition.}, Journal = {Optical Engineering}, Month = {July}, Volume = {33}, Number = {7}, Pages = {2170--2174}, Note = {Special issue on Adapted Wavelet Analysis}, Year = {1994}) @InCollection(cmqw:2, URL = {http://www.math.wustl.edu/~victor/papers/cmqw.pdf}, Author = {Ronald Raphael Coifman and Yves Meyer and Stephen R. Quake and Mladen Victor Wickerhauser}, Title = {Signal Processing and Compression with Wavelet Packets}, Abstract = { Some new algorithms for signal processing and data compression arise from the discovery of certain orthogonal functions which we shall call wavelet packets. Wavelet packets generalize the compactly supported wavelets of I. Daubechies and Y. Meyer. The algorithms combine fast factored tranformations with a tree-structure search for an optimal orthonormal basis subset, some processing of the coefficients, and then reconstruction of the transformed sequence.}, Editor = {James S. Byrnes and Jennifer L. Byrnes and Kathryn A. Hargreaves and Karl Berry}, BookTitle = {Wavelets and Their Applications}, Publisher = {Kluwer Academic Publishers}, Address = {Dordrecht/Boston/London}, Series = {NATO ASI Series C: Mathematical and Physical Sciences}, Volume = {442}, Note = {Proceedings of the NATO Advanced Study Institute at Il Ciocco, Barga, Italy in August, 1992}, Year = {1994}, ISBN = {0-7923-3078-1}, Pages = {363--379}) @InCollection(fgw:p2dwpt, URL = {http://www.math.wustl.edu/~victor/papers/parallel.pdf}, Author = {Eric Goirand and Mladen Victor Wickerhauser and Marie Farge}, Title = {A Parallel Two Dimensional Wavelet Packet Transform and Its Application to Matrix-Vector Multiplication}, Abstract = { This paper describes an implementation on an MIMD computer of the 2-dimensional periodic wavelet packet transform, the 2-dimensional ``best basis'' choice algorithm, and the nonstandard matrix multiplication algorithm. Our implementation also works for the wavelet transform numerical algorithms of Beylkin, Coifman and Rokhlin. It is one way to obtain a fast functional calculus for certain classes of linear operators: those operators, which sparsify in the wavelet basis or the ``best basis'' of wavelet packets, can be applied to vectors in a lower order of complexity. The purpose of parallelizing the transform is to distribute the cost of the initial sparsification ``investment'' over a large number of machines. This one-time cost is O(N^2 log N) with a nonnegligible constant; we envision applications in which N=10^6, for example evolutions of 2-dimensional fluid velocity fields on 1000x1000 point grids. In a first part, we study a parallel algorithm (on a MIMD machine) to compute the two-dimensional wavelet packet transform. Then, we apply it to compute the multiplication of a matrix by a vector in parallel. We will compute matrix coefficients for operators with respect to an orthonormal basis of separable wavelet packets, using the 2-dimensional version of the fast wavelet packet transform. The main idea is to lift an NxN matrix, which maps R^N to R^N, into the space of maps from R^{N log N} to R^{N log N}. Any of a large number of NxN-coefficient subsets of this lifting can be used to represent the operator, so we may pick the subset in which the matrix is most sparse. The choice is made with the ``best-basis'' algorithm and is itself a fast algorithm. The number of basissubsets of this type grows like 4^N for an NxN matrix, but computing all of the coefficients with respect to all of the basis functions requires just O(N^2 log N) operations. The algorithm chooses the ``best basis'' in which the operator appears most sparse; it has complexity O(N^2). We have reason to believe that the equations of motion for important physical systems sparsify by nearly an order of magnitude in this collection of bases. We thus obtain lower complexity matrix application and matrix multiplication algorithms from the new representation. Of course the method is not perfectly general: the speedup depends very much upon the problem. However, others have shown that for broad classes of operators we can expect an order of magnitude asymptotic complexity reduction for matrix application.}, BookTitle = {Wavelet Applications in Chemical Engineering}, Editor = {Rodolphe L. Motard and Babu Joseph}, Publisher = {Kluwer Academic Publishers}, Address = {Norwell, Massachusetts}, ISBN = {0-7923-9461-5}, Pages = {275--319}, Year = {1994}) @Article(w:mcc1, URL = {http://www.math.wustl.edu/~victor/papers/rovinj.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {Large-rank Approximate Principal Component Analysis with Wavelets for Signal Feature Discrimination and the Inversion of Complicated Maps}, Journal = {Journal of Chemical Information and Computer Science}, Volume = {34}, Abstract = { Principal orthogonal decomposition can be used to solve two related problems: distinguishing elements from a collection by making d measurements, and inverting a complicated map from a p-parameter configuration space to a d-dimensional measurement space. In the case where d is more than 1000 or so, the classical O(d^3) singular value decomposition algorithm becomes very costly, but it can be replaced with an approximate best-basis method that has complexity O(d^2\log d). This can be used to compute an approximate Jacobian for a complicated map from R^p to R^d in the case p < < d.}, Number = {5}, Month = {September/October}, Pages = {1036--1046}, Year = {1994}) @Book(w:awaftts, Author = {Mladen Victor Wickerhauser}, Title = {Adapted Wavelet Analysis from Theory to Software}, URL = {http://www.math.wustl.edu/~victor/awaftts}, Abstract = { This text goes beyond the existing literature to aid the engineer and applied mathematician in writing computer programs to analyze real data. It addresses the properties of wavelet and related transforms, to establish criteria by which the proper analysis tool may be chosen, and then details software implementations to perform the needed computation. It will also be useful to the pure mathematician who is familiar with some parts of wavelet theory but has questions about the applications. The worked exercises make this a useful textbook for self-study, or for a course in the theory and practice of wavelet analysis. Beginning with an overview of the mathematical prerequisites, successive chapters rigorously examine the properties of the waveforms used in adapted wavelet analysis: discrete ``fast'' Fourier transforms, orthogonal and biorthogonal wavelets, wavelet packets, and localized trigonometric or lapped orthogonal functions. Other chapters discuss the ``best basis'' method, time-frequency analysis, and combinations of these algorithms useful for signal analysis, de-noising, and compression. Each chapter discusses the technicalities of implementation, giving examples in pseudocode backed up with machine-readable Standard C source code available on the optional diskette. Each chapter finishes with a list of worked exercises in both the mathematics and the programming of adapted wavelet algorithms. Especially emphasized are the pitfalls and limitations of the algorithms, with examples and suggestions given to show how to avoid them.}, Publisher = {AK Peters, Ltd.}, Address = {Wellesley, Massachusetts}, ISBN = {1-56881-041-5}, Pages = {xii + 486}, Year = {1994}) @Article(w:oe, URL = {http://www.math.wustl.edu/~victor/papers/oe.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {Two Fast Approximate Wavelet Algorithms for Image Processing, Classification, and Recognition}, Abstract = { We use large libraries of template waveforms with remarkable orthogonality properties to recast the relatively complex principal orthogonal decomposition (POD) into an optimization problem with a fast solution algorithm. Then it becomes practical to use POD to solve two related problems: recognizing or classifying images, and inverting a complicated map from a low-dimensional configuration space to a high-dimensional measurement space. In the case where the number N of pixels or measurements is more than 1000 or so, the classical O(N^3) POD algorithm becomes very costly, but it can be replaced with an approximate best-basis method that has complexity O(N^2 log N). A variation of POD can also be used to compute an approximate Jacobian for the complicated map.}, Journal = {Optical Engineering}, Month = {July}, Volume = {33}, Number = {7}, Pages = {2225--2235}, Note = {Special issue on Adapted Wavelet Analysis}, Year = {1994}) @InProceedings(w:spie2242, URL = {http://www.math.wustl.edu/~victor/papers/spie2242.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {Wavelet Approximations to {J}acobians and the Inversion of Complicated Maps}, Editor = {Harold H. Szu}, BookTitle = {Wavelet Applications}, Organization = {SPIE}, Publisher = {SPIE}, Series = {SPIE Proceedings}, Volume = {2242}, ISBN = {0-8194-1546-4}, Address = {Orlando, Florida}, Month = {5--8 April}, Pages = {100--118}, Year = {1994})

## 1993

@Article(ww:alttsp, URL = {http://www.math.wustl.edu/~victor/papers/alttasp.pdf}, Author = {Eva Wesfreid and Mladen Victor Wickerhauser}, Title = {Adapted Local Trigonometric Transform and Speech Processing}, Abstract = { We use an algorithm based on the adapted-window Malvar transform to decompose digitized speech signals into a local time-frequency representation. We present some applications and experimental results for signal compression and automatic voiced-unvoiced segmentation. This decomposition provides a method of parameter simlification which appears to be useful for detecting fundamental frequencies and characterizing formants. Note: Additional figures are in sono1.eps and sono2.eps in the file archive.}, Journal = {IEEE Transactions on Signal Processing}, Number = {12}, Volume = {41}, Pages = {3596--3600}, Month = {December}, Year = {1993}) @Misc(ow:wsq, Title = {{WSQ} -- the {FBI}/{Y}ale/{L}os {A}lamos [{W}]avelet-packet [{S}]calar [{Q}]uantization fingerprint compression algorithm, for {W}indows 3.1 or higher}, Author = {He Ouyang and Mladen Victor Wickerhauser}, HowPublished = {Noncompliant with latest standard---no longer available. See the certified codes elsewhere at this site.}, Year = {1993}, Month = {8 September}) @InProceedings(afww, Author = {Christophe D'Alessandro and Xiang Fang and Eva Wesfreid and Mladen Victor Wickerhauser}, Title = {Speech Signal Segmentation via {M}alvar Wavelets}, Pages = {305--308}, BookTitle = {Progress in Wavelet Analysis and Applications}, Editor = {Yves Meyer and Sylvie Roques}, Series = {Proceedings of the International Conference ``Wavelets and Applications,'' Toulouse, France, 8--13 June 1992}, Publisher = {Editions Frontieres}, Organization = {Observatoire Midi-Pyr{\'e}n{\'e}es de l'Universit{\'e} Paul Sabatier}, Address = {Gif-sur-Yvette, France}, ISBN = {2-86332-130-7}, Year = {1993}) @InCollection(cmqw:3, URL = {http://www.math.wustl.edu/~victor/papers/cmqw.pdf}, Author = {Ronald Raphael Coifman and Yves Meyer and Stephen R. Quake and Mladen Victor Wickerhauser}, Title = {Signal Processing and Compression with Wavelet Packets}, Abstract = { We describe some new algorithms for signal processing and data compression based on a collection of orthogonal functions which we shall call wavelet packets. Wavelet packets generalize the compactly supported wavelets of I. Daubechies and Y. Meyer. The algorithms we describe combine the projection of a sequence onto wavelet packet components, the selection of an optimal orthonormal basis subset, some linear or quasilinear processing of the coefficients, and then reconstruction of the transformed sequence.}, Pages = {77--93}, BookTitle = {Progress in Wavelet Analysis and Applications}, Editor = {Yves Meyer and Sylvie Roques}, Series = {Proceedings of the International Conference ``Wavelets and Applications,'' Toulouse, France, 8--13 June 1992}, Publisher = {Editions Frontieres}, Organization = {Observatoire Midi-Pyr{\'e}n{\'e}es de l'Universit{\'e} Paul Sabatier}, Address = {Gif-sur-Yvette, France}, ISBN = {2-86332-130-7}, Year = {1993}) @InCollection(cw:d-psam, URL = {http://www.math.wustl.edu/~victor/papers/wawa.pdf}, Author = {Ronald Raphael Coifman and Mladen Victor Wickerhauser}, Title = {Wavelets and Adapted Waveform Analysis: A Toolkit for Signal Processing and Numerical Analysis.}, Abstract = {Our goal is to describe tools for adapting methods of analysis to various tasks occurring in harmonic and numerical analysis and signal processing. The main point of this presentation is that by choosing an orthonormal basis, in which space and frequency are suitably localized, one can achieve both understanding of structure and efficiency in computation. We describe a fingerprint image segmentation algorithm, an alternative factorization for the FFT, and a wavelet-based denoising algorithm.}, Note = {Minicourse lecture notes}, Pages = {119--153}, BookTitle = {Different Perspectives on Wavelets}, Series = {Proceedings of Symposia in Applied Mathematics}, Number = {47}, Editor = {Ingrid Daubechies}, ISBN = {0-8218-5503-4}, Publisher = {American Mathematical Society}, Address = {San Antonio, Texas}, Month = {11-12 January}, Year = {1993}) @InCollection(w:bawpb, URL = {http://www.math.wustl.edu/~victor/papers/bestbase.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {Best-adapted Wavelet Packet Bases}, Abstract = { This paper is a review of the construction of orthogonal wavelet packets, using the quadrature mirror filter algorithm slightly generalized to the case of p>2 or p=2 wavelets and scaling functions. It is part of the AMS short course on ``Wavelets and Applications'' held in San Antonio, 11-12 January 1993.}, Note = {Minicourse lecture notes}, Pages = {155--171}, BookTitle = {Different Perspectives on Wavelets}, Series = {Proceedings of Symposia in Applied Mathematics}, Number = {47}, Editor = {Ingrid Daubechies}, ISBN = {0-8218-5503-4}, Publisher = {American Mathematical Society}, Address = {San Antonio, Texas}, Month = {11-12 January}, Year = {1993}) @Article(w:slob, URL = {http://www.math.wustl.edu/~victor/papers/crasslob.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {Smooth Localized Orthonormal Bases}, Abstract = { We describe an orthogonal decomposition of square-integrable functions on the line, which maps smooth functions to smooth periodic functions. It generalizes previous constructions by Malvar, Coifman and Meyer. The adjoint of the decomposition can be used to construct smooth orthonormal windowed exponential, wavelet and wavelet packet bases.}, Journal = {Comptes Rendus de l'Acad{\'e}mie des Sciences de Paris}, Series = {I}, Volume = {316}, Pages = {423--427}, Year = {1993}) @InProceedings(w:cwatfa, URL = {http://www.math.wustl.edu/~victor/papers/cwatfa.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {Computation with Adapted Time-Frequency Atoms}, Abstract = { Operators can be represented by their coefficients with respect to an orthonormal basis of functions well localized in both time and frequency. Such building blocks will be called time-frequency atoms. Bases of functions of this type abound and one may be chosen to minimize the number of nonnegligible coefficients for a given operator. In this note we will use particular libraries of such atoms to represent operators efficiently and thereby obtain a ``fast'' functional calculus. We obtain lower complexity matrix application and matrix multiplication algorithms from the new representation. The main idea is to lift an NxN matrix into the space of maps on (N log N)x(N log N). Any of a large number of NxN-coefficient subsets of this lifting can be used to represent the operator, so we may pick the subset in which the matrix is most sparse. The choice is made with the ``best-basis'' algorithm and is itself a fast algorithm. The best-basis implementations described here can use either wavelet packets or adapted local trigonometric libraries. They provide a generalization of the ``nonstandard form'' introduced by Beylkin, Coifman, and Rokhlin.}, Pages = {175--184}, BookTitle = {Progress in Wavelet Analysis and Applications}, Editor = {Yves Meyer and Sylvie Roques}, Series = {Proceedings of the International Conference ``Wavelets and Applications,'' Toulouse, France, 8--13 June 1992}, Publisher = {Editions Frontieres}, Organization = {Observatoire Midi-Pyr{\'e}n{\'e}es de l'Universit{\'e} Paul Sabatier}, Address = {Gif-sur-Yvette, France}, ISBN = {2-86332-130-7}, Year = {1993}) @Misc(wplab, URL = {http://www.math.wustl.edu/~victor/software/WPLab/WPLab3.app.tar.gz}, Title = {{WPL}ab version 3 (for {NeXT} computers)}, Author = {David Rochberg and Mladen Victor Wickerhauser}, HowPublished = {Available by anonymous file transfer}, Year = {1993})

## 1992

@InProceedings(cmw:iciam91, URL = {http://www.math.wustl.edu/~victor/papers/adaptwave1.pdf}, Title = {Adapted Waveform Analysis, Wavelet-Packets and Applications}, Author = {Ronald Raphael Coifman and Yves Meyer and Mladen Victor Wickerhauser}, Abstract = { Adapted wave form analysis, refers to a collection of FFT like adapted transform algorithms. Given a function or an operator these methods provide a special orthonormal basis relative to which the function is well represented, and the operator is described by a sparse matrix. The selected basis functions are chosen inside predefined libraries of oscillatory localized functions (waveforms). These algorithms are of complexity N log N, opening the door for a large range of applications in signal and image processing, as well as in numerical analysis. Our goal is to describe and relate traditional windowed Fourier Transform methods to wavelet, wavelet-packet base algorithms by making explicit their dual nature and relative role in analysis and computation.}, Pages = {41--50}, BookTitle = {ICIAM 91: Proceedings of the 2nd International Conference on Industrial and Applied Mathematics, 8--12 July, 1991}, Editor = {Robert E. O'Malley Jr.}, Publisher = {SIAM Press}, ISBN = {0-89871-302-1}, Organization = {SIAM}, Address = {Philadelphia}, Year = {1992}) @InCollection(aww, URL = {http://www.math.wustl.edu/~victor/papers/aww.pdf}, Author = {Pascal Auscher and Guido Leopold Weiss and Mladen Victor Wickerhauser}, Title = {Local Sine and Cosine Bases of {C}oifman and {M}eyer and the Construction of Smooth Wavelets}, Abstract = { We give a detailed account of the local cosine and sine bases of Coifman and Meyer. We describe some of their applications; in particular, based on an approach by Coifman and Meyer, we show how these local bases can be used to obtain arbitrarily smooth wavelets. The understanding of this material requires only a minimal knowledge of the Fourier transform and classical analysis. It is our intention to make this presentation accessible to all who are interested in Wavelets and their applications.}, Pages = {237--256}, Editor = {Charles K. Chui}, BookTitle = {Wavelets--A Tutorial in Theory and Applications}, Publisher = {Academic Press}, Address = {Boston}, ISBN = {0-12-174590-2}, Year = {1992}) @InCollection(cmw:spwp, URL = {http://www.math.wustl.edu/~victor/papers/sizeprop.pdf}, Author = {Ronald Raphael Coifman and Yves Meyer and Mladen Victor Wickerhauser}, Title = {Size Properties of Wavelet Packets}, Abstract = { We investigate the frequency localization of wavelet packets and prove that they do not enjoy sharp frequency localization. By S. Bernstein's inequalities, a sharp frequency localization would imply a uniform bound on the supremum norm of the basic wavelet-packets w_n(x). But theorem 3 shows that the average growth of ess sup |w_n| is n^gamma for some positive gamma. The fact that gamma is rather small plays a key role in the construction of a large library of wavelet packet orthonormal bases.}, Pages = {453--470}, BookTitle = {Wavelets and Their Applications}, Editor = {Mary Beth Ruskai and Gregory Beylkin and Ronald Raphael Coifman and Ingrid Daubechies and St{\'e}phane Mallat and Yves Meyer and Louise Raphael}, Publisher = {Jones and Bartlett}, Address = {Boston}, ISBN = {0-86720-225-4}, Year = {1992}) @InCollection(cmw:wasp, URL = {http://www.math.wustl.edu/~victor/papers/wasp.pdf}, Author = {Ronald Raphael Coifman and Yves Meyer and Mladen Victor Wickerhauser}, Abstract = { Wavelet Analysis consists of a versatile collection of tools for the analysis and manipulation of signals such as sound and images,as well as more general digital data sets. The user is provided with a collection of standard libraries of waveforms, which can be chosen to fit specific classes of signals. These libraries come equipped with fast numerical algorithms enabling realtime implementation of a variety of signal processing tasks, such as data compression, extraction of parameters for recognition and diagnostics, transformation and manipulation of data. The process of analysis of data is usually started by comparing acquired segments of data with stored waveforms.}, Title = {Wavelet Analysis and Signal Processing}, Pages = {153--178}, BookTitle = {Wavelets and Their Applications}, Editor = {Mary Beth Ruskai and Gregory Beylkin and Ronald Raphael Coifman and Ingrid Daubechies and St{\'e}phane Mallat and Yves Meyer and Louise Raphael}, Publisher = {Jones and Bartlett}, Address = {Boston}, ISBN = {0-86720-225-4}, Year = {1992}) @InCollection(hpw, URL = {http://www.math.wustl.edu/~victor/papers/burgers.pdf}, Author = {Fr{{\'e}}d{{\'e}}ric Heurtaux and Fabrice Planchon and Mladen Victor Wickerhauser}, Title = {Scale Decomposition in {B}urgers' equation}, Abstract = { The wavelet representation of a time-dependent signal can be used to study the propagation of energy between the different scales in the signal. Burgers' evolution operator (in 1 and 2 dimensions) can itself be described >from this scaling point of view. Using wavelet-based algorithms we can depict the transfer of energy between scales. We can write the instantaneous evolution operator in the wavelet basis; then large off-diagonal terms will correspond to energy transfers between different scales. We can project the solution onto each fixed-scale wavelet subspace and compute the energy; then the rate of change of this energy by scale can detect and quantify any cascades that may be present. These methods improve the classical Fourier-transform-based scale decomposition which uses the notion that wavenumber=scale. The wavelet basis functions underlying our scale decompositions have finite, well-defined position uncertainty (i.e., scale) whereas Fourier basis functions have formally unbounded position uncertainty.}, Pages = {505--523}, Editor = {John J. Benedetto and Michael Frazier}, BookTitle = {Wavelets: Mathematics and Applications}, Series = {Studies in Advanced Mathematics}, Publisher = {CRC Press}, Address = {Boca Raton, Florida}, ISBN = {0-8493-8271-8}, Year = {1992}) @InCollection(cw:wawa, URL = {http://www.math.wustl.edu/~victor/papers/wawa.pdf}, Author = {Ronald Raphael Coifman and Mladen Victor Wickerhauser}, Title = {Wavelets and Adapted Waveform Analysis}, Abstract = {Our goal is to describe tools for adapting methods of analysis to various tasks occuring in harmonic and numerical analysis and signal processing. The main point of this presentation is that by choosing an orthonormal basis, in which space and frequency are suitably localized, one can achieve both understanding of structure and efficiency in computation. We describe a fingerprint image segmentation algorithm, an alternative factorization for the FFT, and a wavelet-based denoising algorithm.}, Pages = {399--423}, Editor = {John J. Benedetto and Michael Frazier}, BookTitle = {Wavelets: Mathematics and Applications}, Series = {Studies in Advanced Mathematics}, Publisher = {CRC Press}, Address = {Boca Raton, Florida}, ISBN = {0-8493-8271-8}, Year = {1992}) @Article(cw:ebafbbs, URL = {http://www.math.wustl.edu/~victor/papers/ebafbbs.pdf}, Author = {Ronald Raphael Coifman and Mladen Victor Wickerhauser}, Title = {Entropy Based Algorithms for Best Basis Selection}, Abstract = { We would like to describe a method permitting efficient compression of a variety of signals such as sound and images. While similar in goals to vector quantization, the new method uses a codebook or library of predefined modulated waveforms with some remarkable orthogonality properties. We can apply the method to two particularly useful libraries of recent vintage, orthogonal wavelet-packets and localized trigonometric functions, for which the time-frequency localization properties of the waveforms are reasonably well controlled. The idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost. We may define several useful cost functionals; one of the most attractive is Shannon entropy, which has a geometric interpretation in this context. Practicality is built into the foundation of this orthogonal best-basis methods. All bases from each library of waveforms described below come equipped with fast O(N log N) transformation algorithms, and each library has a natural dyadic tree structure which provides O(N log N) search algorithms for obtaining the best basis. The libraries are rapidly constructible, and never have to be stored either for analysis or synthesis. It is never necessary to construct a waveform from a library in order to compute its correlation with the signal. The waveforms are indexed by three parameters with natural interpretations (position, frequency, and scale), and we have experimented with feature-extraction methods that use best-basis compression for front-end complexity reduction. The method relies heavily on the remarkable orthogonality properties of the new libraries. It is obviously a nonlinear transformation to represent a signal in its own best basis, but since the transformation is orthogonal once the basis is chosen, compression via the best-basis method is not drastically affected by noise: the noise energy in the transform values cannot exceed the noise energy in the original signal. Furthermore, we can use information cost functionals defined for signals with normalized energy, since all expansions in a given library will conserve energy. Since two expansions will have the same energy globally, it is not necessary to normalize expansions to compare their costs. This feature greatly enlarges the class of functionals usable by the method, speeds the best-basis search, and provides a geometric interpretation in certain cases.}, Journal = {IEEE Transactions on Information Theory}, Volume = {32}, Pages = {712--718}, Month = {March}, Year = {1992}) @Article(fgmpw, URL = {http://www.math.wustl.edu/~victor/papers/fgmpw.tar.gz}, Author = {Marie Farge and Eric Goirand and Yves Meyer and Fr{\'e}d{\'e}ric Pascal and Mladen Victor Wickerhauser}, Title = {Improved Predictability of Two-Dimensional Turbulent Flows Using Wavelet Packet Compression}, Abstract = { We propose to use new orthonormal wavelet packet bases, more efficient than the Fourier basis, to compress two-dimensional turbulent flows. We define the ``best basis'' of wavelet packets as the one which, for a given enstrophy density, condenses the $L^2$ norm into a minimum number of non-negligible wavelet packet coefficients. Coefficents below a threshold are discarded, reducing the number of degrees of freedom. We then compare the predictability of the original flow evolution with several such reductions, varying the number of retained coefficients, either from a Fourier basis, or from the best-basis of wavelet packets. We show that for a compression ratio of 1/2, we still have a deterministic predictability using the wavelet packet best-basis, while it is lost when using the Fourier basis. Likewise, for compression ratios of 1/20 and 1/200 we still have statistical predictability using the wavelet packet best-basis, while it is lost when using the Fourier basis. In fact, the significant wavelet packet coefficients in the best-basis appear to correspond to coherent structures. The weak coefficients correspond to vorticity filaments, which are only passively advected by the coherent structures. In conclusion, the wavelet packet best-basis seems to distinguish the low-dimensional dynamically active part of the flow from the high-dimensional passive components. It gives us some hope of drastically reducing the number of degrees of freedom, which varies as Reynolds, in the computation of two-dimensional turbulent flows.}, Journal = {Fluid Dynamics Research}, Volume = {10}, Pages = {229--250}, Year = {1992}) @InCollection(w:acoustic, URL = {http://www.math.wustl.edu/~victor/papers/acoustic.ps.gz}, Author = {Mladen Victor Wickerhauser}, Title = {Acoustic signal compression with wavelet packets}, Abstract = {The wavelet transform generalizes to produce a library of orthonormal bases of modulated wavelet packets. Each basis comes with a fast transform; these bases are similar to adapted windowed Fourier transforms. There is a notion of the ``best basis'' for a signal, given a cost function. This paper discusses some early results in acoustic signal compression using a simple counting cost function.}, Pages = {679--700}, Editor = {Charles K. Chui}, BookTitle = {Wavelets--A Tutorial in Theory and Applications}, Publisher = {Academic Press}, Address = {Boston}, ISBN = {0-12-174590-2}, Year = {1992}) @Article(w:dsp, URL = {http://www.math.wustl.edu/~victor/papers/dsp.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {High-Resolution Still Picture Compression}, Abstract = { We consider the problem of storing, transmitting, and manipulating digital electronic images. Because of the file sizes involved, transmitting images will always consume large amounts of bandwidth, and storing images will always require hefty resources. Because of the large number N of pixels in a high resolution image, manipulation of digital images is infeasible without low-complexity algorithms, i.e., O(N) or O(N log(N)). Our goal will be to describe some new methods which are firmly grounded in harmonic analysis and the mathematical theory of function spaces, which promise to combine effective image compression with low-complexity image processing. We shall take a broad perspective, but we shall also compare specific new algorithms to the state of the art.}, Month = {October}, Volume = {2}, Number = {4}, Pages = {204--226}, Journal = {Digital Signal Processing: a Review Journal}, Year = {1992}) @Manual(w:awa2, URL = {http://www.fmah.com}, Author = {Mladen Victor Wickerhauser}, Title = {Adapted Waveform Analysis Library, v2.0}, Note = {Software Documentation}, Organization = {Fast Mathematical Algorithms and Hardware Corporation}, Address = {Hamden, Connecticut}, Month = {June}, Year = {1992})

## 1991

@InCollection(zsw, Author = {Lareef Zubair and Kannan R. Sreenivasan and Mladen Victor Wickerhauser}, Title = {Characterization and Compression of Turbulent Signals and Images using Wavelet Packets}, BookTitle = {Studies in Turbulence}, Pages = {489--513}, Editor = {T. Gadsky and S. Sirkar and C. Speziale}, Publisher = {Springer Verlag}, Address = {New York}, Year = {1991}) @InCollection(w:inria, URL = {http://www.math.wustl.edu/~victor/papers/lwpa.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {{INRIA} Lectures on Wavelet Packet Algorithms}, Abstract = { We begin by defining continuous wavelet packets on R. These are square-integrable functions with prescribed smoothness and other properties, which we shall develop to establish the main notions. Our construction will be directed toward numerical applications, so we will restrict ourselves to the quadrature mirror filter algorithm. Next we will define several discrete algorithms and explore their advantages and disadvantages. We will show the correspondence between wavelet packets and coefficients computed from sampled signals, and relate the convergence of this approximation to the smoothness of the signal. We will define information cost functions and the ``best-basis'' method. We will count operations and consider practical matters like the memory requirements of the algorithms, periodizing, the spreading of the support of aperiodic wavelet packets, and the combinatorics of constructing wavelet packet bases of increasing generality. In parallel, we will develop smooth orthogonal local trigonometric transforms. These are properly considered transposes of wavelet packet methods, or alternatively conjugates of wavelet packet methods by the Fourier transform. We will describe both continuous and discrete local cosine transforms, and an adaptive local cosine transform useful for signal segmentation. We will examine several compression methods, both linear and nonlinear. Linear methods include uniform and nonuniform quantization. Nonlinear methods include discarding small coefficients, coalescing to the center of energy within bands, and Karhunen--Loeve methods. We will examine the peculiarities of each method, and discuss the errors in the lossy versions of these algorithms. This will illustrate the relative advantages of wavelet packets, windowed Fourier transforms, and wavelet bases. We will then generalize to multidimensions by separation of variables. We will explore the combinatorics of higher dimensional wavelets. We will identify matrices with two-dimensional signals or ``pictures,'' and we will show how each picture compression algorithm yields a nonstandard matrix multiplication algorithm. As a demonstration of the analytic power of best-basis methods, we will perform an automatic analysis of a few canonical signals in the phase plane. The signals will be decomposed into as precise a set of modulated lumps as the Heisenberg uncertainty principle allows, and the product of the analysis will be displayed in an intuitively satisfying manner. Finally, we will produce several fast numerical algorithms driven by the best-basis method. Among these will be fast approximate Karhunen--Loeve factor analysis, signal segmentation in time and frequency, feature-preserving encryption, and matrix multiplication.}, Editor = {Pierre-Louis Lions}, BookTitle = {Probl{\'e}mes Non-Lin{\'e}aires Appliqu{\'e}s, Ondelettes et Paquets D'Ondes}, Note = {Minicourse lecture notes}, Publisher = {INRIA}, Address = {Roquencourt, France}, Month = {17--21 June}, Pages = {31-99}, Year = {1991}) @InProceedings(w:fakle, URL = {http://www.math.wustl.edu/~victor/papers/fakle.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {Fast Approximate Factor Analysis}, Abstract = { The principal orthogonal factor analysis or Karhunen-Loeve algorithm may be sped up by a low-complexity preprocessing step. A fast transform is selected from a large library of wavelet-like orthonormal bases, so as to maximize transform coding gain for an ensemble of vectors. Only the top few coefficients in the new basis, in order of variance across the ensemble, are then decorrelated by diagonalizing the autocovariance matrix. The method has computational complexity O(d*d*log d+ d'*d'*d') and O(d*log d + d'*d') respectively for training and classifying a $d$-dimensional system, where d'< < d. One application is described, the reduction of an ensemble of 16,384-pixel face images to a 10-parameter space using a desktop computer, retaining 90 percent of the variance of the ensemble.}, Pages = {23--32}, Editor = {Martine J. Silbermann and Hemant D. Tagare}, BookTitle = {Curves and Surfaces in Computer Vision and Graphics {II}}, Organization = {SPIE}, Series = {SPIE Proceedings}, Volume = {1610}, Pages = {iii + 395}, ISBN = {0-8194-0747-X}, Address = {Boston}, Month = {October}, Year = {1991}) @Book(cw:mmnotes, URL = {http://www.fmah.com}, Author = {Ronald Raphael Coifman and Mladen Victor Wickerhauser}, Title = {{M}artin--{M}arietta Wavelet Lectures}, Publisher = {Martin--Marietta Corporation}, Month = {21--25 October}, Year = {1991}) @Misc(fgppw:video, Author = {Marie Farge and Eric Goirand and Thierry Philipovitch and Fre{\'e}d{\'e}ric Pascal and Mladen Victor Wickerhauser}, Title = {Wavelet Packets Compression of a 2D Turbulent Flow}, HowPublished = {Video recording of a computer simulation performed at LMD-CNRS, Paris}, Year = {1991}) @Misc(wplab1, URL = {http://www.math.wustl.edu/~victor/software/WPLab/WPLab1.5.gz}, Title = {{WPL}ab version 1.5 (for {NeXT} computers)}, Author = {Mladen Victor Wickerhauser}, HowPublished = {Available by anonymous file transfer}, Month = {6 April}, Year = {1991})

## 1990

@Article(cw:bo, URL = {http://www.math.wustl.edu/~victor/papers/benj-ono.pdf}, Author = {Ronald Raphael Coifman and Mladen Victor Wickerhauser}, Title = {The Scattering Transform for the {B}enjamin--{O}no Equation}, Abstract = { We use constructive methods to investigate the spectral theory of the Benjamin--Ono equation. Since the linearization series used previously is singular, we replace it with an improved series obtained by finite-rank renormalization. This introduces additional scattering data, which are shown to be dependent upon a single function, though not the usual one. We then prove the continuity of the direct and inverse scattering transforms defined by the improved series for small complex potentials. For all such potentials, the eigenvalues of the spectral problem cannot accumulate at 0. Rapidly decaying potentials have regular scattering data, prohibiting rapidly decaying solitons. In the selfadjoint case (real potentials), we obtain explicit cancellation of certain singularities. This leads to an alternate existence proof for the Cauchy problem for the equation. It also proves existence and gives estimates for some previously formal invariant quantities associated to the Benjamin--Ono hierarchy.}, Journal = {Inverse Problems}, Volume = {6}, Pages = {825--861}, Year = {1990}) @TechReport(w:pic, URL = {http://www.math.wustl.edu/~victor/papers/pic.tar.gz}, Author = {Mladen Victor Wickerhauser}, Title = {Picture Compression by Best-Basis Sub-Band Coding}, Abstract = { We introduce a generalization of sub-band coding which may be used to compress digitized pictures or sequences of pictures. The method selects a most efficient orthogonal representation of the picture from among a large number of possibilities. The efficiency functional need only be additive across direct sum decompositions. We present some results of the method using Shannon entropy as the efficiency functional, and mean-square deviation as the error criterion.}, Type = {Preprint}, Institution = {Yale University}, Year = {1990}) @TechReport(w:nsmult, URL = {http://www.math.wustl.edu/~victor/papers/nsmatrix.pdf}, Author = {Mladen Victor Wickerhauser}, Title = {Nonstandard Matrix Multiplication}, Abstract = { We describe an algorithm for multiplying matrices in the compressed coordinates obtained by wavelet packet transforms. This generalizes the ``nonstandard matrix multiplication'' of Belykin, Coifman, and Rokhlin.}, Type = {Preprint}, Institution = {Yale University}, Month = {15 May}, Year = {1990})

## 1988

@TechReport(gw:elemwave, URL = {http://www.math.wustl.edu/~victor/papers/elemwave.pdf}, Author = {Elliot Gootman and Mladen Victor Wickerhauser}, Title = {Elementary Wavelets}, Abstract = { Necessary and sufficient conditions are given for some functions in L^2(R) with compactly supported Fourier transforms to generate orthonormal bases under the action of integer translations and power-of-two dilations.}, Type = {Preprint, 02021-88}, Institution = {Mathematical Sciences Research Institute}, Address = {Berkeley, California}, Year = {1988}) @Article(w:kp, Author = {Mladen Victor Wickerhauser}, Title = {Hamilton's Form for the {K}adomtsev--{P}etviashvili Equation}, Abstract = { The scattering transform for the Kadomtsev--Petviashvili equation (KP-II) is a local symplectomorphism. Pulling back the Hamiltonians for the linear evolutions of scattering data gives Hamiltonians for the KP-II hierarchy: they are values of the associated scattering data at distinguished points. This method yields simple proofs that KP-II has infinitely many commuting flows and simplifies their calculation. It also provides a Plancherel-type theorem.}, Journal = {Journal of Mathematical Physics}, Volume = {29}, Pages = {2300--2302}, Year = {1988})

## 1987

@Article(w:cmp, Author = {Mladen Victor Wickerhauser}, Title = {Inverse Scattering for the Heat Operator and Evolutions in 2+1 Variables}, Abstract = { The asymptotic behavior of functions in the kernel of the perturbed heat operator D^2_x - D_y - u(x,y) suffice to determine u. An explicit formula is derived using the d-bar method of inverse scattering, complete with estimates for small and moderately regular potentials u. If u evolves so as to satisfy the Kadomtsev-Petviashvili (KP-II) equation, the asymptotic data evolve linearly and boundedly. Thus the KP-II equation has solutions bounded for all time. A method for calculating nonlinear evolutions related to KP-II is presented. The related evolutions include the so-called ``KP-II Hierarchy'' and many others.}, Journal = {Communications in Mathematical Physics}, Volume = {108}, Pages = {67--89}, Year = {1987})

## 1985

@PhDThesis(w:phd, Author = {Mladen Victor Wickerhauser}, Title = {Nonlinear Evolutions of the Heat Operator}, Abstract = { Scattering data, which is the asymptotic behavior of solutions q = q(x,y) to the perturbed heat equation D^_x q - Dy q = uq, is computed, and shown to determine the perturbing function u=u(x,y). An explicit formula is derived using the d-bar method of inverse scattering, complete with estimates for small and moderately regular u. A method of calculating nonlinear evolutions of u which correspond to linear evolutions of the scattering data is presented, and shown to generate the Kadomtsev--Petviashvili II hierarchy of evolutions.}, School = {Yale University}, Address = {New Haven, Connecticut}, Month = {May}, Year = {1985})

## 1981

@TechReport(w:cyber, Author = {Mladen Victor Wickerhauser}, Title = {{C}yber 2xx Performance on an Implicit Factored {N}avier--{S}tokes Algorithm}, Abstract = { By modeling the execution of a particular numerical algorithm, we determine that a proposed supercomputer architecture is capable of nearly one billion floating-point operations per second.}, Institution = {NASA Ames Research Center}, Type = {Preprint}, Year = {1981})

Questions? Return to M. Victor Wickerhauser's home page for contact information.

Last modified on October 23, 2002.