Math 541
Topics in Applied Mathematics: Wavelet Algorithms

Prof. M. Victor Wickerhauser

NEWS

  • HW #3, due Fri, Nov 20th, is now available.

    See Alfred V. Aho and Neil J. A. Sloane, "Some Doubly Exponential Sequences", in Fibonacci Quarterly 11(1970),429--437, for the exact count of unit dyadic decompositions of [0,1). Alternatively, see Eq.16 on p.9 of my survey paper Some Problems Related to Wavelet Packet Bases and Convergence.

    See the link to Daubechies' software to generate wavelet filter coefficients.

    Dowload Maxima, a public software implementation of the Macsyma computer algebra system, from its SourceForge archive.

  • EXAMPLES

    Daubechies' software to generate wavelet filter coefficients.

    Syllabus

    Through readings in seminal papers and books, the course will develop understanding of analytic and algorithmic issues in wavelet analysis and its applications.

    Various software packages will be used in the course, in particular R.

    Topics. Lifting implementation of discrete wavelet transforms; shift-invariant wavelet transforms; SURE denoising; filter design and families of wavelets; wavelets on intervals; source coding for redundancy removal; zerotrees.

    Prerequisites. Math 4111 and 449, or permission of the instructor.

    Time. Classes meet Mondays, Wednesdays, and Fridays, 12:00 noon to 1:00 pm, in Earth and Planetary Sciences, room 102.

    Texts. The instructor will assign readings from various journal articles and books, including the following:

    Assignments: In the first part of the course, homework sets requiring proofs, computations, or simple computer programs will be assigned to all students approximately every two weeks.

    Toward the end of the course, following lectures and demonstrations by the instructor, students will be assigned portions of articles or book chapters to read, present in class, and demonstrate with their own software implementations.

    Collaboration outside of class is permitted and encouraged, but each student must turn in individually-prepared work.

    Homework asignments:

    Tests. There will be no tests or examinations.

    Grading. Grades will be based partially on homework and partially on an evaluation of the student's in-class presentation.

    Office Hours. See the instructor in Cupples I, room 105a, on Mondays between 4pm and 5pm, or by appointment.


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