Surfacelets: Constructions and Applications
Yue Lu
Abstract:
We propose a new signal representation, called the surfacelet transform,
that can be used to capture and represent signal singularities lying on
smooth manifolds of co-dimension 1 (e.g. surfaces in R3). Such
singularities are often observed in 3-D medical signals and image
sequences (video), where the signals are mostly smooth except on some
boundary surfaces. The proposed surfacelets constitute a tight frame in
L2(ZN), and has a strong connection with the local Radon transform.
One attractive feature of the surfacelet transform is that the
decomposition and reconstruction can be efficiently implemented by a
tree-structured filter bank, with their computation complexity
equivalent to a few FFTs (Fast Fourier Transform) applied on the same
data. This advantage in computational efficiency makes the proposed
surfacelet transform a feasible tool in many real-world applications,
including video processing (denoising, enhancement, compression),
seismic signal processing, and medical image analysis for computer-aided
diagnosis.
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