ECE 544 MD - Wavelets in Signal Processing

Official Description

Lectures and discussions related to advanced topics and new areas of interest in signal processing: speech, image, and multidimensional processing. Course Information: May be repeated 8 hours in a term to a total of 20 hours. Credit towards a degree from multiple offerings of this course is not given if those offerings have significant overlap, as determined by the ECE department. Prerequisite: As specified each term. It is expected that each offering will have a 500-level course as prerequisite or co-requisite.

Subject Area

Signal Processing

Course Director

Description

Wavelets have established themselves as an important tool in modern signal processing as well as in applied mathematics. The objective of this course is to establish the theory necessary to understand and use wavelets and related constructions. A particular emphasis will be put on constructions that are amenable to efficient algorithms, since ultimately these are the ones that are likely to have an impact. We thus study applications in signal processing, communications, and sensing where time-frequency transforms like wavelets play an important role. The course has computer and research projects involving independent study.

Topics

  1. Introduction and background: why wavelets, filter banks, and multiresolution analysis? signal spaces and operators; review of Fourier theory; multirate signal processing; time-frequency analysis.
  2. Discrete-time bases and filter banks: series expansions of discrete-time signals; analysis and design of filter banks; orthogonal and biorthogonal filter banks; tree-structured filter banks; discrete wavelet transform.
  3. Continuous-time bases and wavelets: multiresolution analysis; iterated filter banks; wavelets and filter banks; wavelet series and its properties; regularity and approximation properties.
  4. Overcomplete expansions and continuous transforms: frame theory; oversampled filter banks; continuous wavelet and short-time Fourier transforms.
  5. Advanced topics: sparse representation; linear and nonlinear approximation in various bases; nonlinear signal estimation; multidimensional filter banks and wavelets; multiscale geometric image processing; compressed sensing.
  6. Applications: speech, audio, image and video compression; denoising; feature extraction; inverse problems.

Detailed Description and Outline

Topics:

  1. Introduction and background: why wavelets, filter banks, and multiresolution analysis? signal spaces and operators; review of Fourier theory; multirate signal processing; time-frequency analysis.
  2. Discrete-time bases and filter banks: series expansions of discrete-time signals; analysis and design of filter banks; orthogonal and biorthogonal filter banks; tree-structured filter banks; discrete wavelet transform.
  3. Continuous-time bases and wavelets: multiresolution analysis; iterated filter banks; wavelets and filter banks; wavelet series and its properties; regularity and approximation properties.
  4. Overcomplete expansions and continuous transforms: frame theory; oversampled filter banks; continuous wavelet and short-time Fourier transforms.
  5. Advanced topics: sparse representation; linear and nonlinear approximation in various bases; nonlinear signal estimation; multidimensional filter banks and wavelets; multiscale geometric image processing; compressed sensing.
  6. Applications: speech, audio, image and video compression; denoising; feature extraction; inverse problems.

Texts

M. Vetterli, J. Kovacevic, and V. K. Goyal, The World of Fourier and Wavelets: Theory, Algorithms and Applications; and research papers.

Last updated

2/13/2013