A Wavelet Tour of Signal Processing: The Sparse Way
This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and École
Polytechnique in Paris.
Key Features
* Provides a broad perspective on the principles and applications of transient signal processing with wavelets
* Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms
* Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection,
multifractal analysis, and time-varying frequency measurements
* Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet
* Content is accessible on several level of complexity, depending on the individual reader's needs
New to the Second Edition
* Optical flow calculation and video compression algorithms
* Image models with bounded variation functions
* Bayes and Minimax theories for signal estimation
* 200 pages rewritten and most illustrations redrawn
* More problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics
Why Read This Book
You should read this book if you want a unified, rigorous yet application-minded presentation of wavelets for signal processing — from multiresolution theory to fast algorithms and practical denoising/compression examples. It gives you the mathematical foundations and the intuition needed to apply wavelets across audio, image, and communications problems.
Who Will Benefit
Graduate students, researchers, and experienced engineers working on DSP, time–frequency analysis, denoising, compression, or multiresolution methods who need a deep, mathematically grounded reference.
Level: Advanced — Prerequisites: Solid calculus and linear algebra, basics of signals and systems and Fourier analysis; familiarity with probability/statistics and discrete-time signal processing is helpful.
Key Takeaways
- Understand the multiresolution analysis framework and how it leads to orthonormal wavelet bases.
- Derive and implement the fast discrete wavelet transform (Mallat algorithm) and its connection to filter banks.
- Design and analyze wavelet and biorthogonal scaling functions and filters for practical DSP tasks.
- Apply wavelets to denoising, thresholding, compression, and other real signal-processing applications.
- Use wavelet packets, frames, and best-basis ideas to adapt bases to signal structure.
- Relate wavelet tools to classical time–frequency and multirate signal-processing concepts.
Topics Covered
- Introduction and motivations: transients, time–frequency localization
- Multiresolution analysis and construction of scaling functions
- Orthonormal wavelet bases and the Mallat decomposition
- Filter banks and the fast wavelet transform
- Biorthogonal wavelets and compactly supported constructions
- Continuous wavelet transform and time–frequency representations
- Wavelet packets and best-basis algorithms
- Frames, stability, and redundancy
- Statistical estimation: denoising and thresholding techniques
- Compression and coding with wavelets
- Multidimensional wavelets and applications to images
- Advanced topics: regularity, vanishing moments, and numerical aspects
- Applications and examples: noise removal, feature extraction, practical case studies
Languages, Platforms & Tools
How It Compares
More comprehensive and application-oriented than Daubechies' Ten Lectures (which is more concise and mathematically focused); complements Vetterli & Kovacevic's Wavelets and Subband Coding, which is more engineering/application heavy.
