A Numerical Tour
of Signal Processing
by Gabriel Peyré
This web page gathers numerical experiments that illustrate the book of Stephane Mallat
A Wavelet Tour of Signal Processing - Third Edition: The Sparse Way.
A Wavelet Tour of Signal Processing.
Third Edition: The Sparse Way.
Stéphane Mallat.
Academic Press, dec. 2008.
- Introduction -
Intro #1 - Basics of Matlab/Scilab Programming
- Image Processing -
Images #1 - Introduction to Image Processing
Images #2 - Edge Detection and Heat Diffusion
- Audio Processing -
Audio #1 - Audio Processing with the Short Time Fourier Transform
Audio #2 - Audio Separation with Sparsity
- Wavelet Processing -
Wavelets #1 - Introduction to Wavelet Processing
Wavelets #2 - Image Approximation with Wavelets
- Denoising -
Denoising #1 - Image Denoising with Linear Methods
Denoising #2 - Image Denoising with Wavelets
- Coding and Compression -
Coding #1 - Entropic Coding
Coding #2 - Statistics of Natural Images
Coding #3 - Wavelet Image Compression
- Total Variation -
TV #1 - Outliers and Median Denoiser
TV #2 - Total Variation Minimization
- Sparsity and Redundant Representations-
Sparsity #1 - Sparse Spikes Deconvolution with Matching Pursuit
Sparsity #2 - Sparse Spikes Deconvolution with Basis Pursuit
Sparsity #3 - Audio Pursuits in a Gabor Dictionary
- Inverse Problem and Compressive Sensing -
Inverse Problems #1 - Variational Image Inpainting
Inverse Problems #2 - Reconstruction from Partial Tomography Measurements
Inverse Problems #3 - Compressed Sensing
Inverse Problems #4 - Reconstruction from Compressive Fourier Measurements
How to use these numerical tours: Each tour is a set of experiments that can be performed using either Matlab or Scilab. At the beginning of each tour, you are asked to download and install the required toolboxes (there exists three toolboxes: general/signal/graph), that contain many useful helper functions. Each tour alternates between code you can copy/paste in Matlab or Scilab, and exercises you need to solve on your own.
Solutions of the numerical exercises:: If you are a teacher and would like to have access to the Matlab files that contain the solution of the numerical exercises, please send me an e-mail.
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