CS: Toolbox Sparsity - A Toolbox for Sparse Coding and Sparse Regularization.

After providing a very nice literature review on L1/TV optimization, Gabriel Peyre just released a matlab toolbox called: Toolbox Sparsity - A toolbox for sparse coding and sparse regularization.

As explained in the introduction section of the page:

This toolbox implements several algorithms to compute sparse expansion in redundant dictionaries and to solve inverse problems with sparse regularization (and also TV regularization).

The content of the toolbox include:

• Overview
• Compressed sensing of exactely sparse signals with Fourier measurements.
• Compressed sensing of noisy approximately sparse signals with Gaussian measurements.
• Tomography inversion of an image with TV regularization.
• Sparse spikes deconvolution with L1 regularization and Matching Pursuit
• Image inpainting with sparse wavelets regularization

The page is a step by step description of examples that are very much noteworthy. The toolbox itself can be downloaded from Matlab Central. I have listed it in the reconstruction section of the Big Picture.

I am also noting the Gabriel has produced a toolbox for the Multiwavelet Alpert Transform. This is very nice. Other Toolboxes Gabriel has made can be found here.