CS: Sparsity and Persistence: Mixed Norms Provide Simple Signal Models with Dependent Coefficients

We mentioned mixed norms recently. Here is version 3 and the latest version of Sparsity and persistence: mixed norms provide simple signal models with dependent coefficients by Matthieu Kowalski and Bruno Torrésani. The abstract reads:

Sparse regression often uses $\ell_p$ norm priors (with p less than 2). This paper demonstrates that the introduction of mixed-norms in such contexts allows one to go one step beyond in signal models, and promote some different, structured, forms of sparsity. It is shown that the particular case of $\ell_{1,2}$ and $\ell_{2,1}$ norms lead to new group shrinkage operators. Mixed norm priors are shown to be particularly efficient in a generalized basis pursuit denoising approach, and are also used in a context of morphological component analysis. A suitable version of the Block Coordinate Relaxation algorithm is derived for the latter. The group-shrinkage operators are then modified to overcome some limitations of the mixed-norms. The proposed group shrinkage operators are tested on simulated signals in specific situations, to illustrate their different behaviors. Results on real data are also used to illustrate the relevance of the approach.

On a different note, Bruno Torrésani has a presentation in French that he made while on some island entitled: Parcimonie, ondelettes et *-lettes which is an introduction to why compressed sensing is needed (see end of presentation).

Credit: NASA, ISS017-E-015170 (4 Sept. 2008) --- Hurricane Ike was still a Category 4 storm on the morning of Sept. 4 when this photo was taken from the International Space Station's vantage point of 220 miles above the Earth.