sparse regularization

Context: Characterization of instrumental effects in astronomical imaging is important in order to extract accurate physical information from the observations. The measured image in a real optical instrument is usually represented by the convolution of an ideal image with a Point Spread Function (PSF).

Following the writing of my previous post, which obtained various interesting comments (many thanks to Gabriel Peyré, Igor Carron and Pierre Vandergheynst), I sent a mail to Michael P. Friedlander and Ewout van den Berg to point them this article and possibly obtain their point of views.

Recently, I was using the SPGL1 toolbox to recover some “compressed sensed” images. As a reminder, SPGL1 implements the method described in “Probing the Pareto Frontier for basis pursuit solutions” of Michael P.