A sparse representation criterion: recovery conditions and implementation issues

Sparse representations techniques have become an active domain of research in signal processing with numerous applications in compression and coding, for instance. They are mostly based on a combined `2 − `1 criterion, where the least-squares-part ensures closeness to the observations and the `1-part sparsity. We replace the least-square-part by a `∞-part and investigate the recovery conditions of the so-obtained `∞ − `1 criterion. We then propose an algorithm, that minimizes the criterion, in a finite number of steps.