Sparse and redundant representations − an emerging and powerful model for signals − suggests that a data source could be described as a linear combination of few atoms from a pre-specified and over-complete dictionary. This model has drawn a considerable attention in the past decade, due to its appealing theoretical foundations, and promising practical results it leads to. Many of the applications that use this model are formulated as a mixture of l₂-l_p (p ≤ 1) optimization expressions. Iterated Shrinkage algorithms are a new family of highly effective numerical techniques for handling these optimization tasks, surpassing traditional optimization techniques. In this paper we aim to give a broad view of this group of methods, motivate their need, present their derivation, show their comparative performance, and most important of all, discuss their potential in various applications.

Date Published: 13 September 2007
PDF: 19 pages
Proc. SPIE 6701, Wavelets XII, 670102 (13 September 2007); doi: 10.1117/12.741299

Published in SPIE Proceedings Vol. 6701:
Wavelets XII
Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editor(s)