A wide-angle view at iterated shrinkage algorithms

M. Elad; B. Matalon; J. Shtok; M. Zibulevsky

doi:10.1117/12.741299

13 September 2007 A wide-angle view at iterated shrinkage algorithms

M. Elad, B. Matalon, J. Shtok, M. Zibulevsky

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Proceedings Volume 6701, Wavelets XII; 670102 (2007) https://doi.org/10.1117/12.741299
Event: Optical Engineering + Applications, 2007, San Diego, California, United States

Abstract

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.

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M. Elad, B. Matalon, J. Shtok, and M. Zibulevsky "A wide-angle view at iterated shrinkage algorithms", Proc. SPIE 6701, Wavelets XII, 670102 (13 September 2007); https://doi.org/10.1117/12.741299

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KEYWORDS

Expectation maximization algorithms

Optimization (mathematics)

Algorithm development

Associative arrays

Denoising

Algorithms

Chemical species

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