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L1-L2 Optimization in Signal and Image Processing

Abstract : Sparse, redundant representations offer a powerful emerging model for signals. This model approximates a data source as a linear combination of few atoms from a prespecified and over-complete dictionary. Often such models are fit to data by solving mixed ¿1-¿2 convex optimization problems. Iterative-shrinkage algorithms constitute a new family of highly effective numerical methods for handling these problems, surpassing traditional optimization techniques. In this article, we give a broad view of this group of methods, derive some of them, show accelerations based on the sequential subspace optimization (SESOP), fast iterative soft-thresholding algorithm (FISTA) and the conjugate gradient (CG) method, present a comparative performance, and discuss their potential in various applications, such as compressed sensing, computed tomography, and deblurring.
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https://hal.inria.fr/inria-00567455
Contributor : Jules Espiau de Lamaestre <>
Submitted on : Monday, February 21, 2011 - 11:54:16 AM
Last modification on : Monday, February 21, 2011 - 11:54:16 AM

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Michael Zibulevsky, Michael Elad. L1-L2 Optimization in Signal and Image Processing. Signal Processing Magazine, IEEE, IEEE Signal Processing Society, 2010, 27 (3), pp.76 -88. ⟨10.1109/MSP.2010.936023⟩. ⟨inria-00567455⟩

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