EFFICIENT SCHEMES FOR TOTAL VARIATION MINIMIZATION UNDER CONSTRAINTS IN IMAGE PROCESSING

Pierre Weiss 1 Laure Blanc-Féraud 1 Gilles Aubert 2
1 ARIANA - Inverse problems in earth monitoring
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - SIS - Signal, Images et Systèmes
Abstract : This paper presents new fast algorithms to minimize total variation and more generally l1-norms under a general convex constraint. Such problems are standards of image processing. The algorithms are based on a recent advance in convex optimization proposed by Yurii Nesterov. Depending on the regularity of the data fidelity term, we solve either a primal problem or a dual problem. First we show that standard first-order schemes allow one to get solutions of precision epsilon in O( 1/epsilon2) iterations at worst. We propose a scheme that allows one to obtain a solution of precision in O( 1/epsilon ) iterations for a general convex constraint. For a strongly convex constraint, we solve a dual problem with a scheme that requires O( 1 /√epsilon ) iterations to get a solution of precision epsilon. Finally we perform some numerical experiments which confirm the theoretical results on various problems of image processing.
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Journal articles
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https://hal.inria.fr/inria-00417725
Contributor : Laure Blanc-Féraud <>
Submitted on : Wednesday, September 16, 2009 - 4:43:06 PM
Last modification on : Monday, November 5, 2018 - 3:52:01 PM

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  • HAL Id : inria-00417725, version 1

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Pierre Weiss, Laure Blanc-Féraud, Gilles Aubert. EFFICIENT SCHEMES FOR TOTAL VARIATION MINIMIZATION UNDER CONSTRAINTS IN IMAGE PROCESSING. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2009, 31 (3), pp.2047-2080. ⟨inria-00417725⟩

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