EFFICIENT SCHEMES FOR TOTAL VARIATION MINIMIZATION UNDER CONSTRAINTS IN IMAGE PROCESSING - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles SIAM Journal on Scientific Computing Year : 2009

EFFICIENT SCHEMES FOR TOTAL VARIATION MINIMIZATION UNDER CONSTRAINTS IN IMAGE PROCESSING

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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Dates and versions

inria-00417725 , version 1 (16-09-2009)

Identifiers

  • HAL Id : inria-00417725 , version 1

Cite

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