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Smoothing techniques for convex problems. Applications in image processing.

Pierre Weiss 1 Mikael Carlavan 2 Laure Blanc-Féraud 2 Josiane Zerubia 2
2 ARIANA - Inverse problems in earth monitoring
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - SIS - Signal, Images et Systèmes
Abstract : In this paper, we present two algorithms to solve some inverse problems coming from the field of image processing. The problems we study are convex and can be expressed simply as sums of lp-norms of affine transforms of the image. We propose 2 different techniques. They are - to the best of our knowledge - new in the domain of image processing and one of them is new in the domain of mathematical programming. Both methods converge to the set of minimizers. Additionally, we show that they converge at least as O(1/N) (where N is the iteration counter) which is in some sense an ``optimal'' rate of convergence. Finally, we compare these approaches to some others on a toy problem of image super-resolution with impulse noise.
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Contributor : Mikael Carlavan <>
Submitted on : Wednesday, September 16, 2009 - 4:21:07 PM
Last modification on : Monday, October 12, 2020 - 10:30:11 AM
Long-term archiving on: : Tuesday, June 15, 2010 - 11:45:34 PM


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  • HAL Id : inria-00417713, version 1



Pierre Weiss, Mikael Carlavan, Laure Blanc-Féraud, Josiane Zerubia. Smoothing techniques for convex problems. Applications in image processing.. SAMPTA, May 2009, Marseille, France. ⟨inria-00417713⟩



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