# Some applications of $l^\infty$-constraints in image processing

1 ARIANA - Inverse problems in earth monitoring
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - SIS - Signal, Images et Systèmes
Abstract : Our goal in this paper is to give algorithms for minimizing generic regularizing functionals under a $l^\infty$-constraint. We show that many classical models using total variation can be stated under this formalism. Among others are the Rudin-Oscher-Fatemi model, the BV-l1 model, BV-$l^\infty$ model and Meyer's cartoon +texture decomposition model. Then we describe a general convergence algorithm to solve such problems. This algorithm is the projected subgradient descent. We finally give numerical results that show the qualities and limits of our model, and we tackle the question of the use of the total variation to treat bounded noises such as quantization noise.
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https://hal.inria.fr/inria-00114051
Contributor : Pierre Weiss <>
Submitted on : Friday, February 9, 2007 - 1:49:17 PM
Last modification on : Monday, October 12, 2020 - 10:30:12 AM
Long-term archiving on: : Tuesday, September 21, 2010 - 11:59:47 AM

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RR-6115.pdf
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• HAL Id : inria-00114051, version 2

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Pierre Weiss, Gilles Aubert, Laure Blanc-Féraud. Some applications of $l^\infty$-constraints in image processing. [Research Report] RR-6115, INRIA. 2006, pp.33. ⟨inria-00114051v2⟩

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