An epigraphical convex optimization approach for multicomponent image restoration using non-local structure tensorReport as inadecuate




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* Corresponding author 1 LTCI - Laboratoire Traitement et Communication de l-Information 2 Phys-ENS - Laboratoire de Physique de l-ENS Lyon 3 LIGM - Laboratoire d-Informatique Gaspard-Monge

Abstract : TV-like constraints-regularizations are useful tools in variational methods for multicomponent image restoration. In this paper, we design more sophisticated non-local TV constraints which are derived from the structure tensor. The proposed approach allows us to measure the non-local variations, jointly for the different components, through various ℓ 1,p matrix norms with p >= 1. The related convex constrained optimization problems are solved through a novel epigraphical projection method. This formulation can be efficiently implemented thanks to the flexibility offered by recent primal-dual proximal algorithms. Experiments carried out for color images demonstrate the interest of considering a Non-Local Structure Tensor TV and show that the proposed epigraphical projection method leads to significant improvements in terms of convergence speed over existing numerical solutions.





Author: Giovanni Chierchia - Nelly Pustelnik - Jean-Christophe Pesquet - Béatrice Pesquet-Popescu -

Source: https://hal.archives-ouvertes.fr/



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