MULTISCALE FOURTH-ORDER MODELS FOR IMAGE RESTORATION, INPAINTING AND LOW-DIMENSIONAL SETS RECOVERY - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2015

MULTISCALE FOURTH-ORDER MODELS FOR IMAGE RESTORATION, INPAINTING AND LOW-DIMENSIONAL SETS RECOVERY

Résumé

We consider a fourth-order variational model for solving image inpainting and restora-tion problems, with emphasis on the recovery of low-order sets (edges, corners) and the curvature. The approach consists of constructing a family of regularized functionals and to select, locally and in an adaptive way, the regularization parameters which control the diffusion of the reconstruction operator. Unlike the usual methods which optimize the parameters a priori and lead, in general, to complex systems of PDEs, our approach is based on a continuous, linear, high-order diffusion model dynamically adjusted at the discrete level. We analyze the method in the framework of the calculus of variations and with the Γ-convergence tools and we show that it yields results that might be ex-pected from more complex systems of PDEs. We obtain simple discrete algorithms based on mixed finite elements. We also consider a new model which couples second and fourth order derivatives, in analogy with the Euler's elastica functional and we show that our simple model performs as well. We present several numerical examples to test our approach and to make some comparisons with existing methods.
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Dates et versions

hal-01114292 , version 1 (09-02-2015)
hal-01114292 , version 2 (03-02-2016)
hal-01114292 , version 3 (09-02-2016)

Identifiants

  • HAL Id : hal-01114292 , version 1

Citer

Zakaria Belhachmi, Moez Kallel, Maher Moakher, Anis Theljani. MULTISCALE FOURTH-ORDER MODELS FOR IMAGE RESTORATION, INPAINTING AND LOW-DIMENSIONAL SETS RECOVERY. 2015. ⟨hal-01114292v1⟩
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