DELEDALLE, Charles-Alban; PAPADAKIS, Nicolas; SALMON, Joseph; VAITER, Samuel

doi:10.1007/s10851-020-00993-2

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DELEDALLE, Charles-Alban
Institut de Mathématiques de Bordeaux [IMB]
Department of Electrical and Computer Engineering [Univ California San Diego] [ECE - UC San Diego]

PAPADAKIS, Nicolas
Institut de Mathématiques de Bordeaux [IMB]

SALMON, Joseph
Institut Montpelliérain Alexander Grothendieck [IMAG]

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Article de revue

Ce document a été publié dans

Journal of Mathematical Imaging and Vision, 7th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2019, 2019-06-30, Hofgeismar. 2021 n° 63, p. 216–236

Springer Verlag

Résumé en anglais

In many linear regression problems, including ill-posed inverse problems in image restoration, the data exhibit some sparse structures that can be used to regularize the inversion. To this end, a classical path is to usel l(12) block-based regularization. While efficient at retrieving the inherent sparsity patterns of the data-the support-the estimated solutions are known to suffer from a systematical bias. We propose a general framework for removing this artifact by refitting the solution toward the data while preserving key features of its structure such as the support. This is done through the use of refitting block penalties that only act on the support of the estimated solution. Based on an analysis of related works in the literature, we introduce a new penalty that is well suited for refitting purposes. We also present a new algorithm to obtain the refitted solution along with the original (biased) solution for any convex refitting block penalty. Experiments illustrate the good behavior of the proposed block penalty for refitting solutions of total variation and total generalized variation models.< Réduire

Mots clés en anglais

Block sparsity

Total variation

Bias correction

Refitting

URI

https://oskar-bordeaux.fr/handle/20.500.12278/192742

DOI

http://dx.doi.org/10.1007/s10851-020-00993-2

Projet Européen

Nonlocal Methods for Arbitrary Data Sources

Project ANR

Generalized Optimal Transport Models for Image processing - ANR-16-CE33-0010

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251