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

doi:10.1137/16M1080318

Métadonnées

Afficher la notice complète

Licence d’utilisation du document

DELEDALLE, Charles-Alban
Institut de Mathématiques de Bordeaux [IMB]

PAPADAKIS, Nicolas
Institut de Mathématiques de Bordeaux [IMB]

SALMON, Joseph
Signal, Statistique et Apprentissage [S2A]
Département Images, Données, Signal [IDS]

Langue

Article de revue

Ce document a été publié dans

SIAM Journal on Imaging Sciences. 2017, vol. 10, n° 1, p. 243-284

Society for Industrial and Applied Mathematics

Résumé en anglais

In this paper, we propose a new framework to remove parts of the systematic errors affecting popular restoration algorithms, with a special focus for image processing tasks. Generalizing ideas that emerged for $\ell_1$ regularization, we develop an approach re-fitting the results of standard methods towards the input data. Total variation regularizations and non-local means are special cases of interest. We identify important covariant information that should be preserved by the re-fitting method, and emphasize the importance of preserving the Jacobian (w.r.t. the observed signal) of the original estimator. Then, we provide an approach that has a ``twicing'' flavor and allows re-fitting the restored signal by adding back a local affine transformation of the residual term. We illustrate the benefits of our method on numerical simulations for image restoration tasks.< Réduire

Mots clés en anglais

Variational methods

Debiasing

Boosting

Twicing

Refitting

Inverse problems

DOI

http://dx.doi.org/10.1137/16M1080318

Project ANR

Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251