# CLEAR: Covariant LEAst-square Re-fitting with applications to image restoration

Abstract : 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 l1 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.
Keywords :
Type de document :
Pré-publication, Document de travail
2016
Domaine :
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https://hal.archives-ouvertes.fr/hal-01333295
Contributeur : Charles-Alban Deledalle <>
Soumis le : mercredi 14 septembre 2016 - 23:25:50
Dernière modification le : vendredi 9 décembre 2016 - 01:03:38
Document(s) archivé(s) le : jeudi 15 décembre 2016 - 16:06:34

### Fichier

clear_hal_version2.pdf
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### Identifiants

• HAL Id : hal-01333295, version 2
• ARXIV : 1606.05158

### Citation

Charles-Alban Deledalle, Nicolas Papadakis, Joseph Salmon, Samuel Vaiter. CLEAR: Covariant LEAst-square Re-fitting with applications to image restoration. 2016. <hal-01333295v2>

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