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.
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Contributeur : Charles-Alban Deledalle <>
Soumis le : mardi 6 décembre 2016 - 14:44:36
Dernière modification le : jeudi 31 août 2017 - 20:11:57
Document(s) archivé(s) le : mardi 21 mars 2017 - 09:50:54


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  • HAL Id : hal-01333295, version 3
  • ARXIV : 1606.05158


Charles-Alban Deledalle, Nicolas Papadakis, Joseph Salmon, Samuel Vaiter. CLEAR: Covariant LEAst-square Re-fitting with applications to image restoration. SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2017, 10 (1), pp.243-284. 〈〉. 〈hal-01333295v3〉



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