Skip to Main content Skip to Navigation
Journal articles

CLEAR: Covariant LEAst-Square Refitting 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 $\ell_1$ 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.
Complete list of metadatas

Cited literature [53 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01333295
Contributor : Charles-Alban Deledalle <>
Submitted on : Tuesday, December 6, 2016 - 2:44:36 PM
Last modification on : Wednesday, June 24, 2020 - 4:19:51 PM
Document(s) archivé(s) le : Tuesday, March 21, 2017 - 9:50:54 AM

File

clear_siims_final.pdf
Files produced by the author(s)

Identifiers

Citation

Charles-Alban Deledalle, Nicolas Papadakis, Joseph Salmon, Samuel Vaiter. CLEAR: Covariant LEAst-Square Refitting with Applications to Image Restoration. SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2017, 10 (1), pp.243-284. ⟨10.1137/16M1080318⟩. ⟨hal-01333295v3⟩

Share

Metrics

Record views

802

Files downloads

524