CLEAR: Covariant LEAst-Square Refitting with Applications to Image Restoration
Language
en
Article de revue
This item was published in
SIAM Journal on Imaging Sciences. 2017, vol. 10, n° 1, p. 243-284
Society for Industrial and Applied Mathematics
English 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 $\ell_1$ ...Read more >
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.Read less <
English Keywords
Variational methods
Debiasing
Boosting
Twicing
Refitting
Inverse problems
ANR Project
Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003
Origin
Hal imported