CLEAR: Covariant LEAst-Square Refitting with Applications to Image Restoration
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | DELEDALLE, Charles-Alban | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | PAPADAKIS, Nicolas | |
| hal.structure.identifier | Signal, Statistique et Apprentissage [S2A] | |
| hal.structure.identifier | Département Images, Données, Signal [IDS] | |
| dc.contributor.author | SALMON, Joseph | |
| hal.structure.identifier | Institut de Mathématiques de Bourgogne [Dijon] [IMB] | |
| dc.contributor.author | VAITER, Samuel | |
| dc.date.created | 2016-06-16 | |
| dc.date.issued | 2017 | |
| dc.description.abstractEn | 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. | |
| dc.description.sponsorship | Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003 | |
| dc.language.iso | en | |
| dc.publisher | Society for Industrial and Applied Mathematics | |
| dc.subject.en | Variational methods | |
| dc.subject.en | Debiasing | |
| dc.subject.en | Boosting | |
| dc.subject.en | Twicing | |
| dc.subject.en | Refitting | |
| dc.subject.en | Inverse problems | |
| dc.title.en | CLEAR: Covariant LEAst-Square Refitting with Applications to Image Restoration | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1137/16M1080318 | |
| dc.subject.hal | Informatique [cs]/Traitement des images | |
| dc.subject.hal | Informatique [cs]/Traitement du signal et de l'image | |
| dc.subject.hal | Mathématiques [math]/Statistiques [math.ST] | |
| dc.subject.hal | Informatique [cs]/Vision par ordinateur et reconnaissance de formes [cs.CV] | |
| dc.subject.hal | Statistiques [stat]/Machine Learning [stat.ML] | |
| dc.identifier.arxiv | 1606.05158 | |
| bordeaux.journal | SIAM Journal on Imaging Sciences | |
| bordeaux.page | 243-284 | |
| bordeaux.volume | 10 | |
| bordeaux.issue | 1 | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01333295 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01333295v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=SIAM%20Journal%20on%20Imaging%20Sciences&rft.date=2017&rft.volume=10&rft.issue=1&rft.spage=243-284&rft.epage=243-284&rft.au=DELEDALLE,%20Charles-Alban&PAPADAKIS,%20Nicolas&SALMON,%20Joseph&VAITER,%20Samuel&rft.genre=article |
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