Wasserstein Loss for Image Synthesis and Restoration

Abstract : This paper presents a novel variational approach to impose statistical constraints to the output of both image generation (to perform typically texture synthesis) and image restoration (for instance to achieve denoising and super-resolution) methods. The empirical distributions of linear or non-linear descriptors are imposed to be close to some input distributions by minimizing a Wasserstein loss, i.e. the optimal transport distance between the distributions. We advocate the use of a Wasserstein distance because it is robust when using discrete distributions without the need to resort to kernel estimators. We showcase different estimators to tackle various image processing applications. These estimators include linear wavelet-based filtering to account for simple textures, non-linear sparse coding coefficients for more complicated patterns, and the image gradient to restore sharper contents. For applications to texture synthesis, the input distributions are the empirical distributions computed from an exemplar image. For image denoising and super-resolution, the estimation process is more difficult; we propose to make use of parametric models and we show results using Generalized Gaussian Distributions.
Type de document :
Article dans une revue
SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2016, 9 (4), pp.1726-1755
Liste complète des métadonnées

Littérature citée [74 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01292843
Contributeur : Gabriel Peyré <>
Soumis le : mercredi 23 mars 2016 - 19:32:00
Dernière modification le : samedi 18 février 2017 - 01:17:42
Document(s) archivé(s) le : lundi 14 novembre 2016 - 03:24:18

Fichier

WassersteinFidelity.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01292843, version 1

Citation

Guillaume Tartavel, Gabriel Peyré, Yann Gousseau. Wasserstein Loss for Image Synthesis and Restoration. SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2016, 9 (4), pp.1726-1755. 〈hal-01292843〉

Partager

Métriques

Consultations de
la notice

497

Téléchargements du document

704