• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail

Wasserstein Loss for Image Synthesis and Restoration

Tartavel, Guillaume; Peyré, Gabriel; Gousseau, Yann (2016), Wasserstein Loss for Image Synthesis and Restoration, SIAM Journal on Imaging Sciences, 9, 4, p. 1726-1755. 10.1137/16M1067494

View/Open
WassersteinFidelity.pdf (5.174Mb)
Type
Article accepté pour publication ou publié
Date
2016
Journal name
SIAM Journal on Imaging Sciences
Volume
9
Number
4
Publisher
Society for Industrial and Applied Mathematics
Pages
1726-1755
Publication identifier
10.1137/16M1067494
Metadata
Show full item record
Author(s)
Tartavel, Guillaume
Peyré, Gabriel
Gousseau, Yann
Abstract (EN)
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.
Subjects / Keywords
Super-resolution; Total variation; Denoising; Generalized Gaussian Distributions; Optimal transport; Wasserstein; impulse noise removal

Related items

Showing items related by title and author.

  • Thumbnail
    Variational Texture Synthesis with Sparsity and Spectrum Constraints 
    Tartavel, Guillaume; Gousseau, Yann; Peyré, Gabriel (2015) Article accepté pour publication ou publié
  • Thumbnail
    Constrained Sparse Texture Synthesis 
    Tartavel, Guillaume; Gousseau, Yann; Peyré, Gabriel (2013) Communication / Conférence
  • Thumbnail
    Synthèse de texture par décomposition parcimonieuse contrainte 
    Peyré, Gabriel; Gousseau, Yann; Tartavel, Guillaume (2013) Communication / Conférence
  • Thumbnail
    The Numerical Tours of Signal Processing. Part 3: Image and Surface Restoration 
    Peyré, Gabriel (2011) Article accepté pour publication ou publié
  • Thumbnail
    Second-order in time schemes for gradient flows in Wasserstein and geodesic metric spaces 
    Legendre, Guillaume; Turinici, Gabriel (2017) Article accepté pour publication ou publié
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo