Non-local Regularization of Inverse Problems

Gabriel Peyré (1) , Sébastien Bougleux (2) , Laurent D. Cohen (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Image

This article proposes a new framework to regularize linear inverse problems using the total variation on non-local graphs. This non-local graph allows to adapt the penalization to the geometry of the underlying function to recover. A fast algorithm computes iteratively both the solution of the regularization process and the non-local graph adapted to this solution. We show numerical applications of this method to the resolution of image processing inverse problems such as inpainting, super-resolution and compressive sampling.

Mots clés: Non local means; denoising; inverse problem; regularization; deblurring; compressed sensing

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Gabriel Peyré, Sébastien Bougleux, Laurent D. Cohen. Non-local Regularization of Inverse Problems. European Conference on Computer Vision (ECCV'08), Oct 2008, Marseilles, France. pp.57-68. ⟨hal-00365030⟩