Non-local Regularization of Inverse Problems

Authors:
Gabriel Peyré;Sébastien Bougleux;Laurent Cohen
Affiliations:
Université Paris-Dauphine, CEREMADE, Paris Cedex 16, France 75775;Université Paris-Dauphine, CEREMADE, Paris Cedex 16, France 75775;Université Paris-Dauphine, CEREMADE, Paris Cedex 16, France 75775
Venue:
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
Year:
2008

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Abstract

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.