Non-local Regularization of Inverse Problems
Résumé
This article proposes a new framework to regularize linear inverse problems using a total variation prior on an adapted non-local graph. The non-local graph is optimized to match the structures of the image to recover. This allows a better reconstruction of geometric edges and textures present in natural images. A fast algorithm computes iteratively both the solution of the regularization process and the non-local graph adapted to this solution. The graph adaptation is particularly efficient to solve inverse problems with randomized measurements such as inpainting random pixels or compressive sensing recovery. Our non-local regularization gives state of the art results for this class of inverse problems. On more challenging problems such as image super-resolution, our method gives results comparable to translation invariant wavelet-based methods.
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