Non-local regularization of inverse problems
Cohen, Laurent D.; Bougleux, Sébastien; Peyré, Gabriel (2011), Non-local regularization of inverse problems, Inverse Problems and Imaging, 5, 2, p. 511-530. http://dx.doi.org/10.3934/ipi.2011.5.511
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00419791
Journal nameInverse Problems and Imaging
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Abstract (EN)This article proposes a new framework to regularize imaging linear inverse problems using an adaptive non-local energy. A 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 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 sparse regularization in a translation invariant wavelet frame.
Subjects / KeywordsNon-local regularization; inpainting; super-resolution; compressive sensing
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