Open AccessNon-local regularization of inverse problems
Author(s) -
Gabriel Peyré,
Sébastien Bougleux,
Laurent D. Cohen
Publication year - 2011
Publication title -
inverse problems and imaging
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.755
H-Index - 40
eISSN - 1930-8345
pISSN - 1930-8337
DOI - 10.3934/ipi.2011.5.511
Subject(s) - regularization (linguistics) , inverse problem , inpainting , computer science , wavelet , inverse , mathematical optimization , mathematics , graph , algorithm , artificial intelligence , image (mathematics) , theoretical computer science , mathematical analysis , geometry
International audienceThis article proposes a new framework to regularize imaging lin- ear 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 pro- cess 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