Robust Locally Linear Analysis with Applications to Image Denoising and Blind Inpainting

We study the related problems of denoising images corrupted by impulsive noise and blind inpainting (i.e., inpainting when the deteriorated region is unknown). Our basic approach is to model the set of patches of pixels in an image as a union of low-dimensional subspaces, corrupted by sparse but per...

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Bibliographic Details
Published inSIAM journal on imaging sciences Vol. 6; no. 1; pp. 526 - 562
Main Authors Wang, Yi, Szlam, Arthur, Lerman, Gilad
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2013
Subjects
Blinds
Convergence
Imaging
Noise
Noise reduction
Subspaces
Unions
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Summary:We study the related problems of denoising images corrupted by impulsive noise and blind inpainting (i.e., inpainting when the deteriorated region is unknown). Our basic approach is to model the set of patches of pixels in an image as a union of low-dimensional subspaces, corrupted by sparse but perhaps large magnitude noise. For this purpose, we develop a robust and iterative method for single subspace modeling and extend it to an iterative algorithm for modeling multiple subspaces. We prove convergence for both algorithms and carefully compare our methods with other recent ideas for such robust modeling. We demonstrate state-of-the-art performance of our method for both imaging problems. [PUBLICATION ABSTRACT]
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ISSN:1936-4954
1936-4954
DOI:10.1137/110843642