Robust locally linear analysis with applications to image denoising and blind inpainting

Yi Wang, Arthur Szlam, Gilad Lerman

Research output: Contribution to journalArticle

26 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)526-562
Number of pages37
JournalSIAM Journal on Imaging Sciences
Volume6
Issue number1
DOIs
StatePublished - Mar 6 2013

Keywords

  • Alternating least squares
  • Blind inpainting
  • Denoising
  • Impulsive noise
  • Locally linear
  • Multiple subspaces modeling
  • Robust pca
  • Subspace clustering

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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