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 language | English (US) |
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Pages (from-to) | 526-562 |
Number of pages | 37 |
Journal | SIAM Journal on Imaging Sciences |
Volume | 6 |
Issue number | 1 |
DOIs | |
State | Published - Mar 6 2013 |
Externally published | Yes |
Keywords
- Alternating least squares
- Blind inpainting
- Denoising
- Impulsive noise
- Locally linear
- Multiple subspaces modeling
- Robust pca
- Subspace clustering
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics