Recovery of sparsely corrupted signals

Authors

Christoph Studer, Patrick Kuppinger, Graeme Pope, and Helmut Bölcskei

Reference

IEEE Transactions on Information Theory, Vol. 58, No. 5, pp. 3115-3130, May 2012

DOI: 10.1109/TIT.2011.2179701

[BibTeX, LaTeX, and HTML Reference]

Abstract

We investigate the recovery of signals exhibiting a sparse representation in a general (i.e., possibly redundant or incomplete) dictionary that are corrupted by additive noise admitting a sparse representation in another general dictionary. This setup covers a wide range of applications, such as image inpainting, super-resolution, signal separation, and recovery of signals that are impaired by, e.g., clipping, impulse noise, or narrowband interference. We present deterministic recovery guarantees based on a novel uncertainty relation for pairs of general dictionaries and we provide corresponding practicable recovery algorithms. The recovery guarantees we find depend on the signal and noise sparsity levels, on the coherence parameters of the involved dictionaries, and on the amount of prior knowledge about the signal and noise support sets.

Keywords

Uncertainty relations, signal restoration, signal separation, coherence-based recovery guarantees, l1-norm minimization, greedy algorithms


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