Recovery of Sparsely Corrupted Signals

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 on the support sets of signal and noise. We finally identify situations under which the recovery guarantees are tight.

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Christoph Studer, Patrick Kuppinger, Graeme Pope, Helmut Bölcskei
• Keywords: CORR 2011, Deterministic Recovery Guarantees, Education, Recovery Guarantees, Sparse Representation