Coherence-based probabilistic recovery guarantees for sparsely corrupted signals

In this paper, we present novel probabilistic recovery guarantees for sparse signals subject to sparse interference, covering varying degrees of knowledge of the signal and interference support. Our results assume that the sparsifying dictionaries are characterized by coherence parameters and we require randomness only in the signal and/or interference. The obtained recovery guarantees show that one can recover sparsely corrupted signals with overwhelming probability, even if the sparsity of both the signal and interference scale (near) linearly with the number of measurements.