Coherence-based recovery guarantees for generalized basis-pursuit de-quantizing

This paper deals with the recovery of signals that admit an approximately sparse representation in some known dictionary (possibly over-complete) and are corrupted by additive noise. In particular, we consider additive measurement noise with bounded ℓ_p-norm for p ≥ 2, and we minimize the ℓ_q quasi-norm (with q ∈ (0, 1]) of the signal vector. We develop coherence-based recovery guarantees for which stable recovery via generalized basis-pursuit de-quantizing (BPDQ_p,q) is possible. We finally show that depending on the measurement-noise model and the choice of the ℓ_p-norm used in the constraint, (BPDQ_p,q) significantly outperforms classical basis pursuit de-noising (BPDN).