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

Authors

Graeme Pope, Christoph Studer, and Michel Baes

Reference

Proc. of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Kyoto, Japan, pp. 3669--3672, Mar. 2012.

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Abstract

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 lp-norm for p>=2, and we minimize the lq 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 (BPDQp,q) is possible. We finally show that depending on the measurement-noise model and the choice of the lp-norm used in the constraint, (BPDQp,q ) significantly outperforms classical basis pursuit de-noising (BPDN).

Keywords

Sparse signal recovery, sparse estimation, de-noising, de-quantizing, deterministic recovery guarantees

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