Coherence-based near-oracle performance guarantees for sparse estimation under Gaussian noise

We consider the problem of estimating a deterministic sparse vector x0 from underdetermined measurements Ax0 + w, where w represents white Gaussian noise and A is a given deterministic dictionary. We analyze the performance of three sparse estimation algorithms: basis pursuit denoising, orthogonal matching pursuit, and thresholding. These approaches are shown to achieve near-oracle performance with high probability, assuming that x0 is sufficiently sparse. Our results are non-asymptotic and are based only on the coherence of A, so that they are applicable to arbitrary dictionaries.

• Type: Conference
• Year: 2010
• Where: ICASSP
• Authors: Zvika Ben-Haim, Yonina C. Eldar, Michael Elad
• Keywords: Deterministic Sparse Vector, ICASSP 2010, Signal Processing, Sparse, Sparse Estimation Algorithms