Journal
SIGNAL PROCESSING
Volume 106, Issue -, Pages 106-113Publisher
ELSEVIER
DOI: 10.1016/j.sigpro.2014.06.010
Keywords
Compressive sensing; Orthogonal matching pursuit; Restricted isometric property; Cumulative coherence; Sparse signal
Categories
Funding
- National Natural Science Foundation of China [61271234, 60972041, 61372122, 60972045]
- Ph.D. Program Foundation of Ministry of Education [20123223110002]
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Recently, lots of work has been done on conditions of guaranteeing sparse signal recovery using orthogonal matching pursuit (OMP). However, none of the existing conditions is both necessary and sufficient in terms of the so-called restricted isometric property, coherence, cumulative coherence (Babel function), or other verifiable quantities in the literature. Motivated by this observation, we propose a new measure of a matrix, named as union cumulative coherence, and present both sufficient and necessary conditions under which the OMP algorithm can uniformly recover sparse signals for all sensing matrices. The proposed condition guarantees a uniform recovery of sparse signals using OMP, and reveals the capability of OMP in sparse recovery. We demonstrate by examples that the proposed condition can be used to more effectively determine the recoverable sparse signals via OMP than the conditions existing in the literature. Furthermore, sparse recovery from noisy measurements is also considered in terms of the proposed union cumulative coherence. (C) 2014 Elsevier B.V. All rights reserved.
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