期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 58, 期 4, 页码 2040-2047出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2011.2177632
关键词
Compressed sensing; convergence rate; orthogonal multimatching pursuit (OMMP); orthogonal super greedy algorithm (OSGA)
资金
- National Science Foundation [DMS-0906260]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0906260] Funding Source: National Science Foundation
The general theory of greedy approximation is well developed. Much less is known about how specific features of a dictionary can be used to our advantage. In this paper, we discuss incoherent dictionaries. We build a new greedy algorithm which is called the orthogonal super greedy algorithm (OSGA). We show that the rates of convergence of OSGA and the orthogonal matching pursuit (OMP) with respect to incoherent dictionaries are the same. Based on the analysis of the number of orthogonal projections and the number of iterations, we observed that OSGA(s) is times simpler (more efficient) than OMP. Greedy approximation is also a fundamental tool for sparse signal recovery. The performance of orthogonal multimatching pursuit, a counterpart of OSGA in the compressed sensing setting, is also analyzed under restricted isometry property conditions.
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