Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 58, Issue 4, Pages 2040-2047Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2011.2177632
Keywords
Compressed sensing; convergence rate; orthogonal multimatching pursuit (OMMP); orthogonal super greedy algorithm (OSGA)
Funding
- National Science Foundation [DMS-0906260]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0906260] Funding Source: National Science Foundation
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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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