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IEEE Trans. Information Theory, 2012, Volume 58, Issue 4, Pages 2040–2047 (Mi tit3)  

The orthogonal super greedy algorithm and applications in compressed sensing

E. Liu, V. N. Temlyakov

Department of Mathematics, University of South Carolina, Columbia, SC, USA

Abstract: 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 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.

Funding Agency Grant Number
National Science Foundation DMS-0906260
This work was supported by the National Science Foundation under Grant DMS-0906260.


DOI: https://doi.org/10.1109/TIT.2011.2177632


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