Generalized Orthogonal Matching Pursuit

Details Generalized Orthogonal Matching Pursuit Generalized Orthogonal Matching Pursuit

2011-11-29

arxiv.org/abs/1111.6664v1

Computer Science

Information Theory

Submitted to IEEE Trans. Inform. Theory

Scientific paper

As a greedy algorithm to recover sparse signals from compressed measurements, the orthogonal matching pursuit (OMP) algorithm has received much attention in recent years. In this paper, we introduce an extension of the orthogonal matching pursuit (gOMP) for pursuing efficiency in reconstructing sparse signals. Our approach, henceforth referred to as generalized OMP (gOMP), is literally a generalization of the OMP in the sense that multiple indices are identified per iteration. Owing to the selection of multiple "correct" indices, the gOMP algorithm is finished with much smaller number of iterations compared to the OMP. We show that the gOMP can perfectly reconstruct any $K$-sparse signals ($K > 1$), provided that the sensing matrix satisfies the RIP with $\delta_{NK} < \frac{\sqrt{N}}{\sqrt{K} + 2 \sqrt{N}}$. We also demonstrate by empirical simulations that the gOMP has excellent recovery performance comparable to $\ell_1$-minimization technique with fast processing speed and competitive computational complexity.

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