Generalized Orthogonal Matching Pursuit
Abstract
As a greedy algorithm to recover sparse signals from compressed measurements, orthogonal matching pursuit (OMP) algorithm has received much attention in recent years. In this paper, we introduce an extension of the OMP 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 $N$ indices are identified per iteration. Owing to the selection of multiple ''correct'' indices, the gOMP algorithm is finished with much smaller number of iterations when 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 $\delta_{NK} < \frac{\sqrt{N}}{\sqrt{K} + 3 \sqrt{N}}$. 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.
 Publication:

IEEE Transactions on Signal Processing
 Pub Date:
 December 2012
 DOI:
 10.1109/TSP.2012.2218810
 arXiv:
 arXiv:1111.6664
 Bibcode:
 2012ITSP...60.6202W
 Keywords:

 Computer Science  Information Theory
 EPrint:
 IEEE Trans. Signal Process., vol. 60, no. 12, pp. 62026216, Dec. 2012