A Sharp Bound on RIC in Generalized Orthogonal Matching Pursuit

Abstract

Abstract. Generalized orthogonal matching pursuit (gOMP) algorithm has received much attention in recent years as a natural extension of orthogonal matching pursuit (OMP). It is used to recover sparse signals in compressive sensing. In this paper, a new bound is obtained for the exact reconstruction of every K-sparse signal via the gOMP algorithm in the noiseless case. at is, if the restricted isometry constant (RIC) δ N K+ of the sensing matrix A satis es δ N K+ < K N + , then the gOMP can perfectly recover every K-sparse signal x from y = Ax. Furthermore, the bound is proved to be sharp. In the noisy case, the above bound on RIC combining with an extra condition on the minimum magnitude of the nonzero components of K-sparse signals can guarantee that the gOMP selects all of support indices of the K-sparse signals.

A sharp recovery condition for block sparse signals by block orthogonal multi-matching pursuit

“…If N = 1, then the above condition (1.4) is a sharp sufficient condition for the recovery of block sparse signals by the BOMP [44]. When d i = 1 (i = 1, 2, · · · , l), the condition (1.4) ensures that the gOMP or OMMP stably recovers the sparse signal [41], [42] and is also sharp [41]. As N = 1 and d i = 1 (i = 1, 2, · · · , l), this condition (1.4) turns to be a sharp sufficient condition for sparse recovery through OMP [43].…”

Recovery of signals by a weighted $\ell_2/\ell_1$ minimization under arbitrary prior support information

“…In last decade, compressed sensing has been a fast growing field of research. A multitude of different recovery algorithms including the ℓ 1 minimization [6]- [12], [37], greedy algorithm [16,21,22,27,43,46], [38]- [40] and iterative threshold algorithm [3,4,23,24,25,33] have been used to recover the sparse signal x under a variety of different conditions on the sensing matrix A.…”

Analysis of the modified multiple OLS (mbm$^2$OLS) algorithm for sparse signal recovery with noise

“…当然, 为了改进 OMP 算法的重构性能, 已有文献提出了多种贪婪算法. 如 A*OMP [16] 、广义协 方差匹配追踪 (generalized covariance-assisted matching pursuit) [17] 和广义正交匹配追踪 (generalized OMP, gOMP) [18][19][20][21] 等. 最近, 在 mOLS 算法基础上, Mukhopadhyay 等 [22] [22] 算法 输入:…”