Improved Bounds on RIP for Generalized Orthogonal Matching Pursuit

Generalized Orthogonal Matching Pursuit (gOMP) is a natural extension of OMP algorithm where unlike OMP, it may select N(≥ 1) atoms in each iteration. In this paper, we demonstrate that gOMP can successfully reconstruct a K-sparse signal from a compressed measurement y = Φx by K iteration if the sensing matrix Φ satisfies restricted isometry property (RIP) of order NK where δNK < √ N √ K+2 √ N . Our bound offers an improvement over the very recent result shown in [1]. Moreover, we present another bound for gOMP of order NK + 1 with δNK+1 < √ N √ K+ √ N which exactly relates to the near optimal bound of δK+1 < 1 √ K+1 for OMP (N = 1) as shown in [2].