Coherence Based Sufficient Condition for Support Recovery Using Generalized Orthogonal Matching Pursuit

Abstract

In an underdetermined system, compressive sensing can be used to recover the support vector. Greedy algorithms will recover the support vector indices in an iterative manner. Generalized Orthogonal Matching Pursuit (GOMP) is the generalized form of the Orthogonal Matching Pursuit (OMP) algorithm where a number of indices selected per iteration will be greater than or equal to 1. To recover the support vector of unknown signal ‘x’ from the compressed measurements, the restricted isometric property should be satisfied as a sufficient condition. Finding the restricted isometric constant is a non-deterministic polynomial-time hardness problem due to that the coherence of the sensing matrix can be used to derive the sufficient condition for support recovery. In this paper a sufficient condition based on the coherence parameter to recover the support vector indices of an unknown sparse signal ‘x’ using GOMP has been derived. The derived sufficient condition will recover support vectors of P-sparse signal within ‘P’ iterations. The recovery guarantee for GOMP is less restrictive, and applies to OMP when the number of selection elements equals one. Simulation shows the superior performance of the GOMP algorithm compared with other greedy algorithms.