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In this paper, we propose a new orthogonal matching pursuit algorithm calledquasi-OMP algorithm which greatly enhances the performance of classicalorthogonal matching pursuit (OMP) algorithm, at some cost of computationalcomplexity. We are able to show that under some sufficient conditions of mutualcoherence of the sensing matrix, the QOMP Algorithm succeeds in recovering thes-sparse signal vector x within s iterations where a total number of 2s columnsare selected under the both noiseless and noisy settings. In addition, we showthat for Gaussian sensing matrix, the norm of the residual of each iterationwill go to zero linearly depends on the size of the matrix with highprobability. The numerical experiments are demonstrated to show theeffectiveness of QOMP algorithm in recovering sparse solutions whichoutperforms the classic OMP and GOMP algorithm.

A Quasi-Orthogonal Matching Pursuit Algorithm for Compressive Sensing