Simplified analysis of orthogonal matching pursuit performance in compressed sensing

We perform theoretical analysis of compressed sensing with Orthogonal Matching Pursuit (OMP) recovery. In the analysis we utilize an OMP simplification where the estimation step in each iteration is assumed to be perfect. We consider the case when the noise is AWGN, the signal is sparse with equal energy nonzero components and the measurement matrix has i.i.d. Gaussian entries. We estimate the probability of perfect support reconstruction. We then extend the analysis to the Multiple Measurement Vector case. The analysis sheds new light on the compressed sensing recovery and gives a close estimate of the OMP reconstruction performance.