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We adopt a maximum a posteriori (MAP) estimation based approach for recovering sparse signals from a small number of measurements formed by computing the inner products of the signal with rows of a matrix. We assume that each component of the sparse signal is independent and identically distributed (i.i.d) random variable drawn from a Gaussian mixture model. We then develop a suitable MAP formulation which results in an iterative algorithm. Simulations are performed to study the performance of the algorithm. We observe that our approach has a number of advantages over other sparse recovery techniques, including robustness to noise, increased performance with limited measurements and lower computation time.