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Finding sparse solutions to under-determined systems of linear equations has recently got a plethora of applications in the field of signal processing. It is assumed that an ideal noiseless signal has sufficiently sparse representation. But in practice a noisy version of such signal can only be observed. In this paper, we propose a new initialization scheme and a stopping condition for the recently introduced Bayesian Pursuit Algorithm (BPA) for sparse representation in the noisy settings. Experimental results show that the proposed modifications lead to a better quality of sparse solution and faster rate of convergence over the existing BPA especially at low noise levels.