Source Estimation in Noisy Sparse Component Analysis

In this paper, a new algorithm for sparse component analysis (SCA) in the noisy underdetermined case (i.e., with more sources than sensors) is presented. The solution obtained by the proposed algorithm is compared to the minimum - norm solution achieved by Linear Programming (LP). Simulation results show that the proposed algorithm is approximately 10 dB better than the LP method with respect to the quality of the estimated sources. It is due to optimality of our solution (in the MAP sense) for source recovery in noisy underdetermined sparse component analysis in the case of spiky model for sparse sources and Gaussian noise.