A Map Framework for Support Recovery of Sparse Signals Using Orthogonal Least Squares

We propose the maximum a posteriori accelerated orthogonal least-squares (MAP-AOLS) algorithm, a novel greedy scheme for accurate reconstruction of a sparse binary signal from its compressed measurements. The algorithm leverages the distributions of the sensing matrix, signal, and noise to find a support set that is optimal in the maximum a posteriori (MAP) sense. This stands in contrast to existing greedy orthogonal least squares (OLS) methods that perform reconstruction without fully exploiting all the available statistical information. In each iteration of the proposed algorithm, the distributions of the sensing matrix, noise, and signal with respect to the support set are used to identify and select the column of the sensing matrix with the largest likelihood ratio of the alternate and null hypotheses. Our extensive simulations demonstrate superiority of MAP-AOLS over existing greedy algorithms with only a minor increase in computational costs. Moreover, the proposed scheme has significantly lower computational complexity than traditional OLS.