Adaptive Step-size Iterative Algorithm for Sparse Signal Recovery

We develop the variational Bayesian plus Euclidean projection (VB-EP) algorithm for sparse signal recovery from compressed measurements. This algorithm is formulated as an iteratively alternating projection strategy. The first step projects the measurements/residuals to the signal level, which is implemented via a Bayesian model; the second step projects the results obtained in the first step to the ell_1-ball to impose sparsity. These two steps are performed iteratively until some criterion is satisfied. The algorithm can infer the step size with variational Bayesian approach in each iteration. We further derive a maximum likelihood estimator of the Bayesian model to speed up the inference with fixed step size. Simulation results verify the superior performance of the proposed algorithm.