SPARSE RECOVERY OF MULTIPLE MEASUREMENT VECTORS IN IMPULSIVE NOISE: A SMOOTH BLOCK SUCCESSIVE MINIMIZATION ALGORITHM

This paper considers the sparse recovery problem of multiple measurement vector (MMV) model corrupted in impulsive noise. To ensure outlier-robust sparse recovery, we formulate an MMV problem that includes the generalized l(p)-norm (1 <p <2) divergence data-fidelity term added to the l(2,0) joint sparsity-promoting regularizer. The l(2,0) joint sparse penalty, however, is non-continuous and hence non-differentiable, which inevitably raises difficulty in optimization when using a gradient-based method. To address this, we build a smooth approximation for the l(2,0)-based sparse metric via the log-sum based sparse-encouraging surrogate function. Then, we propose a block successive upper-bound minimization algorithm for the smooth MMV problem by solving a series of subproblems based on the block coordinate descent (BCD) method. Furthermore, local convergence of the proposed algorithm to a stationary point of the smooth problem is proved. Experiments demonstrate its efficiency and robust recovery performance for suppressing impulsive noise.