Sparse Signal Recovery from Fixed Low-Rank Subspace via Compressive Measurement

This paper designs and evaluates a variant of CoSaMP algorithm, for recovering the sparse signal s from the compressive measurement v = A(Uw+s) given a fixed low-rank subspace spanned by U. Instead of firstly recovering the full vector then separating the sparse part from the structured dense part, the proposed algorithm directly works on the compressive measurement to do the separation. We investigate the performance of the algorithm on both simulated data and video compressive sensing. The results show that for a fixed low-rank subspace and truly sparse signal the proposed algorithm could successfully recover the signal only from a few compressive sensing (CS) measurements, and it performs better than ordinary CoSaMP when the sparse signal is corrupted by additional Gaussian noise.