Randomized Simultaneous Hard Thresholding Pursuit Algorithm for Multiple Measurement Vectors

In this paper, we propose a new algorithm named Randomized Simultaneous Hard Thresholding Pursuit(RSHTP) for the multiple measurements vector (MMV) problem in compressed sensing. In the proposed algorithm, the gradient is calculated only with respect to few of the signals at each iteration that are chosen randomly. This reduces the computational cost which is significant when the problem size is large. A deterministic convergence analysis is carried out where we present theoretical guarantees using the restricted isometric property (RIP). Simulation studies show that the proposed algorithm enjoys at par performance even at a moderate rate of column selection in each iteration.