Heavy Ball based Hard Thresholding Algorithms for Multiple Measurement Vectors

In this paper, we present two heavy ball based hard thresholding algorithms aimed at recovering jointly sparse signals in multiple measurement vector (MMV) scenario, arising in compressed sensing. The proposed Simultaneous Heavy Ball based Iterative Hard Thresholding (SHBIHT) and Simultaneous Heavy Ball based Hard Thresholding Pursuit (SHBHTP) algorithms use heavy ball based acceleration technique, which uses the current estimate as well as the previous estimate in the gradient based update. By exploiting the MMV structure, we use a weighted momentum rather than a common momentum for each of the signals. In the first algorithm, hard thresholding is carried out on the gradient based update whereas the other algorithm requires solving a least squares problem (pursuit step) on top of the hard thresholded update. Theoretical analysis is carried out using the Restricted Isometry Property (RIP) and sufficient conditions for convergence are derived. It is observed through simulations that the proposed heavy ball based algorithms for MMV problem provide computational advantage in terms of total time required for convergence while performing at-par with existing algorithms in terms of recovery performance.