An Armijo-Type Hard Thresholding Algorithm for Joint Sparse Recovery

Joint sparse recovery (JSR) in compressed sensing simultaneously recovers sparse signals with a common sparsity structure from their multiple measurement vectors obtained through a common sensing matrix. In this paper, we present an Armijo-type hard thresholding (AHT) algorithm for joint sparse recovery. Under the restricted isometry property (RIP), we show that the AHT can converge to a local minimizer of the optimization problem for JSR. Furthermore, we compute the AHT convergence rate with the above conditions. Numerical experiments show the good performance of the new algorithm for JSR.