A New Projection Type Algorithm for Compressive Sensing

Compressive sensing (CS) is to recover a sparse signal from an undetermined linear system, which has received considerable interest, and some customized iterative methods for solving CS have been proposed in recent years. In this paper, we further consider an algorithm for solving the CS. To this end, a new projection-type algorithm (PTA) is proposed to solve CS based on a new formulation of the problem, which needs only one projection onto the nonnegative quadrant and only one value of the mapping per iteration. Global convergence results of the new algorithm is established. Furthermore, we illustrate the efficiency of given algorithm through some numerical examples on sparse signal recovery.