A Convergent Algorithm for Compressive Sensing

ABSTRACT In this paper, we further consider an algorithm for solving the compressive sensing (CS). To this end, we firstly establish some equivalent reformulations of CS. Based on these, a new projection-type algorithm (PTA) is proposed for solving CS. Global convergence results of the new algorithm is established. Furthermore, we also prove that the method is sublinearly convergent. Finally, we show the efficiency of given algorithm via some numerical examples on sparse signal recovery. Keywords: Compressive sensing, projection-type algorithm, global convergence.