Sparse signal reconstruction in compressive sensing via derivative-free iterative method

Finding sparse solutions to under-determined or ill-conditioned equations is a problem that usually arise in compressive sensing. In this article, a derivative-free iterative method is presented for recovering sparse signal in compressive sensing by approximating the solution to a convex constrained nonlinear equation. The proposed method is derived from the modified Polak-Ribiere-Polyak conjugate gradient method for unconstrained optimization. The global convergence is established under mild assumptions. Preliminary numerical results in recovering sparse signal are given to show that the proposed method is efficient.