Adaptive forward-backward orthogonal matching pursuit for compressed sensing

In this paper we propose a novel iterative greedy algorithm for solving under-determined linear system of equations y = Ax when the solution vector x is known a priori to be sparse. The proposed algorithm falls into the general category of two stage thresholding (TST) algorithms. The proposed algorithm follows an iterative procedure to estimate the support of the sparse solution vector in a dynamic way. Therefore, it has the capability of correcting any indices of the estimated support that were erroneously incorporated in early stages. The proposed algorithm depends on a parameter a called the forward step-size. In this paper we propose an approach for computing the value of a adaptively in each iteration. Following this approach, the simulation results show that the proposed algorithm outperforms state of the art algorithms used for solving the same problem.