Convergence of the Generalized Alternating Projection Algorithm for Compressive Sensing

The convergence of the generalized alternating projection (GAP) algorithm is studied in this paper to solve the compressive sensing problem y = Ax + n. By assuming that A Ats is invertible, we prove that GAP converges linearly within a certain range of step-size under the restricted isometry property (RIP) condition of delta_2K, where K is the sparsity of. The theoretical analysis is extended to the adaptively iterative thresholding (AIT) algorithms, for which the convergence rate is also derived based on delta_2K. We prove that, under the same conditions, the convergence rate of GAP is faster than AIT. Extensive simulation results verify the theoretical assertions.