Sparse signal recovery via alternating projection method

Sparse signal recovery has attracted great attention in recent years with the development of compressive sensing. Alternating projection method is employed for this kind of recovery in this paper. The method is intuitive and can be easily implemented. The performance of the method is almost the same as that of basis pursuit (BP), while the computational cost is much lower. Restricted isometry constants and singular values of the coefficient matrix are utilized for the theoretical analyses of the method. Two sufficient conditions for the convergence and two estimates of the convergence rate are given. Numerical experiments are presented to show the performance of the method.