Fletcher-reeves Conjugate Gradient for Sparse Reconstruction: Application to image compressed sensing

GPSR-BB (Gradient Projection for Sparse Reconstruction) algorithm is a popular CS (compressed sensing) reconstruction method. lt performs well for questions which have sparse solution. This approach is originally developed in the context of unconstrained minimization of a smooth nonlinear function F, and it uses the search direction of the Quasi-Newton method. So its shortcomings is the same as the Quasi-Newton method. For some reasons, the Hessian matrix of F can´t be computed directlyit leads to a performance loss of the algorithm. Based on GPSR-BB approach, a new gradient projection methods called CGSR-FR (Conjugate Gradient for Sparse Reconstruction) is proposed in this paper. Simulation experiments show that CGSR-FR approache perform better than GPSR-BB approache in image compression sampling.