A modified spectral conjugate gradient projection method for signal recovery

In this paper, signal recovery problems are first reformulated as a nonlinear monotone system of equations such that the modified spectral conjugate gradient projection method proposed by Wan et al. can be extended to solve the signal recovery problems. In view of the equations' analytic properties, an improved projection-based derivative-free algorithm (IPBDF) is developed. Compared with the similar algorithms available in the literature, an advantage of IPBDF is that the search direction is always sufficiently descent as well as being close to the quasi-Newton direction, without requirement of computing the Jacobian matrix. Then, IPBDF is applied into solving a number of test problems for reconstruction of sparse signals and blurred images. Numerical results indicate that the proposed method either can recover signals in less CPU time or can reconstruct the images with higher quality than the other similar ones.