Signal recovery with convex constrained nonlinear monotone equations through conjugate gradient hybrid approach

Abstract

In recent years there is a vast application of conjugate gradient methods to restore the disturbed signals in compressive sensing. This research aims at developing a scheme, which is more effective for restoring disturbed signals than the popular PCG method (Liu & Li, 2015). To realize the desired goal, a new conjugate gradient approach combined with the projection scheme of Solodov and Svaiter [Kluwer Academic Publishers, pp. 355-369(1998)] for solving monotone nonlinear equations with convex constraints is presented. The main idea employed in this algorithm is to approximate the Jacobian matrix via acceleration parameter in order to propose an effective conjugate gradient parameter. In addition, the step length is calculated using inexact line search technique. The proposed approach is proved to converge globally under some mild conditions . The numerical experiment, depicts the efficacy our method. Apart from generating search directions that are vital for global convergence, a significant contribution of the new method lies in its applications to solve the ℓ1-norm regularization problem in signal recovery. Experiments with the scheme and the effective PCG solver, existing in the previous literature, shows that the new method provides much better results.