Image Deblurring Problems through Accelerated Hager-Zhang Projection Method for Convex Constrained Monotone Nonlinear Equations

Abstract

Many researchers have developed interest in finding new choices for the HagerZhang nonnegative parameter and developed schemes that generate descent search directions. In this paper, a conjugate gradient method with the projection technique of Solodov and Svaiter [Kluwer Academic Publishers, (1998), pp. 355-369] to solve constrained monotone nonlinear equations is presented. The proposed method is based on presenting a new value of the Hager-Zhang parameter θ. This is achieved by combining the conjugate gradient method with the Newton method approach. Moreover, to solve the large-scale problems, the Jacobian matrix is approximated via acceleration parameter. Under some mild conditions, the proposed method is proven to be globally convergent and numerical experiments conducted show the efficacy of the proposed method. In addition, the proposed method is successfully applied to handle the `1−norm regularization problem in image recovery, which exhibits a better result than the existing method in the previous literature.