A Novel Class of Hybrid Conjugate Gradient Methods for Unconstrained Optimization with Applications to Image Denoising

This paper presents a new hybrid conjugate gradient (CG) method for solving large-scale unconstrained optimization problems where classical CG algorithms may not perform well. This new method integrates four classical algorithms, namely, Liu and Storey, Fletcher and Reeves, Dai and Yuan, and Polak, Ribiere, and Polyak, using a convex combination of CGs and an inexact line search based on strong Wolfe conditions, and adheres to the Dai-Liao conjugate condition to enhance convergence properties. The theoretical study established the conditions for sufficient descent and global convergence of the hybrid CG method. Numerical studies demonstrated that the proposed method significantly reduced the number of iterations and computational time, achieving superior evaluation efficiency compared with other CG methods. In particular, the effectiveness of the proposed algorithm is validated for image impulse denoising, where it can recover high-quality images while preserving significant features, implying its practical applicability to real-world signal and image processing problems.