一个应用于图像恢复问题的修正共轭梯度算法

doi:10.15960/j.cnki.issn.1007-6093.2026.01.015

Abstract

Abstract: It is well-known that, under the WWP (weak Wolfe-Powell) line search technique, the global convergence of the PRP conjugate gradient method for non-convex functions is still open. In this paper, a hybrid conjugate gradient method is proposed for large-scale unconstrained optimization problems. In this method, the modified BFGS method is mixed with the modified PRP conjugate gradient method, and the weak Wolfe-Powell line search technique is used to find the step size, and the search direction has the property of sufficient descent. Theoretically, the global convergence of nonconvex functions is ensured by assuming reasonable conditions. In numerical experiments, the parameter estimation of the Muskingum model reduces the amount of computation and storage, which illustrates the effectiveness of MPRP. In different noise situations, the MPRP is proved to be highly competitive by comparing the recovery of multiple images. In addition, the restoration of the image is more significant under the image of low impulse noise.

Key words: non-convex functions, PRP algorithm, weak Wolfe-Powell line search, global convergence, image recovery

CLC Number:

O221

LIU Cong, JIAN Ailun, YUAN Gonglin. A modified conjugate gradient algorithm with its applications in image recovery problems[J]. Operations Research Transactions, 2026, 30(1): 207-216.

References

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A modified conjugate gradient algorithm with its applications in image recovery problems

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