Novel Hybrid Conjugate Gradient Technique Based on the Newton Direction Applied to Image Restoration Problem

We introduce a novel hybrid conjugate gradient method for unconstrained optimization, combining the AlBayati-AlAssady and Rivaie-Mustafa-Ismail-Leong approaches, where the convex combination parameter is determined to ensure alignment between the conjugate gradient direction and the Newton direction. Through rigorous theoretical analysis, we establish that the proposed method guarantees sufficient descent properties and achieves global convergence under the strong Wolfe line search conditions.Numerical experiments on image restoration confirm that our method exhibits competitive or superior performance compared to the Fletcher-Reeves algorithm, especially when processing images with higher noise levels.