Image Noise Reduction and Solution of Unconstrained Minimization Problems via New Conjugate Gradient Methods

The conjugate gradient (CG) directions are among the important components of the CG algorithms. These directions have proven their effectiveness in many applications—more specifically, in image processing due to their low memory requirements. In this study, we derived a new conjugate gradient coefficient based on the famous quadratic model. The derived algorithm is distinguished by its global convergence and essential descent properties, ensuring robust performance across diverse scenarios. Extensive numerical testing on image restoration and unconstrained optimization problems have demonstrated that the new formulas significantly outperform existing methods. Specifically, the proposed conjugate gradient scheme has shown superior performance compared to the traditional Fletcher–Reeves (FR) conjugate gradient method. This advancement not only enhances computational efficiency on unconstrained optimization problems, but also improves the accuracy and quality of image restoration, making it a highly valuable tool in the field of computational imaging and optimization.