A key component of conjugate gradient (CG) algorithms is the directions used in the CG approach. Because of their low memory requirements, these directed methods have proven effective in various applications, especially image processing. For this study, we have developed a new conjugate gradient coefficient based on the well-known quadratic model, that will accelerate the convergence and increase the accuracy of the CG approach. Because the new method uses the second order curvature and provides improved direction. So, the global convergence and critical descent characteristics of the final algorithm provide reliable performance in a range of scenarios. The results of extensive numerical testing on picture restoration show that the new formulae perform noticeably better than the current techniques. In particular, the performance of the suggested conjugate gradient (CG) scheme has been better than that of the conventional Fletcher-Reeves (FR) conjugate gradient approach. This development is a key tool in the field of computational imaging and optimization as it not only increases computing efficiency but also boosts picture restoration, image quality and its' accuracy.
Hassan et al. (Mon,) studied this question.