Diagonal Variable Matrix Method in Solving Inverse Problem in Image Processing

¹ Centre for Mathematical Sciences, Universiti Tunku Abdul Rahman, Malaysia
² Centre for Advanced and Sustainable Materials Research, Universiti Tunku Abdul Rahman, Malaysia
³ Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Malaysia

^* e-mail: simhs@utar.edu.my

Abstract

In this paper, we introduce a new gradient method called the Diagonal Variable Matrix method. Our proposed method is aimed to minimize H_k+1 over the log-determinant norm subject to weak secant relation. The derived diagonal matrix H_k+1 is the approximation of the inverse Hessian matrix, which enables the calculation of the search direction, d_k = −H_k+1g_k, where g_k denotes the gradient of the objective function. The proposed method is coupled with the backtracking Armijo line search. The proposed method is specifically designed to reduce the number of iterations and training duration, particularly in the context of solving large-dimensional problems. Finally, as a practical illustration, the proposed method is applied to solve the image deblurring problem, and its performance is analyzed using image quality metrics. The results demonstrate that the proposed method outperforms various conjugate gradient (CG) methods and multiple damping gradient method.