Diagonal Variable Matrix Method in Solving Inverse Problem in Image Processing

Abstract

In this paper, we introduce a new gradient method called the Diagonal Variable Matrix method. Our proposed method is aimed to minimize Hk+1 over the log-determinant norm subject to weak secant relation. The derived diagonal matrix Hk+1 is the approximation of the inverse Hessian matrix, which enables the calculation of the search direction, dk = −Hk+1gk, where gk 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.