Work

A parameterized Schur complement preconditioner for linear system arising from additive HQ image restoration

Year: 2025

Type: article

Abstract: Image restoration is to estimate the clean image from the recorded image, it is a highly ill-posed inverse problem. Regularization method is an important approach for solving such problem, which can usually be achieved by minimizing a cost function consisting of a data-fidelity term and a regularization term. In this paper, we consider the additive half-quadratic (HQ) regularized method for image restoration problem, and utilize the Newton method to solve it. At each Newton iteration step, a system of linear equations with symmetric positive definite coefficient matrix arises. In order to solve the linear system efficiently, we design a parameterized approximation matrix of the Schur complement inverse matrix, and construct a block preconditioner with parameter correspondingly, according to the block triangular factorization of coefficient matrix and the form of its Schur complement, then the preconditioned conjugate gradient (PCG) method is applied to solve the linear system of equations. Spectral analyses of the preconditioned matrix are also given, numerical experimental results demonstrate the effectiveness of the proposed parameterized preconditioner for solving linear system arising from additive HQ image restoration problem.

Source: Results in Applied Mathematics

DOI: 10.1016/j.rinam.2025.100667

Authors: Peipei Zhao, Pengyu Zhang

Institution: Taiyuan Normal University

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,770

Funders: Program for Innovation Team Building at Institutions of Higher Education in Chongqing, Special Funds for the Basic Research and Development Program in the Central Non-profit Research Institutesof China