A generalized matrix Krylov subspace method for TV regularization

TL;DR

This paper introduces a novel matrix Krylov subspace method combined with augmented Lagrangian and ADM techniques to efficiently solve TV regularization problems involving blurred and noisy images.

Contribution

It develops a generalized matrix Krylov subspace approach integrated with augmented Lagrangian and ADM methods for improved TV regularization solutions.

Findings

Efficiently solves TV regularization with blur and noise.

Uses generalized matrix Krylov subspaces for sub-problem solutions.

Demonstrates improved convergence and accuracy.

Abstract

This paper presents an efficient algorithm to solve total variation (TV) regularizations of images contaminated by a both blur and noise. The unconstrained structure of the problem suggests that one can solve a constrained optimization problem by transforming the original unconstrained minimization problem to an equivalent constrained minimization one. An augmented Lagrangian method is developed to handle the constraints when the model is given with matrix variables, and an alternating direction method (ADM) is used to iteratively find solutions. The solutions of some sub-problems are belonging to subspaces generated by application of successive orthogonal projections onto a class of generalized matrix Krylov subspaces of increasing dimension.