An Investigation on Semismooth Newton based Augmented Lagrangian Method for Image Restoration

TL;DR

This paper introduces semismooth Newton methods within an augmented Lagrangian framework to efficiently solve nonlinear subproblems in image restoration, providing convergence analysis and competitive algorithms.

Contribution

It develops novel semismooth Newton algorithms for augmented Lagrangian methods in image restoration, with proven convergence properties.

Findings

Algorithms demonstrate high efficiency in image restoration tasks.

The methods achieve global convergence and local linear convergence.

Results show competitive performance compared to existing techniques.

Abstract

Augmented Lagrangian method (also called as method of multipliers) is an important and powerful optimization method for lots of smooth or nonsmooth variational problems in modern signal processing, imaging, optimal control and so on. However, one usually needs to solve the coupled and nonlinear system together and simultaneously, which is very challenging. In this paper, we proposed several semismooth Newton methods to solve the nonlinear subproblems arising in image restoration, which leads to several highly efficient and competitive algorithms for imaging processing. With the analysis of the metric subregularities of the corresponding functions, we give both the global convergence and local linear convergence rate for the proposed augmented Lagrangian methods with semismooth Newton solvers.