Preconditioned alternating direction method of multipliers for inverse problems with constraints

Date

2017

Authors

Jiao, Yuling
Jin, Qinian
Lu, Xiliang
Wang, Weijie

Journal Title

Journal ISSN

Volume Title

Publisher

IOP Publishing

Abstract

We propose a preconditioned alternating direction method of multipliers (ADMM) to solve linear inverse problems in Hilbert spaces with constraints, where the feature of the sought solution under a linear transformation is captured by a possibly non-smooth convex function. During each iteration step, our method avoids solving large linear systems by choosing a suitable preconditioning operator. In case the data is given exactly, we prove the convergence of our preconditioned ADMM without assuming the existence of a Lagrange multiplier. In case the data is corrupted by noise, we propose a stopping rule using information on noise level and show that our preconditioned ADMM is a regularization method; we also propose a heuristic rule when the information on noise level is unavailable or unreliable and give its detailed analysis. Numerical examples are presented to test the performance of the proposed method.

Description

Keywords

Citation

Source

Inverse Problems

Type

Journal article

Book Title

Entity type

Access Statement

License Rights

DOI

10.1088/1361-6420/33/2/025004

Restricted until

2099-12-31