Jiao, YulingJin, QinianLu, XiliangWang, Weijie2017-02-172017-02-170266-5611http://hdl.handle.net/1885/112460We 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.Y Jiao is partially supported by National Natural Science Foundation of China No. 11501579 and No. 2016CFB486; Q Jin is partially supported by the discovery project grant DP150102345 of Australian Research Council; and X Lu is partially supported by the National Natural Science Foundation of China No. 11471253 and No. 91630313.application/pdf© 2017 IOP Publishing Ltd201710.1088/1361-6420/33/2/025004