Alternating Direction Method of Multipliers for Linear Inverse Problems

In this paper we propose an iterative method using alternating direction method of multipliers (ADMM) strategy to solve linear inverse problems in Hilbert spaces with a general convex penalty term. When the data is given exactly, we give a convergence analysis of our ADMM algorithm without assuming the existence of a Lagrange multiplier. In case the data contains noise, we show that our method is a regularization method as long as it is terminated by a suitable stopping rule. Various numerical simulations are performed to test the efficiency of the method.