  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 general convex penalty term. When the data is given
exactly, we give a convergence analysis of our ADMM algorithm without assuming
the existence of 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.
