  In this paper, we develop a dual alternating direction method of multipliers
(ADMM) for an image decomposition model. In this model, an image is divided
into two meaningful components, i.e., a cartoon part and a texture part. The
optimization algorithm that we develop not only gives the cartoon part and the
texture part of an image but also gives the restored image (cartoon part +
texture part). We also present the global convergence and the local linear
convergence rate for the algorithm under some mild conditions. Numerical
experiments demonstrate the efficiency and robustness of the dual ADMM (dADMM).
Furthermore, we can obtain relatively higher signalto-noise ratio (SNR)
comparing to other algorithms. It shows that the choice of the algorithm is
also important even for the same model.
