  From a dual perspective of the sparse representation model, Nam et al.
proposed the cosparse analysis model. In this paper, we aim to investigate the
convergence of the alternating direction method of multipliers (ADMM) for the
cosparse optimization problem. First, we examine the variational inequality
representation of the cosparse optimization problem by introducing auxiliary
variables. Second, ADMM is used to solve cosparse optimization problem.
Finally, by utilizing a tight frame with a uniform row norm and building upon
lemmas and the strict contraction theorem, we establish a worst-case
$\mathcal{O}(1/t)$ convergence rate in the ergodic sense.
