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

Convergence analysis on the alternating direction method of multipliers for the cosparse optimization problem