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In this paper, we consider a primal-dual domain decomposition method fortotal variation regularized problems appearing in mathematical imageprocessing. The model problem is transformed into an equivalent constrainedminimization problem by tearing-and-interconnecting domain decomposition. Then,the continuity constraints on the subdomain interfaces are treated byintroducing Lagrange multipliers. The resulting saddle point problem is solvedby the first order primal-dual algorithm. We apply the proposed method to imagedenoising, inpainting, and segmentation problems with either $L^2$-fidelity or$L^1$-fidelity. Numerical results show that the proposed method outperforms theexisting state-of-the-art methods.

A Finite Element Nonoverlapping Domain Decomposition Method with Lagrange Multipliers for the Dual Total Variation Minimizations