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arXiv · 1901.00682

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

Chang-Ock Lee·Jongho Park
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Abstract

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

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Chang-Ock Lee, Jongho Park. 2019-10-28. A Finite Element Nonoverlapping Domain Decomposition Method with Lagrange Multipliers for the Dual Total Variation Minimizations. https://doi.org/10.1007/s10915-019-01085-z

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