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

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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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Authors and Affiliations

  1. Department of Mathematical Sciences, KAIST, Daejeon, 34141, Korea

    Chang-Ock Lee & Jongho Park

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  1. Chang-Ock Lee
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  2. Jongho Park
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Correspondence to Jongho Park.

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The first author’s work was supported by NRF Grant funded by MSIT (NRF-2017R1A2B4011627) and the second author’s work was supported by NRF Grant funded by the Korean Government (NRF-2015-Global Ph.D. Fellowship Program)

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Lee, CO., Park, J. A Finite Element Nonoverlapping Domain Decomposition Method with Lagrange Multipliers for the Dual Total Variation Minimizations. J Sci Comput 81, 2331–2355 (2019). https://doi.org/10.1007/s10915-019-01085-z

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  • DOI: https://doi.org/10.1007/s10915-019-01085-z

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