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

  • Chang-Ock Lee
  • Jongho ParkEmail author
Article
  • 18 Downloads

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.

Keywords

Total variation Lagrange multipliers Domain decomposition Parallel computation Image processing 

Mathematics Subject Classification

65N30 65N55 65Y05 68U10 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesKAISTDaejeonKorea

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