Inpainting of Cyclic Data Using First and Second Order Differences

  • Ronny Bergmann
  • Andreas Weinmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8932)


Cyclic data arise in various image and signal processing applications such as interferometric synthetic aperture radar, electroencephalogram data analysis, and color image restoration in HSV or LCh spaces. In this paper we introduce a variational inpainting model for cyclic data which utilizes our definition of absolute cyclic second order differences. Based on analytical expressions for the proximal mappings of these differences we propose a cyclic proximal point algorithm (CPPA) for minimizing the corresponding functional. We choose appropriate cycles to implement this algorithm in an efficient way. We further introduce a simple strategy to initialize the unknown inpainting region. Numerical results both for synthetic and real-world data demonstrate the performance of our algorithm.


Inpainting variational models with higher order differences cyclic data phase-valued data cyclic proximal point algorithm 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Ronny Bergmann
    • 1
  • Andreas Weinmann
    • 2
  1. 1.Department of MathematicsTechnische Universität KaiserslauternKaiserslauternGermany
  2. 2.Department of MathematicsTechnische Universität München and Fast Algorithms for Biomedical Imaging Group, Helmholtz-Zentrum MünchenMünchenGermany

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