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Published in:
2015 | OriginalPaper | Chapter
Inpainting of Cyclic Data Using First and Second Order Differences
Authors : Ronny Bergmann, Andreas Weinmann
Published in: Energy Minimization Methods in Computer Vision and Pattern Recognition
Publisher: Springer International Publishing
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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.