Cyclic data arise in various image and signal processing ap- plications such as interferometric synthetic aperture radar, electroen- cephalogram 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 cy- cles 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 perfor- mance of our algorithm.
['Ronny Bergmann', 'Andreas Weinmann']
Inpainting of Cyclic Data using First and Second Order Differences