A Second-Order TV-Type Approach for Inpainting and Denoising Higher Dimensional Combined Cyclic and Vector Space Data

作者：Bergmann Ronny^*; Weinmann Andreas

来源：Journal of Mathematical Imaging and Vision, 2016, 55(3): 401-427.

DOI：10.1007/s10851-015-0627-3

• Higher order total variation minimization
• Vector-valued TV
• Cyclic data
• Combined denoising and inpainting
• Cyclic proximal point algorithm

In this paper, we consider denoising and inpainting problems for higher dimensional combined cyclic and linear space-valued data. These kinds of data appear when dealing with nonlinear color spaces such as HSV, and they can be obtained by changing the space domain of, e.g., an optical flow field to polar coordinates. For such nonlinear data spaces, we develop algorithms for the solution of the corresponding second-order total variation-type problems for denoising, inpainting as well as the combination of both. We provide a convergence analysis and apply the algorithms to concrete problems.

• 出版日期2016-7