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In this paper we consider denoising and inpainting problems for higherdimensional combined cyclic and linear space valued data. These kind of dataappear when dealing with nonlinear color spaces such as HSV, and they can beobtained by changing the space domain of, e.g., an optical flow field to polarcoordinates. For such nonlinear data spaces, we develop algorithms for thesolution of the corresponding second order total variation (TV) type problemsfor denoising, inpainting as well as the combination of both. We provide aconvergence analysis and we apply the algorithms to concrete problems.

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