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

TL;DR

This paper introduces second order TV-type algorithms for denoising and inpainting of higher-dimensional data combining cyclic and linear components, relevant for nonlinear color spaces and optical flow fields.

Contribution

It develops novel algorithms for second order TV problems tailored to nonlinear cyclic and linear data spaces, with convergence analysis and practical applications.

Findings

Algorithms effectively denoise and inpaint complex data.

Convergence of the proposed methods is theoretically established.

Applications demonstrate improved results on real-world data.

Abstract

In this paper we consider denoising and inpainting problems for higher dimensional combined cyclic and linear space valued data. These kind 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 (TV) type problems for denoising, inpainting as well as the combination of both. We provide a convergence analysis and we apply the algorithms to concrete problems.