Recent Advances in Denoising of Manifold-Valued Images
For researchers working on manifold-valued image processing, this is a survey of existing methods, not a novel contribution.
This chapter reviews recent advances in denoising manifold-valued images using variational models and minimization algorithms, highlighting software toolboxes like Manopt and MVIRT. No concrete numerical results are provided.
Modern signal and image acquisition systems are able to capture data that is no longer real-valued, but may take values on a manifold. However, whenever measurements are taken, no matter whether manifold-valued or not, there occur tiny inaccuracies, which result in noisy data. In this chapter, we review recent advances in denoising of manifold-valued signals and images, where we restrict our attention to variational models and appropriate minimization algorithms. The algorithms are either classical as the subgradient algorithm or generalizations of the half-quadratic minimization method, the cyclic proximal point algorithm, and the Douglas-Rachford algorithm to manifolds. An important aspect when dealing with real-world data is the practical implementation. Here several groups provide software and toolboxes as the Manifold Optimization (Manopt) package and the manifold-valued image restoration toolbox (MVIRT).