Total variation regularization for manifold-valued data

Andreas Weinmann; Laurent Demaret; Martin Storath

doi:10.1137/130951075

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arXiv · 1312.7710

Total variation regularization for manifold-valued data

Andreas Weinmann·Laurent Demaret·Martin Storath

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Abstract

We consider total variation minimization for manifold valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with $\ell^p$-type data terms in the manifold case. These algorithms are based on iterative geodesic averaging which makes them easily applicable to a large class of data manifolds. As an application, we consider denoising images which take their values in a manifold. We apply our algorithms to diffusion tensor images, interferometric SAR images as well as sphere and cylinder valued images. For the class of Cartan-Hadamard manifolds (which includes the data space in diffusion tensor imaging) we show the convergence of the proposed TV minimizing algorithms to a global minimizer.

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BibTeX RIS

Andreas Weinmann, Laurent Demaret, Martin Storath. 2013-12-30. Total variation regularization for manifold-valued data. https://doi.org/10.1137/130951075

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