Total Variation Regularization for Manifold-Valued Data

We consider total variation (TV) minimization for manifold-valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with l(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 and 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.


Published in:
Siam Journal On Imaging Sciences, 7, 4, 2226-2257
Year:
2014
Publisher:
Philadelphia, Siam Publications
ISSN:
1936-4954
Keywords:
Laboratories:




 Record created 2015-02-20, last modified 2018-03-17

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