Diffusion Tensor Regularization with Metric Double Integrals
| Autor: | Frischauf, Leon, Melching, Melanie, Scherzer, Otmar |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this paper we propose a variational regularization method for denoising and inpainting of diffusion tensor magnetic resonance images. We consider these images as manifold-valued Sobolev functions, i.e. in an infinite dimensional setting, which are defined appropriately. The regularization functionals are defined as double integrals, which are equivalent to Sobolev semi-norms in the Euclidean setting. We extend the analysis of Ciak, Melching and Scherzer "Regularization with Metric Double Integrals of Functions with Values in a Set of Vectors", in: Journal of Mathematical Imaging and Vision (2019) concerning stability and convergence of the variational regularization methods by a uniqueness result, apply them to diffusion tensor processing, and validate our model in numerical examples with synthetic and real data. Comment: 10 figures |
| Databáze: | arXiv |
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