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arXiv · 2004.01585

Diffusion Tensor Regularization with Metric Double Integrals

Leon Frischauf·Melanie Melching·Otmar Scherzer
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Abstract

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.

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Leon Frischauf, Melanie Melching, Otmar Scherzer. 2020-04-03. Diffusion Tensor Regularization with Metric Double Integrals. https://arxiv.org/abs/2004.01585

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