334. An Optimal Transport-based approach to Total-Variation regularization for the Diffusion MRI problem
Invited abstract in session FD-7: Optimal Transport for Machine Learning and Inverse Problems, stream Optimization for Inverse Problems and Machine Learning.
Friday, 14:10 - 15:50Room: M:I
Authors (first author is the speaker)
| 1. | Rodolfo Assereto
|
| Department of Mathematics and Scientific Computing, University of Graz |
Abstract
Diffusion Magnetic Resonance Imaging (dMRI) is a non-invasive imaging technique that draws structural information from the interaction between water molecules and biological tissues. Common ways of tackling the derived inverse problem include, among others, Diffusion Tensor Imaging (DTI), High Angular Resolution Diffusion Imaging (HARDI) and Diffusion Spectrum Imaging (DSI). However, these methods are structurally unable to recover the full diffusion distribution, only providing partial information about particle displacement. In our work, we introduce a Total-Variation (TV) regularization defined from an optimal transport perspective using 1-Wasserstein distances. Such a formulation produces a variational problem that can be handled by well-known algorithms enjoying good convergence properties, such as the primal-dual proximal method by Chambolle and Pock. It allows for the reconstruction of the complete diffusion spectrum from measured undersampled k/q space data.
Keywords
- Convex and non-smooth optimization
- Optimization in industry, business and finance
Status: accepted
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