Image reconstruction in dynamic inverse problems with temporal models

2020/07/20 by Andreas Hauptmann, Hauptmann, Andreas, Ozan Öktem +3 · 1 citation
Medicine · Computer Science · Mathematics · #Medical Imaging Techniques and Applications #Medical Image Segmentation Techniques #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2007.10238

Abstract

The paper surveys variational approaches for image reconstruction in dynamic inverse problems. Emphasis is on methods that rely on parametrised temporal models. These are here encoded as diffeomorphic deformations with time dependent parameters, or as motion constrained reconstruction where the motion model is given by a partial differential equation. The survey also includes recent development in integrating deep learning for solving these computationally demanding variational methods. Examples are given for 2D dynamic tomography, but methods apply to general inverse problems.

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• Regularization for time-dependent inverse problems: Geometry of Lebesgue-Bochner spaces and algorithms

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