University of Oulu

Hauptmann A., Öktem O., Schönlieb C. (2021) Image Reconstruction in Dynamic Inverse Problems with Temporal Models. In: Chen K., Schönlieb CB., Tai XC., Younces L. (eds) Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging. Springer, Cham.

Image reconstruction in dynamic inverse problems with temporal models

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Author: Hauptmann, Andreas1,2; Öktem, Ozan3,4; Schönlieb, Carola5
Organizations: 1University of Oulu, Research Unit of Mathematical Sciences, Oulu, Finland
2University College London, Department of Computer Science, London, United Kingdom
3Department of Mathematics, KTH - Royal Institute of Technology, Stockholm, Sweden
4Department of Information Technology, Division of Scientific Computing, Uppsala University, Uppsala, Sweden
5Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge UK
Format: article
Version: accepted version
Access: embargoed
Persistent link:
Language: English
Published: Springer, 2021
Publish Date: 2023-12-08


This paper surveys variational approaches for image reconstruction in dynamic inverse problems. Emphasis is on variational methods that rely on parametrized temporal models. These are encoded here as diffeomorphic deformations with time-dependent parameters or as motion-constrained reconstructions where the motion model is given by a differential equation. The survey also includes recent developments 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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ISBN: 978-3-030-03009-4
Pages: 1 - 31
DOI: 10.1007/978-3-030-03009-4_83-1
Host publication: Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging
Host publication editor: Chen, Ke
Schönlieb, Carola-Bibiane
Tai, Xue-Cheng
Younces, Laurent
Type of Publication: A3 Book chapter
Field of Science: 111 Mathematics
113 Computer and information sciences
Copyright information: © 2021 Springer. This is a post-peer-review, pre-copyedit version of an article published in Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging. The final authenticated version is available online at