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Image Reconstruction in Dynamic Inverse Problems with Temporal Models

In: Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Author

Listed:
  • Andreas Hauptmann

    (University of Oulu, Research Unit of Mathematical Sciences
    University College London, Department of Computer Science)

  • Ozan Öktem

    (Uppsala University, Department of Information Technology, Division of Scientific Computing
    KTH – Royal Institute of Technology, Department of Mathematics)

  • Carola Schönlieb

    (University of Cambridge, Department of Applied Mathematics and Theoretical Physics)

Abstract

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.

Suggested Citation

  • Andreas Hauptmann & Ozan Öktem & Carola Schönlieb, 2023. "Image Reconstruction in Dynamic Inverse Problems with Temporal Models," Springer Books, in: Ke Chen & Carola-Bibiane Schönlieb & Xue-Cheng Tai & Laurent Younes (ed.), Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, chapter 48, pages 1707-1737, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-98661-2_83
    DOI: 10.1007/978-3-030-98661-2_83
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