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Journal of Inverse and Ill-posed Problems

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Volume 26, Issue 2


Towards dynamic PET reconstruction under flow conditions: Parameter identification in a PDE model

Louise Reips
  • Corresponding author
  • Department of Mathematics, Universidade Federal de Santa Catarina,Campus Blumenau, CEP 89065-300 Blumenau-SC, Brazil
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/ Martin BurgerORCID iD: http://orcid.org/0000-0003-2619-2912 / Ralf Engbers
  • Institute for Computational and Applied Mathematics and Cells in Motion Cluster of Excellence, Westfälische Wilhelms-Universität (WWU) Münster, Einsteinstr. 62, 48149 Münster, Germany
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Published Online: 2017-08-12 | DOI: https://doi.org/10.1515/jiip-2015-0016


The aim of this paper is to discuss potential advances in PET kinetic models and direct reconstruction of kinetic parameters. As a prominent example we focus on a typical task in perfusion imaging and derive a system of transport-reaction-diffusion equations, which is able to include macroscopic flow properties in addition to the usual exchange between arteries, veins, and tissues. For this system we propose an inverse problem of estimating all relevant parameters from PET data. We interpret the parameter identification as a nonlinear inverse problem, for which we formulate and analyze variational regularization approaches. For the numerical solution we employ gradient-based methods and appropriate splitting methods, which are used to investigate some test cases.

Keywords: Parameter identification; dynamic PET; inverse problems; image processing; forward-backward splitting; reaction; diffusion; transport

MSC 2010: 35K57


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About the article

Received: 2015-02-02

Revised: 2017-04-11

Accepted: 2017-06-30

Published Online: 2017-08-12

Published in Print: 2018-04-01

This work was carried out when Louise Reips was with the Institute for Computational and Applied Mathematics, WWU Münster. Martin Burger and Ralf Engbers acknowledge partial support by the German Science Foundation (DFG) via SFB 656, Subproject B2, and Cells-in-Motion Cluster of Excellence (EXC 1003 – CiM), WWU Münster, Germany.

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 26, Issue 2, Pages 185–200, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2015-0016.

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