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

Reips L, Burger M, Engbers R (2018)

Publication Status: Published

Publication Type: Journal article

Publication year: 2018

Journal

Journal of Inverse and Ill-posed Problems De Gruyter

Publisher: WALTER DE GRUYTER GMBH

Book Volume: 26

Pages Range: 185-200

Journal Issue: 2

DOI: 10.1515/jiip-2015-0016

Abstract

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.

Authors with CRIS profile

Martin Burger Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

Westfälische Wilhelms-Universität (WWU) Münster DE Germany (DE) Federal University of Santa Catarina / Universidade Federal de Santa Catarina (UFSC) BR Brazil (BR)

How to cite

APA:

Reips, L., Burger, M., & Engbers, R. (2018). Towards dynamic PET reconstruction under flow conditions: Parameter identification in a PDE model. Journal of Inverse and Ill-posed Problems, 26(2), 185-200. https://dx.doi.org/10.1515/jiip-2015-0016

MLA:

Reips, Louise, Martin Burger, and Ralf Engbers. "Towards dynamic PET reconstruction under flow conditions: Parameter identification in a PDE model." Journal of Inverse and Ill-posed Problems 26.2 (2018): 185-200.

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