The inverse problem of magnetorelaxometry imaging

Föcke L, Baumgarten D, Burger M (2018)

Publication Status: Published

Publication Type: Journal article

Publication year: 2018

Journal

Inverse Problems Institute of Physics: Hybrid Open Access

Publisher: IOP PUBLISHING LTD

Book Volume: 34

Article Number: ARTN 115008

Journal Issue: 11

DOI: 10.1088/1361-6420/aadbbf

Abstract

The aim of this paper is to provide a solid mathematical discussion of the inverse problem in magnetorelaxometry imaging (MRXI), a currently developed technique for quantitative biomedical imaging using magnetic nanoparticles. We provide a detailed discussion of the mathematical modeling of the forward problems including possible ways to magnetically activate the particles and measure its magnetic response, leading to a severely ill-posed linear inverse problem. Moreover, we formulate an idealized version of the inverse problem for infinitesimal small activation coils, which allows for a more detailed analysis of uniqueness issues.We propose a variational regularization approach to compute stable approximations of the solution and discuss its discretization and numerical solution. Results on synthetic data are presented and improvements to methods used previously in practice arc demonstrated.

Authors with CRIS profile

Lea Föcke Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik) Martin Burger Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

UMIT - Private Universität für Gesundheitswissenschaften, Medizinische Informatik und Technik GmbH AT Austria (AT)

How to cite

APA:

Föcke, L., Baumgarten, D., & Burger, M. (2018). The inverse problem of magnetorelaxometry imaging. Inverse Problems, 34(11). https://doi.org/10.1088/1361-6420/aadbbf

MLA:

Föcke, Lea, Daniel Baumgarten, and Martin Burger. "The inverse problem of magnetorelaxometry imaging." Inverse Problems 34.11 (2018).

BibTeX: Download