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On the degree of ill-posedness of multi-dimensional magnetic particle imaging

Kluth, T; Jin, B; Li, G; (2018) On the degree of ill-posedness of multi-dimensional magnetic particle imaging. Inverse Problems , 34 (9) , Article 095006. 10.1088/1361-6420/aad015. Green open access

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Abstract

Magnetic particle imaging is an imaging modality of relatively recent origin, and it exploits the nonlinear magnetization response for reconstructing the concentration of nanoparticles. Since being first invented in 2005, it has received much interest in the literature. In this work, we study one prototypical mathematical model in multi-dimension, i.e. the equilibrium model, which formulates the problem as a linear Fredholm integral equation of the first kind. We analyze the degree of ill-posedness of the associated linear integral operator by means of the singular value decay estimate for Sobolev smooth bivariate functions, and discuss the influence of various experimental parameters on the decay rate. In particular, applied magnetic fields with a field free point and a field free line are distinguished. The study is complemented with extensive numerical experiments

Type: Article
Title: On the degree of ill-posedness of multi-dimensional magnetic particle imaging
Open access status: An open access version is available from UCL Discovery
DOI: 10.1088/1361-6420/aad015
Publisher version: https://doi.org/10.1088/1361-6420/aad015
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: magnetic particle imaging, degree of ill-posedness, equilibrium model, singular value decay, Sobolev smooth bivariate functions
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10052335
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