On the degree of ill-posedness of multi-dimensional magnetic particle imaging
On the degree of ill-posedness of multi-dimensional magnetic particle imaging
View/Date of Publication
12.2017Publisher
Institut für Numerische Simulation (INS)Publisher Location
BonnMetadata
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Citable Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11827
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 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. 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.
Subjects
magnetic particle imaging, degree of ill-posedness, equilibrium model, singular value decay, Sobolev smooth bivariate functions
Classification (DDC)
510 Mathematik 518 Numerische AnalysisFirst Publication
https://ins.uni-bonn.de/publication/preprintsRelated Publications
https://doi.org/10.1088/1361-6420/aad015Part of Series
INS Preprints ; 1718Kluth, Tobias; Jin, Bangti; Li, Guanglian: On the degree of ill-posedness of multi-dimensional magnetic particle imaging. In: INS Preprints, 1718.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11827
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11827
@unpublished{handle:20.500.11811/11827,
author = {{Tobias Kluth} and {Bangti Jin} and {Guanglian Li}},
title = {On the degree of ill-posedness of multi-dimensional magnetic particle imaging},
publisher = {Institut für Numerische Simulation (INS)},
year = 2017,
month = dec,
INS Preprints},
volume = 1718,
note = {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 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. 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.},
url = {https://hdl.handle.net/20.500.11811/11827}
}
author = {{Tobias Kluth} and {Bangti Jin} and {Guanglian Li}},
title = {On the degree of ill-posedness of multi-dimensional magnetic particle imaging},
publisher = {Institut für Numerische Simulation (INS)},
year = 2017,
month = dec,
INS Preprints},
volume = 1718,
note = {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 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. 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.},
url = {https://hdl.handle.net/20.500.11811/11827}
}
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