Mathematical analysis of the 1D model and reconstruction schemes for magnetic particle imaging

被引：10

作者：

Erb, W. ^{[1
]}

Weinmann, A. ^{[2
,3
]}

Ahlborg, M. ^{[4
]}

Brandt, C. ^{[5
]}

Bringout, G. ^{[4
]}

Buzug, T. M. ^{[4
]}

Frikel, J. ^{[6
]}

Kaethner, C. ^{[4
]}

Knopp, T. ^{[7
,8
]}

Maerz, T. ^{[2
]}

Moeddel, M. ^{[7
,8
]}

Storath, M. ^{[9
]}

Weber, A. ^{[10
]}

机构：

[1] Univ Hawaii Manoa, Honolulu, HI 96822 USA

[2] Darmstadt Univ Appl Sci, Darmstadt, Germany

[3] Helmholtz Ctr Munich, Munich, Germany

[4] Univ Lubeck, Lubeck, Germany

[5] Univ Hamburg, Hamburg, Germany

[6] Ostbayer Tech Hsch Regensburg, Regensburg, Germany

[7] Univ Klinikum Hamburg Eppendorf, Hamburg, Germany

[8] Tech Univ Hamburg, Hamburg, Germany

[9] Heidelberg Univ, Heidelberg, Germany

[10] Bruker BioSpin MRI GmbH, Ettlingen, Germany

来源：

INVERSE PROBLEMS | 2018年 / 34卷 / 05期

关键词：

magnetic particle imaging; model-based reconstruction; reconstruction operator; inverse problems; ill-posedness; RESOLUTION; INTERPOLATION; FORMULATION; RELAXATION; NODES; MPI; 2D;

D O I：

10.1088/1361-6420/aab8d1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Magnetic particle imaging (MPI) is a promising new in vivo medical imaging modality in which distributions of super-paramagnetic nanoparticles are tracked based on their response in an applied magnetic field. In this paper we provide a mathematical analysis of the modeled MPI operator in the univariate situation. We provide a Hilbert space setup, in which the MPI operator is decomposed into simple building blocks and in which these building blocks are analyzed with respect to their mathematical properties. In turn, we obtain an analysis of the MPI forward operator and, in particular, of its ill-posedness properties. We further get that the singular values of the MPI core operator decrease exponentially. We complement our analytic results by some numerical studies which, in particular, suggest a rapid decay of the singular values of the MPI operator.

引用

页数：21

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[3]

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[4]

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