Mathematical analysis of the 1D model and reconstruction schemes for magnetic particle imaging
Mathematical analysis of the 1D model and reconstruction schemes for magnetic particle imaging
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DOI：
10.1088/1361-6420/aab8d1
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发表时间：
2018-05-01
期刊：
影响因子：
2.1
通讯作者：
Weber, A.
中科院分区：
文献类型：
--
作者：
Erb, W.;Weinmann, A.;Weber, A.
磁粒子成像（MPI）是一种很有前途的新的体内医学成像模式，其中超顺磁性纳米粒子的分布基于它们在施加的磁场中的响应进行跟踪。在本文中，我们提供了一个数学分析的模型MPI运营商在单变量的情况下。我们提供了一个希尔伯特空间设置，其中MPI算子被分解成简单的积木，并在这些积木分析其数学性质。反过来，我们得到的MPI向前运营商的分析，特别是它的不适定性。我们进一步得到MPI核算子的奇异值呈指数下降。我们补充我们的分析结果的一些数值研究，特别是，建议快速衰减的MPI算子的奇异值。
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.