The inverse problem of magnetorelaxometry imaging
The inverse problem of magnetorelaxometry imaging
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DOI：
10.1088/1361-6420/aadbbf
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发表时间：
2018-11-01
期刊：
影响因子：
2.1
通讯作者：
Burger, Martin
中科院分区：
文献类型：
--
作者：
Foecke, Janic;Baumgarten, Daniel;Burger, Martin
本文的目的是提供一个坚实的数学讨论的逆问题，磁弛豫成像（MRXI），目前开发的定量生物医学成像技术，使用磁性纳米粒子。我们提供了一个详细的讨论的数学建模的正问题，包括可能的方式来磁激活的粒子和测量其磁响应，导致严重不适定的线性逆问题。此外，我们制定了一个理想化的版本的反问题的无穷小的小激活线圈，这使得一个更详细的分析的唯一性issues.We提出了一个变分正则化的方法来计算稳定的近似的解决方案，并讨论其离散化和数值解。合成数据的结果和改进以前在实践中使用的方法证明。
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.