Magnetic Particle Imaging is an emerging imaging modality through which it is possible to detect tracers containing superparamagnetic nanoparticles. The exposure of the particles to dynamic magnetic fields generates a non-linear response that is used to locate the particles and produce an image of their distribution. The bounding box that can be covered by a single scan curve depends on the strength of the gradients of the magnetic fields applied, which is limited due to the risk of causing peripheral nerve stimulation (PNS) in the patients. To address this issue, multiple scans are performed by practitioners. The scan data must be merged together to produce reconstructions of larger regions of interest. In this paper we propose a mathematical framework which generalizes the current multi-patch scanning by utilizing transformations. We show the flexibility of this framework in a variety of different scanning approaches. Moreover, we describe an iterative reconstruction algorithm, show its convergence to a minimizer and perform numerical experiments on simulated data.

翻译：磁粒子成像是一种新兴的成像方式，通过它能够检测含有超顺磁性纳米粒子的示踪剂。粒子受到动态磁场激发会产生非线性响应，该响应可用于定位粒子并生成其分布图像。单次扫描曲线所能覆盖的边界框取决于所施加磁场的梯度强度，而该强度因可能引发患者外周神经刺激而受到限制。为解决此问题，操作人员需执行多次扫描，并将扫描数据合并以重建更大感兴趣区域。本文提出一个利用变换来推广当前多斑块扫描的数学框架，通过多种不同扫描方法展示了该框架的灵活性。此外，我们描述了一种迭代重建算法，证明了其收敛到极小值点，并在模拟数据上进行了数值实验。