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. The scan data must be merged together to produce reconstructions of larger regions of interest. In this paper we propose a mathematical framework which can deal with rather general multi-patching scenarios including rigid transformations of the field of view (FoV), the specimen and of the scanner. We show the flexibility of this framework in a variety of different scanning scenarios. Moreover, we describe an iterative reconstruction algorithm that yields a reconstruction of the target distribution by minimizing a convex functional which includes positivity constraints and sparsity enforcing priors. We 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技术，通过该技术可以检测含有超顺磁性纳米颗粒的示踪剂。将粒子暴露于动态磁场中会产生非线性响应，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，而由于存在引起患者外周神经刺激的风险，该强度受到限制。为解决这一问题，需进行多次扫描。扫描数据必须合并在一起，以重建更大的感兴趣区域。本文提出了一种数学框架，能够处理较为通用的多区块扫描场景，包括对视野、样本及扫描仪进行刚性变换的情况。我们在多种不同的扫描场景中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，该算法通过最小化包含正性约束和稀疏性先验的凸泛函，得到目标分布的重建结果。我们证明了该算法收敛于极小值，并在模拟数据上进行了数值实验。