Development, analysis and application of mathematical methods for Magnetic Particle Imaging (MathMPI)

磁颗粒成像（MPI）是一种新兴的成像方式，通过测量磁性纳米颗粒对外加磁场的非线性磁化响应来确定磁性纳米颗粒的空间分布。MPI提供了高动态空间和时间分辨率，与其他层析成像方法相比，它不使用任何电离辐射。这使得MPI成为一种非常有前途的生物医学诊断成像方式。该项目首次系统地研究了与MPI相关的数学问题。该网络的中心目标是开发、分析和应用数学方法来提高MPI的重建质量。特别是，针对MPI的具体需求，我们开发了详细的重建算法，分析和完善了基础MPI模型，并在实际生物医学数据上对新方法进行了数值测试。为了实现这些目标，该网络为来自不同科学领域的研究人员提供了一个跨学科的平台，包括应用数学、建模、图像处理、医学物理以及电气工程。在这个网络中组织的两次会议计划以学习小组的形式举行。这种形式特别适合跨学科的团队合作，产生协同作用，加强网络内的沟通。

Magnetic Particle Imaging (MPI) is an emerging imaging modality that determines the spatial distribution of magnetic nanoparticles by measuring the non-linear magnetization response of the particles to an applied magnetic field. MPI offers a high dynamic spatial and temporal resolution and, in contrast to other tomographic methods, it does not employ any ionizing radiation. This makes MPI a very promising imaging modality for biomedical diagnostics. This project addresses for the first time the systematic study of mathematical questions related to MPI. The central goal of this network is the development, analysis and application of mathematical methods to improve the reconstruction quality in MPI. In particular, taylored to the specific needs of MPI we develop elaborate reconstruction algorithms, analyze and refine the underlying MPI models and test the new methods numerically on real biomedical data. To achieve these goals this network provides an interdisciplinary platform for researchers from various scientific fields including applied mathematics, modeling, image processing, medical physics as well as electrical engineering. Two of the meetings organized in this network are planned in form of study groups. This format is particularly suitable for interdisciplinary teamwork, generating synergies and strengthen the communication within the network.