Various imaging modalities allow for time-dependent image reconstructions from measurements where its acquisition also has a time-dependent nature. Magnetic particle imaging (MPI) falls into this class of imaging modalities and it thus also provides a dynamic inverse problem. Without proper consideration of the dynamic behavior, motion artifacts in the reconstruction become an issue. More sophisticated methods need to be developed and applied to the reconstruction of the time-dependent sequences of images. In this context, we investigate the incorporation of motion priors in terms of certain flow-parameter-dependent PDEs in the reconstruction process of time-dependent 3D images in magnetic particle imaging. The present work comprises the method development for a general 3D+time setting for time-dependent linear forward operators, analytical investigation of necessary properties in the MPI forward operator, modeling aspects in dynamic MPI, and extensive numerical experiments on 3D+time imaging including simulated data as well as measurements from a rotation phantom and in-vivo data from a mouse.

翻译：多种成像模态允许从具有时间依赖性的测量数据中重建时间相关的图像。磁粒子成像（MPI）属于此类成像模态，因此也涉及动态逆问题。若未充分考虑动态特性，重建图像中会出现运动伪影。需开发并应用更复杂的方法来重建时间依赖的图像序列。在此背景下，我们研究在磁粒子成像中，将基于特定流动参数偏微分方程的运动先验引入三维时间依赖图像重建过程。本工作包括：面向一般三维加时间（3D+time）框架下时间依赖线性正算子的方法开发、MPI正算子必要性质的解析研究、动态MPI建模方面的探讨，以及基于模拟数据、旋转体模测量数据和小鼠活体数据的三维加时间成像的广泛数值实验。