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Various imaging modalities allow for time-dependent image reconstructionsfrom measurements where its acquisition also has a time-dependent nature.Magnetic particle imaging (MPI) falls into this class of imaging modalities andit thus also provides a dynamic inverse problem. Without proper considerationof the dynamic behavior, motion artifacts in the reconstruction become anissue. More sophisticated methods need to be developed and applied to thereconstruction of the time-dependent sequences of images. In this context, weinvestigate the incorporation of motion priors in terms of certainflow-parameter-dependent PDEs in the reconstruction process of time-dependent3D images in magnetic particle imaging. The present work comprises the methoddevelopment for a general 3D+time setting for time-dependent linear forwardoperators, analytical investigation of necessary properties in the MPI forwardoperator, modeling aspects in dynamic MPI, and extensive numerical experimentson 3D+time imaging including simulated data as well as measurements from arotation phantom and in-vivo data from a mouse.

Dynamic image reconstruction with motion priors in application to 3D magnetic particle imaging