Abstract. 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 three dimensional (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.

Magnetic particle imaging (MPI) is an emerging medical imaging modality which is based on the non-linear response of magnetic nanoparticles to an applied magnetic field. It is an important feature of MPI that even fast dynamic processes can be captured for 3D volumes. The high temporal resolution in turn leads to large amounts of data which have to be handled efficiently. But as the system matrix of MPI is non-sparse, the image reconstruction gets computationally demanding. Therefore, currently only basic image reconstruction methods such as Tikhonov regularization are used. However, Tikhonov regularization is known to oversmooth edges in the reconstructed image and to have only a limited noise reducing effect. In this work, we develop an efficient edge preserving and noise reducing reconstruction method for MPI. As regularization model, we propose to use the nonnegative fused lasso model, and we devise a discretization that is adapted to the acquisition geometry of the preclinical MPI scanner considered in this work. We develop a customized solver based on a generalized forward-backward scheme which is particularly suitable for the dense and not well-structured system matrices in MPI. Already a non-optimized prototype implementation processes a 3D volume within a few seconds so that processing several frames per second seems amenable. We demonstrate the improvement in reconstruction quality over the state-of-the-art method in an experimental medical setup for an in-vitro angioplasty of a stenosis.

We analyze the Schelling model of segregation in which a society of n individuals live in a ring. Each individual is one of two races and is only satisfied with his location so long as at least half his 2w nearest neighbors are of the same race as him. In the dynamics, randomly-chosen unhappy individuals successively swap locations. We consider the average size of monochromatic neighborhoods in the final stable state. Our analysis is the first rigorous analysis of the Schelling dynamics. We note that, in contrast to prior approximate analyses, the final state is nearly integrated: the average size of monochromatic neighborhoods is independent of n and polynomial in w.

We present a theoretically well-founded retrieval model for dynamically generating rankings based on interactive user feedback. Unlike conventional rankings that remain static after the query was issued, dynamic rankings allow and anticipate user activity, thus providing a way to combine the otherwise contradictory goals of result diversification and high recall. We develop a decision-theoretic framework to guide the design and evaluation of algorithms for this interactive retrieval setting. Furthermore, we propose two dynamic ranking algorithms, both of which are computationally efficient. We prove that these algorithms provide retrieval performance that is guaranteed to be at least as good as the optimal static ranking algorithm. In empirical evaluations, dynamic ranking shows substantial improvements in retrieval performance over conventional static rankings.