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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.<\/jats:p>","DOI":"10.1137\/23m1580401","type":"journal-article","created":{"date-parts":[[2024,7,15]],"date-time":"2024-07-15T04:02:55Z","timestamp":1721016175000},"page":"1539-1586","source":"Crossref","is-referenced-by-count":3,"title":["Dynamic Image Reconstruction with Motion Priors in Application to Three Dimensional Magnetic Particle Imaging"],"prefix":"10.1137","volume":"17","author":[{"given":"Christina","family":"Brandt","sequence":"first","affiliation":[{"name":"Department of Mathematics, Universit\u00e4t Hamburg, 20146, Hamburg, Germany. Current address: Institute of Mathematics and Computer Science, University of Greifswald, 17489, Greifswald, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tobias","family":"Kluth","sequence":"additional","affiliation":[{"name":"Center for Industrial Mathematics, University of Bremen, 28359, Bremen, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1589-8517","authenticated-orcid":true,"given":"Tobias","family":"Knopp","sequence":"additional","affiliation":[{"name":"Institute for Biomedical Imaging, Hamburg University of Technology and University Medical Center Hamburg-Eppendorf, 22529, Hamburg, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lena","family":"Westen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Universit\u00e4t Hamburg, 20146, Hamburg, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,7,15]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-7280-2"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198502456.001.0001"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.3934\/ipi.2021059"},{"key":"ref4","unstructured":"J. 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