Reliable and fast medical imaging techniques are indispensable for diagnostics in clinical everyday life. A promising example of those is given by magnetic particle imaging (MPI) invented by Gleich and Weizenecker . MPI is a tracer-based imaging method allowing for the reconstruction of the spatial distribution of magnetic nanoparticles via exploiting their non-linear magnetization response to changing magnetic fields. We dedicate ourselves towards MPI using a field-free line (FFL) for spatial encoding . For data acquisition the FFL is moved through the field of view resulting in a scanning geometry resembling the one in computerized tomography. Indeed, in the ideal setting, corresponding MPI data can be traced back to the Radon transform of the particle concentration . We jointly reconstruct Radon data and particle concentration by means of total variation regularization and have a look at some numerical examples. We conclude with problems that arise when leaving the ideal setting. For example, in practice, we are confronted with imperfections of the applied magnetic fields leading to deformed low-field volumes and, when ignored, image artifacts.
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 Knopp T, Erbe M, Sattel T F, Biederer S, and Buzug T M 2011 A Fourier slice theorem for magnetic particle imaging using a field-free line Inverse Problems 27 095004