Magnetic Particle Imaging (MPI) is a recently developed imaging technique that allows for both high spatial and temporal resolution. Compared with other classical modalities there is no exposition to ionizing radiation. These features make it a promising modality in medical applications. However, the corresponding imaging task constitutes a severely ill-posed inverse problem which requires regularization techniques to produce acceptable results. Currently used reconstruction methods are based on a time-consuming and memory-intensive calibration process. This calibration process is at the core of the measurement-based approach. To avoid the calibration, model-based approaches are of interest in MPI. In this thesis we outline the main contributions obtained both to the model-based approach and to the measurement-based approach. The main contribution in measurement-based approach is the employment of a Plug-and-Play reconstruction algorithm that uses a pretrained deep-learning-based Gaussian denoiser in a zero-shot fashion, with additional L1-prior, to achieve fast and competitive reconstructions on the OpenMPI dataset. Concerning the model-based approach, we consider a two-stage algorithm based on a reconstruction formula for Field-Free Point (FFP) MPI. This algorithm consists of two stages: the Core Stage and the Deconvolution Stage. We provide a variational formulation of the Core Stage and improve the Deconvolution Stage with TV-like regularization and with a Nonnegative Fused LASSO algorithm, for which we also prove convergence. The two-stage algorithm is capable to deal with scans that are not dependent on the scanning trajectory. We show how this property can be leveraged in multi-patch MPI in a simulated scenario. As a further contribution to model-based MPI, we have also provided reconstruction formulae for the case of 3D Field-Free Line (FFL) MPI. Such formulae were missing in the literature at the beginning of this project. We show the applicability of the 3D FFL reconstruction formulae in simulated scenarios. Finally, we further develop our methodology to apply the two-stage model-based algorithm to real MPI data. In particular, we show the first reconstruction with our algorithm on real 2D MPI data collected by a Bruker's scanner. The results are interesting in view of the fact that these are the first reconstructions obtained on real multi-dimensional (2D) MPI with a method that does not depend on the specific choice of the scanning trajectory. To highlight the flexibility of our method, we additionally display reconstructions from data obtained with an MPI scanner that does not use Lissajous trajectories. The results obtained demonstrate that the methods developed in this work are capable of competitive reconstruction quality, while offering flexibility for future general-purpose model-based MPI reconstructions.
Vladyslav Gapyak (Thu,) studied this question.