Magnetic particle imaging (MPI) is a new medical imaging technique capable of recovering the distribution of superparamagnetic particles from their measured induced signals. In literature there are two main MPI reconstruction techniques: measurement-based (MB) and x-space (XS). The MB method is expensive because it requires a long calibration procedure as well as a reconstruction phase that can be numerically costly. On the other side, the XS method is simpler than MB but the exact knowledge of the field free point (FFP) motion is essential for its implementation. Our simulation work focuses on the implementation of a new approach for MPI reconstruction: it is called hybrid x-space (HXS), representing a combination of the previous methods. Specifically, our approach is based on XS reconstruction because it requires the knowledge of the FFP position and velocity at each time instant. The difference with respect to the original XS formulation is how the FFP velocity is computed: we estimate it from the experimental measurements of the calibration scans, typical of the MB approach. Moreover, a compressive sensing technique is applied in order to reduce the calibration time, setting a fewer number of sampling positions. Simulations highlight that HXS and XS methods give similar results. Furthermore, an appropriate use of compressive sensing is crucial for obtaining a good balance between time reduction and reconstructed image quality. Our proposal is suitable for open geometry configurations of human size devices, where incidental factors could make the currents, the fields and the FFP trajectory irregular.
In this work we propose a novel application of Partial Differential Equations (PDEs) inpainting techniques to two medical contexts. The first one concerning recovering of concentration maps for superparamagnetic nanoparticles, used as tracers in the framework of Magnetic Particle Imaging. The analysis is carried out by two set of simulations, with and without adding a source of noise, to show that the inpainted images preserve the main properties of the original ones. The second medical application is related to recovering data of corneal elevation maps in ophthalmology. A new procedure consisting in applying the PDEs inpainting techniques to the radial curvature image is proposed. The images of the anterior corneal surface are properly recovered to obtain an approximation error of the required precision. We compare inpainting methods based on second, third and fourth-order PDEs with standard approximation and interpolation techniques.
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