Magnetic particle imaging visualizes the spatial distribution of superparamagnetic nanoparticles. Because of its key features of excellent sensitivity, high temporal and spatial resolution and biocompatibility of the tracer material it can be used in multiple medical imaging applications. The common reconstruction technique for Lissajous-type trajectories uses a system matrix that has to be previously acquired in a time-consuming calibration scan, leading to long downtimes of the scanning device. In this work, the system matrix is determined by a hybrid approach. Using the hybrid system matrix for reconstruction, the calibration downtime of the scanning device can be neglected. Furthermore, the signal to noise ratio of the hybrid system matrix is much higher, since the size of the required nanoparticle sample can be chosen independently of the desired voxel size. As the signal to noise ratio influences the reconstruction process, the resulting images have better resolution and are less affected by artefacts. Additionally, a new approach is introduced to address the background signal in image reconstruction. The common technique of subtraction of the background signal is replaced by extending the system matrix with an entry that represents the background. It is shown that this approach reduces artefacts in the reconstructed images.
