Magnetic particle imaging exploits the non-linear magnetization of superparamagnetic iron-oxide particles to generate a tomographic image in a defined field-of-view. For reconstruction of the particle distribution, a time-consuming calibration step is required, in which system matrices get measured using a robot. To achieve artifact-free images, system matrices need to cover not only the field-of-view but also a larger area around it. Especially for large measurements – inevitable for future clinical application – this leads to long calibration time and high consumption of persistent memory. In this work, we analyze the signal in the outer part of the system matrix and motivate the usage of extrapolation methods to computationally expand the system matrix after restricting the calibration to the field-of-view. We propose a suitable extrapolation method and show its applicability on measured 2D and 3D data. In doing so, we achieve a considerable reduction of calibration time and consumption of persistent memory while preserving an artifact-free result.