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In multi-patch magnetic particle imaging an artifact-free image can be obtained by using a joint reconstruction and measuring the system matrices not only in the field-of-view but also in a huge overscan. This leads to a long calibration time and heavy memory consumption and therefore an unsuitability of this method for large three-dimensional measurements. In this work we propose to measure the system matrices only in the field-of-view and use a diffusion based extrapolation step to extant the system matrices computationally into the overscan. In this way we massively reduce the calibration time while maintaining a nearly artifact-free image.