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In magnetic particle imaging the calibration step for a system matrix based reconstruction is very time and memory consuming. System matrices need to be measured not only in the physical field of view, but also in a bigger overscan region to avoid artifacts, especially in the case of multi-patch magnetic particle imaging. There are several methods to reduce the total number of voxels that need to be measured, e.g. compressed sensing and system matrix extrapolation. In this work, we show that a combination of these two methods is possible by using compressed sensing on a sparse sampling pattern only in the field of view and extrapolating the signal in the overscan region afterwards. We demonstrate on measured data, that such a combination gives superior results than using only compressed sensing on the whole system matrix. This is clearly manifested in the reduction of noise in the reconstruction result, especially when using a high undersampling factor.