A calibration method for an MPI (=magnetic particle imaging) apparatus for conducting an MPI experiment, wherein the calibration method comprises m calibration MPI measurements with a calibration test piece and uses these measurements to create an image reconstruction matrix with which the signal contributions of N voxels within an investigation volume of the MPI apparatus are determined, wherein compressed sensing steps are applied in the calibration method with a transformation matrix that sparsifies the image construction matrix, and wherein only a number M