1. A method for calibrating an MPI apparatus for performing an MPI experiment of a volume under investigation, the method comprising the steps of: a) determining compressed sensing steps using a transformation matrix that sparsifies an image reconstruction matrix, the transformation matrix comprising analytic transformations, a modelled MPI-system matrix, a simulated or a measured system matrix; b) carrying out M calibration MPI measurements for M voxels of a calibration sample, the M voxels being selected in a random or pseudo-random fashion; and c) using the transformation matrix of step a) and the measurements of step b) to create and store an image reconstruction matrix with which signal contributions of N voxels within the volume under investigation are determined, wherein M<N.