In Magnetic Particle Imaging (MPI) the reconstruction requires the knowledge of a so called system function. This function describes the relation between spatial position and frequency response and is currently measured once for a scanner set-up and a tracer material. For reasonable resolutions and fields of view the system function becomes quite large, resulting in large acquisition times to obtain reasonable signal-to-noise. However, the system function has a number of properties which can be used to improve signal-to-noise. According to the present invention use is made of the spatial symmetry and/or identical responses at different frequencies for this purpose.