An arrangement for detecting and/or locating a magnetic material in a region of action, which arrangement comprises: - selection means for generating a magnetic selection field having a pattern in space of its magnetic field strength such that a first sub-zone having a low magnetic field strength and a second sub-zone having a higher magnetic field strength are formed in the region of action, - drive means for changing the position in space of the two sub-zones (301, 302) in the region of action by means of a magnetic drive field so that the magnetization of the magnetic material changes locally, - receiving means for acquiring detection signals, which detection signals depend on the magnetization in the region of action, which magnetization is influenced by the change in the position in space of the first and second sub-zone (301, 302), - storage means for storing at least a subset of measured system function data of the arrangement's system function, said system function comprising a system function data set describing the relation between spatial position of the magnetic material and the system response for said arrangement and the trajectory along which said first sub-zone is moved for the acquisition of said system function data, - processing means for generating processed system function data having a higher SNR than said measured system function data by processing said measured system function data using additional knowledge about the structure of the system function, and - reconstruction means for reconstructing the spatial distribution of the magnetic material in the region of action from the detection signals and said processed system function data, characterised in that said processing means are adapted for combining signals acquired at different spatial positions, which share information due to the spatial symmetries existing in the frequency components of the system function, using knowledge about the frequency dependent parity of the frequency components. - selection means for generating a magnetic selection field having a pattern in space of its magnetic field strength such that a first sub-zone having a low magnetic field strength and a second sub-zone having a higher magnetic field strength are formed in the region of action, - drive means for changing the position in space of the two sub-zones (301, 302) in the region of action by means of a magnetic drive field so that the magnetization of the magnetic material changes locally, - receiving means for acquiring detection signals, which detection signals depend on the magnetization in the region of action, which magnetization is influenced by the change in the position in space of the first and second sub-zone (301, 302), - storage means for storing at least a subset of measured system function data of the arrangement's system function, said system function comprising a system function data set describing the relation between spatial position of the magnetic material and the system response for said arrangement and the trajectory along which said first sub-zone is moved for the acquisition of said system function data, - processing means for generating processed system function data having a higher SNR than said measured system function data by processing said measured system function data using additional knowledge about the structure of the system function, and - reconstruction means for reconstructing the spatial distribution of the magnetic material in the region of action from the detection signals and said processed system function data, characterised in that said processing means are adapted for combining signals acquired at different spatial positions, which share information due to the spatial symmetries existing in the frequency components of the system function, using knowledge about the frequency dependent parity of the frequency components.