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, according to a Lissajous trajectory or pattern, 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 a subset of 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, and - reconstruction means for reconstructing the spatial distribution of the magnetic material in the region of action from the detection signals and the stored subset of the system function data, using additional knowledge about the structure of the system function, wherein said reconstruction means are adapted for generating a reduced representation of the system function by applying a Chebyshev or cosine-type transform along the spatial dimension and solving the much sparser reconstruction problem arising after the transform. - 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, according to a Lissajous trajectory or pattern, 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 a subset of 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, and - reconstruction means for reconstructing the spatial distribution of the magnetic material in the region of action from the detection signals and the stored subset of the system function data, using additional knowledge about the structure of the system function, wherein said reconstruction means are adapted for generating a reduced representation of the system function by applying a Chebyshev or cosine-type transform along the spatial dimension and solving the much sparser reconstruction problem arising after the transform.