An apparatus obtains data comprising magnetic flux density data and an association of the magnetic flux density data to grid points of at least one grid, each grid point representing at least a geographical location. The apparatus applies at least one frequency transform to a representation of the magnetic flux density data and their association to grid points to obtain frequency components. The apparatus provides compressed magnetic flux density data comprising a subset of the obtained frequency components for at least one of storage and transmission. The same apparatus or another apparatus applies at least one inverse frequency transform to the frequency components in order to recover the magnetic flux density data and their association with different grid points and provides the recovered magnetic flux density data and their association with different grid points for supporting a positioning of a mobile device.