Localization of magnetic sources producing the SPMR fields is done by solving the inverse problem of electromagnetism. The forward electromagnetic problem consists of modeling the sources as magnetic dipoles for each magnetic source or more complex configurations that model each source as a distributed source. Examples of the latter are multiple models, Bayesian models, or distributed dipole models. The magnetic dipole model has the form
where r and p are the location and dipole moment vectors of the magnetic dipole, and  is the magnetic permeability of free space.
For a subject containing N sources, a minimum of 4N measurements of the magnetic field are required to determine the coordinates and magnetic moment of each source. In the case where the particles have been aligned by the external magnetizing field in a particular orientation,  3N measurements are required to obtain solutions. This latter situation leads to increased accuracy for finding the locations of objects as fewer variables are required in the inverse solution algorithm. Increased number of measurements provides an over-determined solution, increasing the localization accuracy.
Solving the inverse problem for magnetic dipole or more complex models is performed with non-linear algorithms. The Levenberg-Marquardt algorithm is one approach to obtaining solutions to this non-linear problem. More complex methods are available from other biomagnetism programs.
Coordinates and magnetic moments, for each source assumed to be present in the sample, are determined from solution of the inverse problem.