An optimal constrained linear inverse method for magnetic source imaging.

Magnetic source imaging is the reconstruction of the current source distribution inside an inaccessible volume from magnetic field measurements made outside the volume. It is possible in many applications to estimate, from prior physiological and anatomical knowledge, the source positions, amplitudes, and correlations, as well as the noise amplitudes and correlations. The optimal constrained linear inverse method (OCLIM) uses this prior knowledge to obtain a minimum mean-square error estimate of the current distribution. OCLIM can be efficiently computed using the Cholesky decomposition, taking about a second on a workstation-class computer for a problem with 64 sources and 144 detectors. Any source and detector configuration is allowed as long as their positions are fixed a priori. Correlations among source and noise amplitudes are permitted. OCLIM reduces to the optimally weighted pseudoinverse method of Shim and Cho if the source amplitudes are independent and identically distributed and to the minimum-norm least-squares estimate in the limit of no measurement noise or no prior knowledge of the source amplitudes. In the general case, OCLIM has better mean-square error than either previous method. OCLIM appears well suited to magnetic imaging, since it exploits prior information, provides the minimum reconstruction error, and is inexpensive to compute.