Measurements of an arbitrary magnetic field having one or more magnetic field components are acquired from a plurality of magnetometers, and a generic model of at least one of the one or more magnetic field components of the arbitrary magnetic field is generated in the vicinity of the magnetometers. The generic magnetic field model comprises an initial number of different basis functions. Maxwell's equations are applied to the generic magnetic field model to reduce the initial number of different basis functions, thereby yielding a Maxwell-constrained model of the magnetic field component(s) of the arbitrary magnetic field, and the magnetic field component(s) of the arbitrary magnetic field are estimated at each of at least one of the magnetometers based on the constrained magnetic field model and the arbitrary magnetic field measurements acquired from each magnetometer.
SYSTEMS AND METHODS THAT EXPLOIT MAXWELL'S EQUATIONS AND GEOMETRY TO REDUCE NOISE FOR ULTRA-FINE MEASUREMENTS OF MAGNETIC FIELDS FROM THE BRAIN USING A NEURAL DETECTION SYSTEM