Referee consensus: a platform technology for nonlinear optimization

Abstract

Electrical current flow within populations of neurons is a fundamental constituent of brain function. The resulting fluctuating magnetic fields may be sampled noninvasively with an array of magnetic field detectors positioned outside the head. This is magnetoencephalography (MEG). Each source may be characterized by 5-6 parameters, the xyz location and the xyz direction. The magnetic field measurements are nonlinear in the location parameters; hence the source location is identifiable only via search of the brain volume. When there is one or a very few sources, this may be practical; solutions for the general problem have poor resolution and are readily defeated. Referee consensus is a novel cost function which enables identification of a source at one location at a time regardless of the number and location of other sources. This "independence" enables solution of the general problem and insures suitability to grid computing. The computation scales linearly with the number of nonlinear parameters. Since the method is not readily disrupted by noise or the presence of multiple unknown source, it is applicable to single trial data. MEG recordings were obtained from 26 volunteers while they performed a cognitive task The single trial recordings were processed on the Open Science Grid (≈300 CPU hours/sec of data) On average 500+ active sources were found throughout. Statistical analyses demonstrated 1-2 mm resolving power and high confidence findings (p < 0.0001) when testing for task specific information in the extracted virtual recordings. Referee consensus is applicable to a variety of systems in addition to MEG, e.g. the connectivity problem, the blurred image, both passive and active SONAR, and seismic tomography. Applicability requires (1) that the measurements be linear in at least one of the source parameters and (2) that a sequence of measurements in time be obtained.