Imaging via stochastic factorization of bioelectric signal matrices

Bioelectric signals are characterized by the fact that remotely sensed data can be organized into a space-time matrix which is the product of a spatial transfer matrix and a space-time matrix of potentials proximate to the source. The imaging problem is then expressed by FG=H+N, where given a matrix of scalp measurements H (for example), and transfer matrix F, it is required to estimate the matrix of cortical potentials G in the context of information regarding statistics of space-time noise matrix N. This source imaging problem is usually approached via sequential regularized solution estimates for the equations FG_:i=H_:i, where the subscript “:i” indicates the i-th matrix column, and one takes into account statistics of N_:i in the regularization. However, the optimal formal treatment of the stated source estimation problem has not been previously described, and is indicated by the new theorem here. The principle extends earlier algorithmic work on the inverse electrocardiography problem, which was not suitable for treating noise sources in the brain source imaging problem. The method´s mathematically determined superior performance characteristics have been confirmed by another investigator who has applied it to the problem of localizing epileptic spikes