Frequency Domain Estimation of the Parameters of Human Brain Electrical Dipoles

Abstract Human brain evoked potentials are elicited by a stimulus and can be recorded by scalp electrodes. Many researchers have proposed models in which evoked potentials are generated by equivalent electrical dipoles in the brain. Each dipole is defined by a set of parameters that specify its location, orientation, and magnitude. Existing approaches to estimation of dipole parameters do not realistically account for errors resulting from background brain electrical activity (“noise”) and thus lead to inefficient estimators and incorrect confidence sets. As an alternative, we derive frequency domain maximum likelihood estimators of the dipole parameters. The frequency domain approach simplifies the representation of the noise process and leads to substantial data reduction. The Fourier coefficients of the noise are approximately complex normal and independent across frequencies. This leads to a multivariate complex normal likelihood with a mean vector that is a nonlinear function of the dipole parameters...

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