ABSTRACT
The correlated-noise problem is important in electroencephalography (EEG) because of the bipolar nature of the potential field recordings, i.e. the noise at the reference electrode spreads to all other channels. This chapter develops algorithms that solve this problem in an efficient way. It derives closed-form expressions for the maximum likelihood (ML) estimates when the dipole locations and basis functions are known and then a concentrated likelihood function to be optimized when the dipole locations and basis functions are unknown. The chapter discusses goodness-of-fit measures which account for spatially correlated noise. It derives the Fisher information matrix (FIM) and Cramer-Rao bound (CRB) for the proposed model. The chapter uses the CRB to construct methods for EEG/magnetoencephalography (MEG) array optimization. Finally, it compares the estimation accuracy of the ML, generalized least squares (GLS), ordinary least-squares (OLS), and scanning methods for simulated data and applies the ML methods to real auditory evoked MEG responses.
