In this thesis we consider the problems of estimating electric sources in the brain using electroencephalography (EEG) and magnetoencephalography (MEG), and combining different biomedical imaging modalities. In the first part, we discuss a number of statistical model selection methods to distinguish between two possible source models using maximum-likelihood (ML) estimation, assuming a spherical head shape, and apply these to real MEG data of epilepsy. One model has a single moving source whereas the other has two stationary sources; these typically result in similar EEG/MEG measurements. The need to decide between such models occurs for example in Jacksonian seizures (e.g. epilepsy) or in intralobular activities, where a model with either two stationary dipole sources or a single moving dipole source may be possible.; In the second part, we propose a number of electric source models that are spatially distributed on a line or a surface in the brain for MEG. We use a realistic head model and discuss the special case of spherical head with radial sensors resulting in more efficient computations. We develop these models with increasing degrees of freedom, then derive forward solutions, ML estimates, Cramer-Rao bound (CRB) expressions for the unknown source parameters. We apply our line-source models to real MEG data of N20 responses, and surface-source models to real MEG data of potassium-chloride (KCl) induced spreading depression in rats.; In the third part, we derive statistical performance bounds on image registration for combining different modalities of imaging or other applications such as motion detection; target recognition, and video processing. These bounds can be useful in evaluating image registration techniques, determining parameter regions where more successful registration is possible, and choosing features to be used for the registration. We consider a wide variety of geometric deformation models, intensity matching of two images using a moving-average model, and these two simultaneously.
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