| Noninvasive imaging techniques are critical for studying cognitive processes as well as determining pathological conditions in the human brain. The ideal measurement technique would simultaneously have high temporal and spatial resolution; unfortunately, this is not possible. Blood flow based techniques such as fMRI, PET, SPECT have relatively high spatial resolution, particularly fMRI (≈1mm), but poor temporal resolution. Direct measurements of electrical activity such as MEG, EEG on the other hand have high temporal resolution (≈1msec), but poor spatial resolution. In all of these cases, spatial information is regained from data by solving a linear inverse problem, which is relatively well-posed for fMRI but very ill-posed for MEG, EEG. Although methods have been developed that attempt to bypass the localisation issue, it remains a key technical challenge central to future progress in the field. Despite the difficulties, considerable effort is still being expended on these inverse problems. One of the major current areas of interest involves detecting brain regions participating in abnormal spontaneous rhythms, since this may play a big role in treating a broad class of neurogenic diseases such as parkinsonianism.; Two broad approaches to the inverse problem are in vogue: the minimum norm (MN) approach and the Backus-Gilbert (BG) technique. Both techniques have advantages and disadvantages. In this thesis, a new approach is developed, termed Local Basis Expansions (LBEX), which captures the MN and BG approaches as special cases, and provides fundamental insight into the nature of the inverse problem. A particular strength of this technique is that it applies to both spontaneous and evoked data, and encompasses nonparametric as well as parametric dipole fitting approaches. Moreover, the LBEX allows to design a new antenna with radiated power constrained to a given solid angle.; This technique was evaluated on both artificial and real data, and the findings are reported in this thesis. |
