Brain Source Localization: A New Method Based on Music Algorithm and Spatial Sparsity

Brain activity can be recorded by means of EEG (Electroencephalogram) electrodes placed on the scalp of the patient. The EEG reflects the activity of groups of neurons located in the head, and the fundamental problem in neurophysiology is the identification of the sources responsible of brain activity, especially if a seizure occurs and in this case it is important to identify it. The studies conducted in order to formalize the relationship between the electromagnetic activity in the head and the recording of the generated external field allow to know pattern of brain activity. The inverse problem, that is given the sampling field at different electrodes the underlying asset must be determined, is more difficult because the problem may not have a unique solution, or the search for the solution is made difficult by a low spatial resolution which may not allow to distinguish between activities involving sources close to each other. Thus, sources of interest may be obscured or not detected and known method in source localization problem as MUSIC (MUltiple SIgnal Classification) could fail. Many advanced source localization techniques achieve a best resolution by exploiting sparsity: if the number of sources is small as a result, the neural power vs. location is sparse. In this work a solution based on the spatial sparsity of the field signal is presented and analyzed to improve MUSIC method. For this purpose, it is necessary to set a priori information of the sparsity in the signal. The problem is formulated and solved using a regularization method as Tikhonov, which calculates a solution that is the better compromise between two cost functions to minimize, one related to the fitting of the data, and another concerning the maintenance of the sparsity of the signal. At the first, the method is tested on simulated EEG signals obtained by the solution of the forward problem. Relatively to the model considered for the head and brain sources, the result obtained allows to have a significant improvement compared to the classical MUSIC method, with a small margin of uncertainty about the exact location of the sources. In fact, the constraints of the spatial sparsity on the signal field allow to concentrate power in the directions of active sources, and consequently it is possible to calculate the position of the sources within the considered volume conductor. Later, the method is tested on the real EEG data too. The result is in accordance with the clinical report even if improvements are necessary to have further accurate estimates of the positions of the sources.