|M.Sc Thesis||Department of Electrical Engineering|
|Supervisor:||Dr. Zibulevsky Michael|
Inverse E/MEG problem is known to be ill-posed and no single solution can be found without utilizing some prior knowledge about the nature of signal sources and the way the signals are propagating and finally collected by the sensors. We propose a new method that recovers locations and time courses of E/MEG sources using spatio-temporal sparse representations. We make two assumptions about the E/MEG sources: the signals are assumed to have a sparse representation in an appropriate domain, e.g. wavelet transform, and the sources are assumed to be spatially local. The fact that E/MEG data comes from physiological source justifies such assumptions. We formulate a large scale convex optimization problem that corresponds to the E/MEG inverse problem. The sparsity and the locality assumptions are incorporated into the optimization problem in the form of convex penalty functions. The considerations about the propagation of the signals and the locations of putative sources are implied by a pre-calculated forward model.
The resulting optimization problem is solved using an augmented Lagrangian framework with truncated Newton method for the inner optimization. We also show that E/MEG inverse problem can be posed as a conic programming.
The proposed method is verified by simulations with both synthetic and real EEG data. The real EEG data was recorded during experiments with simple cognitive tasks and external magnetic stimulations. Our method was shown to be capable of recovering locations and time courses of real physiological sources, synthetic sources and the mixtures of both.