|M.Sc Student||Model Dmitri|
|Subject||Multi-Sensor Signal Separation, Localization and|
Classification Using Nonlinear Optimization
|Department||Department of Electrical Engineering||Supervisor||Dr. Michael Zibulevsky|
This thesis consists of two contributions in the field of multi-channel signal processing. The first topic of this thesis is a developing of multiple-source reconstruction and localization technique for wide-band signals in sensor arrays. The proposed approach may handle both straight-path-only and reverberant model of signal propagation, based on the knowledge of impulse responses for all location-sensor pairs. We assume that source signals are spatially sparse, as well as have sparse (say, wavelet-type) representation in time domain. This prior is expressed via a large scale convex optimization problem, which involves l1 and non-squared l2 norm minimization. The optimization is carried out by the Truncated Newton method, using preconditioned Conjugate Gradients in inner iterations. Presented numerical experiments demonstrate an advantage of our approach comparing to existing source localization methods in such aspects as super-resolution, robustness to noise and very limited data size. Our approach doesn't require accurate initialization, and also can recover correlated sources.
The second contribution of this thesis is the developing of Electro-Encephalography (EEG) signals analysis methods. This is done in the framework of Brain-Computer interface (BCI), in which our goal is to distinguish between two mental tasks a person is concentrating on. In order to improve the classification performance, we use two-stage preprocessing of multi-sensor data. At first, we perform spatial filtering, by taking weighted linear combination of sensors. At the second step, we perform time-domain filtering. Filter coefficients are learned from the data by maximizing the between class discrimination and minimizing the total variation of result average or, alternatively, suppressing the signal at the windows, where it is known to be absent. No other information on signals of interest is assumed to be available. This leads to a constrained optimization problem, which involves l1-l2 norm minimization. We also suggest solution using eigenvalue decomposition approach. We evaluate our method both on synthetic and real EEG data, and demonstrate the advantage of our approach comparing to the existing methods.