Subspace Techniques for Brain Signal Enhancement

This chapter presents a collection of subspace-based techniques derived from other research areas to estimate biomedical signals from human. Extracting certain signals from the body such as the brain is challenging; this is due to the presence of unwanted signals in the form of colored noise, making the overall signal-to-noise ratio as low as -10 dB. In relation to the enhancement of brain signals, researchers have proposed various techniques utilizing different sorts of averaging and filtering which includes Kalman filtering, Wiener filtering, wavelets, cumulants, etc. In this article, several subspace-based techniques proposed in different areas are tested and applied to enhance biomedical signals. As for any subspace method, the corrupted signal is separated into two parts called the signal subspace and noise only subspace. Signal enhancement is then performed using the signal subspace portion only. The article focuses on the main differences of these subspace-based approachesin the aspects of bio-signal model development, creation and/or selection of the pertinent vector(s) and/or matrices, contaminated signal decorrelation and desired signal reconstruction processes. Some modifications are also incorporated in some of the borrowed algorithms to suit bio-signal processing. Further, one of the critical issues that remain to be resolved when signal subspace scheme is used is simultaneous diagonalization of matrices. This problem is sufficiently addressed and the solutions to overcome it are included. Further, the subspace methods under study are applied to estimate visual evoked potentials (VEPs) which are highly corrupted by spontaneous electroencephalogram (EEG) signals. Thorough simulations using realistically generated VEPs and EEGs at SNRs ranging from 0 to -10 dB have been performed. Later, the performance of the algorithms is assessed in their abilities to detect the latencies of the P100, P200 and P300 components. Next, the validity and the effectiveness of the algorithms to detect the P100's (used in objective assessment of visual pathways) are evaluated using real patient data collected from a hospital. The efficiencies of the studied techniques are then compared among one another. Both the simulation and real human data show that the subspace methods generate reasonably low errors and high success rate. As such, a subspace scheme is a promising technique that can be further refined and eventually applied in the real world as a single-trial estimator of biomedical signals, which are presently extracted by means of multi-trial ensemble averaging.