Multichannel signal decomposition and separation in the time-frequency domain

The extraction of signals or components from observed data is a fundamental and challenging problem in many signal processing applications. In many practical situations, observations may be modeled as linear mixtures of a number of source signals, i.e. a linear multi-input multi-output system. A typical example is speech recordings made in an acoustic environment in the presence of background noise and/or competing speakers. Other examples include multichannel biological signal recordings such as the electroencephalogram, passive sonar applications and cross-talk in data communications. The well-known approaches to the signal decomposition and separation problems include second or higher order statistics based methods, principal component analysis, and independent component analysis. Most of these methods are developed in the time domain, and thus inherently assume the stationarity of the underlying signals. However, most real world signals are non-stationary and have highly complex time-varying characteristics. For non-stationary signals, common signal analysis techniques such as the standard Fourier transform are not useful since the transient part of the signal such as spikes and high frequency bursts cannot be easily detected from the Fourier transform. These problems could be overcome by using non-stationary signal analysis tools such as the quadratic time-frequency distributions (TFDs). TFDs provide a two-dimensional representation of the time-varying energy information in the signal, and are suitable for tracking the non-stationary behavior of signals. Hence, there have been efforts to perform the signal decomposition and separation in the time-frequency domain.;In this dissertation, the multichannel signal decomposition problem in the time-frequency domain is first considered. A new adaptive signal component extraction method is proposed based on the minimum entropy criterion. This method decomposes the signals into the components that are well-concentrated on the time-frequency plane. Unlike the traditional Gabor decomposition, the signal is expressed as a finite sum of the components extracted by the proposed algorithm whose time and frequency centers are determined by the signal and not by a pre-determined dictionary. Next, the overdetermined blind source separation problem is addressed in the time-frequency domain. We present a novel approach to achieve source separation using an information-theoretic cost function. Jensen-Renyi divergence, as adapted to time-frequency distributions, is introduced as an effective cost function to extract sources that are disjoint on the time-frequency plane. The sources are extracted through a series of Givens rotations and the optimal rotation angle is found using the steepest descent algorithm. The proposed method is applied to several example signals to illustrate its effectiveness and the performance is quantified through simulations. After that, the underdetermined blind source separation problem is discussed. The proposed approach takes advantage of the high resolution of time-frequency distributions for obtaining a sparse representation, and separates the sources by a simple clustering algorithm followed by a convex optimization problem. Compared to other time-frequency based separation methods, the approach presented is characterized by simplicity and ease of implementation. Finally, the proposed approach for the case of underdetermined blind source separation is applied to real signals such as electroencephalogram signals to further evaluate its performance. The experimental results show that the proposed method is more effective at extracting well-localized neuronal sources in time and frequency than ICA.