Empirical analysis for non-stationary signal de-noising, de-trending and discrimination applications

This dissertation focuses on the study and development of methods for empirical analysis of non-stationary signals in the context of de-noising, de-trending and discrimination applications. For this purpose, Empirical Mode Decomposition (EMD), which is a relatively new signal decomposition technique, is chosen as the starting point. EMD does not rely on any fixed basis, but instead defines a signal adaptive decomposition methodology. The use of EMD for signal de-noising and de-trending is demonstrated through formulation of a methodology for mental task classification using EEG signals. Furthermore, a methodology for analysis and classification of pathological speech signals is developed, whereby a high classification accuracy through use of meaningful instantaneous features is demonstrated. Following this, a novel modification of EMD, named Empirical Mode Decomposition-Modified Peak Selection (EMD-MPS), is proposed. EMD-MPS allows a time-scale based decomposition of signals, which is not possible using the original EMD algorithm. The EMD-MPS algorithm is defined, and its properties empirically established, thereby validating the expected behaviour of EMD-MPS. Importantly, EMD-MPS is shown to provide new insight into the decomposition behaviour of the original EMD algorithm. Also, a novel hierarchical decomposition methodology, which uses the time-scale based decomposition of EMD-MPS to divide a signal into selected frequency bands, is developed and illustrated using synthetic and real world signals. EMD-MPS is also used for time-scale based de-noising and de-trending of signals, first demonstrated using synthetic and real signals, and then validated by practical applications such as mental task classification and seizure detection. An empirical sparse dictionary learning framework based on EMD with application to signal classification is then proposed and developed in the dissertation. As part of this framework, a discriminative dictionary learning algorithm is developed, and characteristics of the empirical dictionary established. The utility of the proposed framework for signal classification is demonstrated using EEG signals. The proposed framework is then applied for automated seizure detection using long-term EEG recordings, and the results are used to discuss the potential and implications for patient specific dictionaries, as well as the associated advantages of the framework when using long-term data.