Non-stationary biosignal modelling

Abstract

Signals of biomedical nature are in the most cases characterized by short, impulse-like events that represent transitions between different phases of a biological cycle. As an example hearth sounds are essentially events that represent transitions between the different hemodynamic phases of the cardiac cycle. Classical techniques in general analyze the signal over long periods thus they are not adequate to model impulse-like events. High variability and the very often necessity to combine features temporally well localized with others well localized in frequency remains perhaps the most important challenges not yet completely solved for the most part of biomedical signal modeling. Wavelet Transform (WT) provides the ability to localize the information in the time-frequency plane; in particular, they are capable of trading on type of resolution for the other, which makes them especially suitable for the analysis of non-stationary signals. State of the art automatic diagnosis algorithms usually rely on pattern recognition based approaches. Hidden Markov Models (HMM’s) are statistically based pattern recognition techniques with the ability to break a signal in almost stationary segments in a framework known as quasi-stationary modeling. In this framework each segment can be modeled by classical approaches, since the signal is considered stationary in the segment, and at a whole a quasi-stationary approach is obtained. Recently Discrete Wavelet Transform (DWT) and HMM’s have been combined as an effort to increase the accuracy of pattern recognition based approaches regarding automatic diagnosis purposes. Two main motivations have been appointed to support the approach. Firstly, in each segment the signal can not be exactly stationary and in this situation the DWT is perhaps more appropriate than classical techniques that usually considers stationarity. Secondly, even if the process is exactly stationary over the entire segment the capacity given by the WT of simultaneously observing the signal at various scales which means at different levels of focus, each one emphasizing different characteristics can be very beneficial regarding classification purposes. This chapter presents an overview of the various uses of the WT and HMM’s in automatic diagnosis in medicine. Their most important properties regarding biomedical applications are firstly described.