Wavelet transforms for non-stationary signal processing

Signal processing and imaging of biomedical phenomena pose significant challenges, with one dominant issue being that biological processes are usually time varying and non-stationary. Many traditional processing approaches are derived on assumptions of statistical stationarity and linear time-invariant propagation channels, which are not valid assumptions for many biomedical problems. In this paper, continuous wavelet transforms are shown to be appropriate tools for characterizing linear time-varying systems and propagation channels and for processing wideband signals in non-stationary Gaussian noise. Wideband processing of signals allows for the processing to be limited by the scattering object's acceleration versus the more common techniques where the processing is limited by the scattering object's velocity. It is shown that the continuous wavelet transform of the output signal with respect to the input signal provides a correct system characterization for time-varying channels and non-stationary signals. Finally, an approach to removing even the wideband limitation of acceleration is presented. Possible biomedical applications of this approach include bloodflow velocimetry and heart motion monitoring.