Matching Pursuit-Based Time-Variant Bispectral Analysis and its Application to Biomedical Signals

Objective: Principle aim of this study is to investigate the performance of a matching pursuit (MP)-based bispectral analysis in the detection and quantification of quadratic phase couplings (QPC) in biomedical signals. Nonlinear approaches such as time-variant bispectral analysis are able to provide information about phase relations between oscillatory signal components. Methods: Time-variant QPC analysis is commonly performed using Gabor transform (GT) or Morlet wavelet transform (MWT), and is affected by either constant or frequency-dependent time-frequency resolution (TFR). The matched Gabor transform (MGT), which emerges from the incorporation of GT into MP, can overcome this obstacle by providing a complex time-frequency plane with an individually tailored TFR for each transient oscillatory component. QPC analysis was performed by MGT, and MWT was used as the state-of-the-art method for comparison. Results: Results were demonstrated using simulated data, which present the general case of QPC, and biomedical benchmark data with a priori knowledge about specific signal components. HRV of children during temporal lobe epilepsy and EEG during burst-interburst pattern of neonates during quiet sleep were used for the biomedical signal analysis to investigate the two main areas of biomedical signal analysis: The cardiovascular-cardiorespiratory system and neurophysiological brain activities, respectively. Simulations were able to show the applicability and reliability of the MGT for bispectral analysis. HRV and EEG analysis demonstrate the general validity of the MGT for QPC detection by quantifying statistically significant time patterns of QPC. Conclusion and Significance: Results confirm that MGT-based bispectral analysis provides significant benefits for the analysis of QPC in biomedical signals.