A Bayesian Residual Transform for Signal Processing

Abstract: Multi-scale decomposition has been an invaluable tool for the processing of physiological signals. Much focus in multi-scale decomposition for processing such signals have been based on scale-space theory and wavelet transforms. In this study, we take a different perspective on multi-scale decomposition by investigating the feasibility of utilizing a Bayesian-based method for multi-scale signal decomposition called Bayesian Residual Transform (BRT) for the purpose of physiological signal processing. In BRT, a signal is modeled as the summation of residual signals, each characterizing information from the signal at different scales. A deep cascading framework is introduced as a realization of the BRT. Signal-to-noise ratio (SNR) analysis using electrocardiography (ECG) signals was used to illustrate the feasibility of using the BRT for suppressing noise in physiological signals. Results in this study show that it is feasible to utilize the BRT for processing physiological signals for tasks such as noise suppression.