Automatic wave recurrences extraction for single-channel decomposition

Recurring waveforms in time-series reflect the underlying system dynamics and are common in physiological signals. Identifying these recurrences enables the signal decomposition into meaningful components. Automatic wave recurrences extraction (AWaRE) is a novel low-cost decomposition method for single time-series pre-processing, based on recurrent waveform detection. AWaRE follows a three-step pipeline: (1) detecting candidate recurrent waveforms via matching signal fragments to the trace, (2) resolving overlapping occurrences using multi-kernel deconvolution, and (3) iterative refining of residuals to identify additional waveform onsets. AWaRE was evaluated on simulated data with varying waveform counts, recurrence rates and noise levels, and compared against two methods with similar computational cost: ensemble empirical mode decomposition with independent component analysis (EEMD-ICA) and a spike sorting approach. Mean absolute reconstruction errors in percentage of the mean absolute of the original signal (given as median ± inter-quartile range) were 85.3 ± 30.8% (EEMD-ICA), 65.5 ± 15.0% (spike sorting) and 24.3 ± 35.9% (AWaRE); waveform train estimation errors were 111.0 ± 34.5%, 103.2 ± 33.4% and 32.6 ± 47.1%; processing times for 10 s of data were 2.05 ± 3.13 s, 0.94 ± 0.27 s and 0.78 ± 2.00 s, respectively. All differences were statistically significant in the paired comparisons. Then, examples of applications in fetal ECG detection, intramuscular EMG decomposition, EEG artifact removal and neural spike sorting are provided, showing that the automatically extracted waveforms have clear physiological meaning. In conclusion, AWaRE enables adaptive time-series decomposition by extracting recurrent waveforms from the signal. It is an efficient and robust tool for biomedical signal analysis, facilitating the study of the activities of different sources through repeated waveform pattern identification.