Beta Iterative Synchronization: An Algorithm for Structural Signal Averaging

Many biomedical signals can be considered as the sets of repetitions due to the occurrence of a repetitive pattern of features. Those features, however, are characterized by some jitter, which often renders standard arithmetic averaging inadequate. Examples include electrocardiogram, ocular pulse or corneal pulse, series of evoked potentials in electro- and magnetoencephalography, among many others. We propose a new approach to structural averaging of such signals. We use the family of beta cumulative distribution functions as a set of candidates for time warping function in order to synchronize repetitions, and then apply a variant of the Procrustes method to find the average signal. For both synthetic and real data, we provide a comparison where we challenge the Dynamic Time Warping (DTW) method and present both theoretical and practical advantages of our algorithm. As an illustrative real-data example, we address corneal pulse waveforms with their dicrotic valleys as the feature of interest. The detection of the dicrotic valleys turned out more reproducible than in the case of DTW while maintaining similar classification performance and having fewer parameters. The proposed method for structural averaging provides effective estimation in the case of the analyzed signals. The method can readily be extended to other biomedical signals characterized by repetitive feature patterns.