Noise Reduction in Rhythmic and Multitrial Biosignals With Applications to Event-Related Potentials

A new noise reduction algorithm is presented for signals displaying repeated patterns or multiple trials. Each pattern is stored in a matrix, forming a set of events, which is termed multievent signal. Each event is considered as an affine transform of a basic template signal that allows for time scaling and shifting. Wavelet transforms, decimated and undecimated, are applied to each event. Noise reduction on the set of coefficients of the transformed events is applied using either wavelet denoising or principal component analysis (PCA) noise reduction methodologies. The method does not require any manual selection of coefficients. Nonstationary multievent synthetic signals are employed to demonstrate the performance of the method using normalized mean square error against classical wavelet and PCA based algorithms. The new method shows a significant improvement in low SNRs (typically $≪$0 dB). On the experimental side, evoked potentials in a visual oddball paradigm are used. The reduced-noise visual oddball event-related potentials reveal gradual changes in morphology from trial to trial (especially for N1-P2 and N2-P3 waves at $Fz$), which can be hypothetically linked to attention or decision processes. The new noise reduction method is, thus, shown to be particularly suited for recovering single-event features in nonstationary low SNR multievent contexts.