Comparative evaluation of different wavelet thresholding methods for neural signal processing

Neural signal decoding is the basis for the development of neuroprosthetic devices and systems. Depending on the part of the nervous system these signals are picked up from, different signal-to-noise ratios (SNR) can be experienced. Wavelet denoising is often adopted due to its capability of reducing, to some extent, the noise falling within the signal spectrum. Several variables influence the denoising quality, but usually the focus in on the selection of the best performing mother wavelet. However, the threshold definition and the way it is applied to the signal have a significant impact on the denoising quality, determining the amount of noise removed and the distortion introduced on the signal. This work presents a comparative analysis of different threshold definition and thresholding mechanisms on neural signals, either largely adopted for neural signal processing or not. In order to evaluate the quality of the denoising in terms of the introduced distortion, which is important when decoding is implemented through spike-sorting algorithms, a synthetic dataset built on real action potentials was used, creating signals with different SNR and characterized by an additive white Gaussian noise (AWGN). The obtained results reveal the superiority of an approach, originally conceived for noisy non-linear time series, over the more typical ones. When compared to the original signal, a correlation above 0.9 was obtained, while in terms of root mean square error (RMSE) an improvement of 13% and 33% was reported with respect to the Minimax and Universal thresholds respectively.