Systematic analysis of wavelet denoising methods for neural signal processing

Objective: Among the different approaches for denoising neural signals, wavelet-based methods are widely used due to their ability to reduce in-band noise. All wavelet denoising algorithms have a common structure, but their effectiveness strongly depends on several implementation choices, including the mother wavelet, the decomposition level, the threshold definition, and the way it is applied (i.e., the thresholding). In this work, we investigated these factors to quantitatively assess their effects on neural signals in terms of noise reduction and morphology preservation, which are important when spike sorting is required downstream. Approach: Based on the spectral characteristics of the neural signal, according to the sampling rate of the signals, we considered two possible decomposition levels and identified the best-performing mother wavelet. Then, we compared different threshold estimation and thresholding methods and, for the best ones, we also evaluated their effect on clearing the approximation coefficients. The assessments were performed on synthetic signals that had been corrupted by different types of noise and on a murine peripheral nervous system dataset, both of which were sampled at about 16 kHz. The results were statistically analysed in terms of their Pearson's correlation coefficients, root-mean-square errors, and signal-to-noise ratios. Main results: As expected, the wavelet implementation choices greatly influenced the processing performance. Overall, the Haar wavelet with a 5-level decomposition, hard thresholding method, and the threshold proposed by Han et al. (2007) achieved the best outcomes. Based on the adopted performance metrics, wavelet denoising with these parametrizations outperformed conventional 300-3000 Hz linear bandpass filtering. Significance: These results can be used to guide the reasoned and accurate selection of wavelet denoising implementation choices in the context of neural signal processing, particularly when spike-morphology preservation is required.