2024 | GYANA RANJAN SAHOO, JACK H. FREED, MADHUR SRIVASTAVA
This paper introduces a universal method for selecting optimal wavelets based on the sparsity of detail components in the wavelet domain. The method, which is an empirical approach, defines a mean of sparsity change (μₛ) parameter to capture the mean variation of noisy detail components. The efficacy of the method is tested on simulated and experimental signals from Electron Spin Resonance (ESR) spectroscopy at various Signal-to-Noise Ratios (SNRs). The results show that μₛ values of signals vary abruptly between wavelets, while noise displays similar values for all wavelets. For low SNR data, the change in μₛ between the highest and second-highest values is approximately 8-10%, and for high SNR data, it is around 5%. The mean of sparsity change increases with the SNR of the signal, indicating that multiple wavelets can be used for denoising a signal, but low SNR signals can only be efficiently denoised with a few wavelets. The optimal wavelet or a collection of optimal wavelets (top five wavelets) should be selected from the highest μₛ values. The code for this method is available on GitHub and the signalsciencelab.com website.
Wavelet selection; decomposition level selection; detail components; signal denoising; sparsity; wavelet denoising; wavelet transform
Wavelet denoising is widely used to improve Signal-to-Noise Ratio (SNR) without distorting the signal. The efficacy of denoising depends on factors such as the mother wavelet, decomposition level, and thresholding criteria. Current methods for wavelet selection are heuristic or trial-and-error, leading to sub-optimal results. This paper presents a generalized method to select the optimal mother wavelet function for denoising using a sparsity parameter to quantify the separation between signal and noisy detail coefficients. The method calculates the mean of sparsity change to identify the wavelet that yields maximum separation across decomposition levels. The sparsity change parameter helps determine the highest decomposition level that contains a noisy detail component. The optimal wavelet and five optimal wavelets are selected based on the highest mean of sparsity change (μₛ). The method is tested on simulated and experimental ESR signals, demonstrating its effectiveness in reducing noise and improving SNR.This paper introduces a universal method for selecting optimal wavelets based on the sparsity of detail components in the wavelet domain. The method, which is an empirical approach, defines a mean of sparsity change (μₛ) parameter to capture the mean variation of noisy detail components. The efficacy of the method is tested on simulated and experimental signals from Electron Spin Resonance (ESR) spectroscopy at various Signal-to-Noise Ratios (SNRs). The results show that μₛ values of signals vary abruptly between wavelets, while noise displays similar values for all wavelets. For low SNR data, the change in μₛ between the highest and second-highest values is approximately 8-10%, and for high SNR data, it is around 5%. The mean of sparsity change increases with the SNR of the signal, indicating that multiple wavelets can be used for denoising a signal, but low SNR signals can only be efficiently denoised with a few wavelets. The optimal wavelet or a collection of optimal wavelets (top five wavelets) should be selected from the highest μₛ values. The code for this method is available on GitHub and the signalsciencelab.com website.
Wavelet selection; decomposition level selection; detail components; signal denoising; sparsity; wavelet denoising; wavelet transform
Wavelet denoising is widely used to improve Signal-to-Noise Ratio (SNR) without distorting the signal. The efficacy of denoising depends on factors such as the mother wavelet, decomposition level, and thresholding criteria. Current methods for wavelet selection are heuristic or trial-and-error, leading to sub-optimal results. This paper presents a generalized method to select the optimal mother wavelet function for denoising using a sparsity parameter to quantify the separation between signal and noisy detail coefficients. The method calculates the mean of sparsity change to identify the wavelet that yields maximum separation across decomposition levels. The sparsity change parameter helps determine the highest decomposition level that contains a noisy detail component. The optimal wavelet and five optimal wavelets are selected based on the highest mean of sparsity change (μₛ). The method is tested on simulated and experimental ESR signals, demonstrating its effectiveness in reducing noise and improving SNR.