Sahoo Gyana Ranjan, Freed Jack H, Srivastava Madhur
Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853, USA.
National Biomedical Center for Advanced ESR Technology, Cornell University, Ithaca, NY 14853, USA.
IEEE Access. 2024;12:45369-45380. doi: 10.1109/access.2024.3377664. Epub 2024 Mar 18.
Wavelet denoising plays a key role in removing noise from signals and is widely used in many applications. In denoising, selection of the mother wavelet is desirable for maximizing the separation of noise and signal coefficients in the wavelet domain for effective noise thresholding. At present, wavelet selection is carried out in a heuristic manner or using a trial-and-error that is time consuming and prone to error, including human bias. This paper introduces a universal method to select optimal wavelets based on the sparsity of Detail components in the wavelet domain, an empirical approach. A mean of sparsity change ( ) parameter is defined that captures the mean variation of noisy Detail components. The efficacy of the presented method is tested on simulated and experimental signals from Electron Spin Resonance spectroscopy at various SNRs. The results reveal that the values of signal vary abruptly between wavelets, whereas for noise it displays similar values for all wavelets. For low Signal-to-Noise Ratio (SNR) data, the change in between highest and second highest value is ≈ 8 - 10% and for high SNR data it is around 5%. The mean of sparsity change increases with the SNR of the signal, which implies that multiple wavelets can be used for denoising a signal, whereas, the signal with low SNR can only be efficiently denoised with a few wavelets. Either a single wavelet or a collection of optimal wavelets (i.e., top five wavelets) should be selected from the highest values. The code is available on GitHub and the signalsciencelab.com website.
小波去噪在去除信号噪声方面起着关键作用，并且在许多应用中被广泛使用。在去噪过程中，选择母小波对于在小波域中最大化噪声和信号系数的分离以实现有效的噪声阈值处理是很有必要的。目前，小波选择是以启发式方式进行的，或者采用试错法，这既耗时又容易出错，还包括人为偏差。本文介绍了一种基于小波域中细节分量稀疏性的通用方法来选择最优小波，这是一种经验方法。定义了一个稀疏性变化均值（ ）参数，它捕捉有噪声细节分量的均值变化。在不同信噪比下，对来自电子自旋共振光谱的模拟信号和实验信号测试了所提出方法的有效性。结果表明，信号的 值在不同小波之间变化剧烈，而对于噪声，所有小波的 值都相似。对于低信噪比（SNR）数据，最高值和次高值之间的 变化约为8 - 10%，对于高信噪比数据，该变化约为5%。稀疏性变化均值随信号的信噪比增加，这意味着多个小波可用于对信号进行去噪，而低信噪比的信号只能用少数小波有效地去噪。应从最高 值中选择单个小波或一组最优小波（即前五个小波）。代码可在GitHub和signalsciencelab.com网站上获取。
