Signal denoising is one of the most important issues in signal processing, and various techniques have been proposed to address this issue. A combined method involving wavelet decomposition and multiscale principal component analysis (MSPCA) has been proposed and exhibits a strong signal denoising performance. This technique takes advantage of several signals that have similar noises to conduct denoising; however, noises are usually quite different between signals, and wavelet decomposition has limited adaptive decomposition abilities for complex signals. To address this issue, we propose a signal denoising method based on ensemble empirical mode decomposition (EEMD) and MSPCA. The proposed method can conduct MSPCA-based denoising for a single signal compared with the former MSPCA-based denoising methods. The main steps of the proposed denoising method are as follows: First, EEMD is used for adaptive decomposition of a signal, and the variance contribution rate is selected to remove components with high-frequency noises. Subsequently, the Hankel matrix is constructed on each component to obtain a higher order matrix, and the main score and load vectors of the PCA are adopted to denoise the Hankel matrix. Next, the PCA-denoised component is denoised using soft thresholding. Finally, the stacking of PCA- and soft thresholding-denoised components is treated as the final denoised signal. Synthetic tests demonstrate that the EEMD-MSPCA-based method can provide good signal denoising results and is superior to the low-pass filter, wavelet reconstruction, EEMD reconstruction, Hankel–SVD, EEMD-Hankel–SVD, and wavelet-MSPCA-based denoising methods. Moreover, the proposed method in combination with the AIC picking method shows good prospects for processing microseismic waves.

中文翻译：

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基于EMD和多尺度PCA的信号去噪方法及其在地震P相到达拾取中的应用

信号去噪是信号处理中最重要的问题之一，已经提出了各种技术来解决这个问题。提出了一种涉及小波分解和多尺度主成分分析（MSPCA）的组合方法，并表现出很强的信号去噪性能。该技术利用几个具有相似噪声的信号进行去噪；然而，信号之间的噪声通常有很大差异，小波分解对复杂信号的自适应分解能力有限。为了解决这个问题，我们提出了一种基于集成经验模式分解（EEMD）和 MSPCA 的信号去噪方法。与之前基于 MSPCA 的去噪方法相比，所提出的方法可以对单个信号进行基于 MSPCA 的去噪。所提出的去噪方法的主要步骤如下：首先，利用EEMD对信号进行自适应分解，选择方差贡献率去除高频噪声成分。随后，在每个分量上构造Hankel矩阵，得到一个高阶矩阵，并采用PCA的主得分和载荷向量对Hankel矩阵进行去噪。接下来，使用软阈值对 PCA 去噪分量进行去噪。最后，PCA 和软阈值去噪分量的叠加被视为最终的去噪信号。综合测试表明，基于EEMD-MSPCA的方法可以提供良好的信号去噪结果，并且优于低通滤波器、小波重建、EEMD重建、Hankel-SVD、EEMD-Hankel-SVD和基于小波-MSPCA的去噪方法。而且，