We develop a data-driven approach for signal denoising that utilizes variational mode decomposition (VMD) algorithm and Cramer Von Misses (CVM) statistic. In comparison with the classical empirical mode decomposition (EMD), VMD enjoys superior mathematical and theoretical framework that makes it robust to noise and mode mixing. These desirable properties of VMD materialize in segregation of a major part of noise into a few final modes while majority of the signal content is distributed among the earlier ones. To exploit this representation for denoising purpose, we propose to estimate the distribution of noise from the predominantly noisy modes and then use it to detect and reject noise from the remaining modes. The proposed approach first selects the predominantly noisy modes using the CVM measure of statistical distance. Next, CVM statistic is used locally on the remaining modes to test how closely the modes fit the estimated noise distribution; the modes that yield closer fit to the noise distribution are rejected (set to zero). Extensive experiments demonstrate the superiority of the proposed method as compared to the state of the art in signal denoising and underscore its utility in practical applications where noise distribution is not known a priori.

我们开发了一种数据驱动的信号降噪方法，该方法利用了变分模式分解（VMD）算法和Cramer Von Misses（CVM）统计信息。与经典的经验模式分解（EMD）相比，VMD具有卓越的数学和理论框架，使其对噪声和模式混合具有鲁棒性。VMD的这些理想特性会在将大部分噪声分离为几种最终模式的同时，大部分信号内容分布在较早的模式中。为了将这种表示用于降噪目的，我们建议估计主要来自噪声模式的噪声分布，然后将其用于检测和拒绝其余模式的噪声。所提出的方法首先使用统计距离的CVM量度选择主要的噪声模式。下一个，在其余模式上本地使用CVM统计信息，以测试这些模式与估计的噪声分布的拟合程度；产生更适合噪声分布的模式将被拒绝（设置为零）。广泛的实验证明，与现有技术相比，该方法在信号降噪方面具有优势，并突显了其在先验未知噪声的实际应用中的实用性。