💥1 概述
文献来源：
摘要:
本文提出了一种多变量信号去噪方法，该方法采用了一种新颖的基于多变量适应度检验 (GoF) 的方法，该方法在离散小波变换 (DWT) 获得的多个数据尺度上应用。在所提出的多变量GoF测试中，我们首先利用平方马氏距离 (MD) 度量将输入的多变量数据从 M 维空间 R M 转换为正实数的单维空间 R + ，即 R M → R + ，其中 M > 1。由于MD度量的性质，R + 中的转换数据遵循着独特的分布。这使得我们能够应用基于经验分布函数 (EDF) 的统计量来进行GoF测试，从而定义一个多元正态性测试。我们进一步提出在从离散小波变换获得的多个输入数据尺度上局部应用上述测试，从而得到一个多变量信号去噪框架。在所提出的方法中，参考累积分布函数 (CDF) 被定义为多变量高斯随机过程的二次转换。因此，所提出的方法检查一组DWT系数是否属于多元参考分布，将属于参考分布的系数丢弃。我们通过对合成和真实世界数据集进行广泛模拟实验，证明了我们提出的方法的有效性。
原文摘要：
Abstract:
A multivariate signal denoising method is proposed which employs a novel multivariate goodness of fit (GoF) test that is applied at multiple data scales obtained from discrete wavelet transform (DWT). In the proposed multivariate GoF test, we first utilize squared Mahalanobis distance (MD) measure to transform input multivariate data residing in M-dimensional space R M to a single-dimensional space of positive real numbers R + , i.e., R M → R + , where M > 1. Owing to the properties of the MD measure, the transformed data in R + follows a distinct distribution. That enables us to apply the GoF test using statistic based on empirical distribution function (EDF) on the resulting data in order to define a test for multivariate normality. We further propose to apply the above test locally on multiple input data scales obtained from discrete wavelet transform, resulting in a multivariate signal denoising framework. Within the proposed method, the reference cumulative distribution function (CDF) is defined as a quadratic transformation of multivariate Gaussian random process. Consequently, the proposed method checks whether a set of DWT coefficients belong to multivariate reference distribution or not; the coefficients belonging to the reference distribution are discarded. The effectiveness of our proposed method is demonstrated by performing extensive simulations on both synthetic and real world datasets.
📚2 运行结果
其他情况就不一一展示。
🎉3 参考文献
部分理论来源于网络，如有侵权请联系删除。
[1]K. Naveed and N. u. Rehman, "Wavelet Based Multivariate Signal Denoising Using Mahalanobis Distance and EDF Statistics," in IEEE Transactions on Signal Processing, vol. 68, pp. 5997-6010, 2020, doi: 10.1109/TSP.2020.3029659.
