Wavelet based multivariate signal denoising using Mahalanobis distance and EDF statistics

TY - JOUR

T1 - Wavelet based multivariate signal denoising using Mahalanobis distance and EDF statistics

AU - Naveed, Khuram

AU - Rehman, Naveed Ur

PY - 2020/10

Y1 - 2020/10

N2 - 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 RM to a single-dimensional space of positive real numbers R+ , i.e., RM→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

AB - 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 RM to a single-dimensional space of positive real numbers R+ , i.e., RM→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

KW - Denoising

KW - Discrete wavelet transform

KW - Goodness of fit (GoF) test

KW - Mahalanobis distance

KW - Multiscale

KW - Multivariate

UR - http://www.scopus.com/inward/record.url?scp=85105854619&partnerID=8YFLogxK

U2 - 10.1109/TSP.2020.3029659

DO - 10.1109/TSP.2020.3029659

M3 - Journal article

SN - 1053-587X

VL - 68

SP - 5997

EP - 6010

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

M1 - 9234624

ER -