TY - JOUR

T1 - A statistical approach to signal denoising based on data-driven multiscale representation

AU - Naveed, Khurram

AU - Akhtar, Muhammad Tahir

AU - Siddiqui, Muhammad Faisal

AU - Rehman, Naveed Ur

PY - 2021/1

Y1 - 2021/1

N2 - 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.

AB - 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.

KW - Cramer Von Mises (CVM) statistic

KW - Empirical distribution function (EDF)

KW - Goodness of fit test (GoF) test

KW - Variational mode decomposition (VMD)

UR - http://www.scopus.com/inward/record.url?scp=85096234610&partnerID=8YFLogxK

U2 - 10.1016/j.dsp.2020.102896

DO - 10.1016/j.dsp.2020.102896

M3 - Journal article

AN - SCOPUS:85096234610

SN - 1051-2004

VL - 108

JO - Digital Signal Processing

JF - Digital Signal Processing

M1 - 102896

ER -