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

Naveed K. Akhtar M.T. Siddiqui M.F. ur Rehman N.
January 2021 Elsevier Inc.

Digital Signal Processing: A Review Journal
2021 #108

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.

Cramer Von Mises (CVM) statistic , Empirical distribution function (EDF) , Goodness of fit test (GoF) test , Variational mode decomposition (VMD)

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Department of Electrical and Computer Engineering, COMSATS University Islamabad (CUI), Park Road, Islamabad, Pakistan
Department of Electrical and Computer Engineering, School of Engineering & Digital Sciences, Nazarbayev University, Kabanbay Batyr Avenue 53, Nur-Sultan City, Kazakhstan
Department of Engineering, Electrical and Computer Engineering, Aarhus University, Aarhus, Denmark

Department of Electrical and Computer Engineering
Department of Electrical and Computer Engineering
Department of Engineering

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