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

Khuram Naveed, Muhammad Tahir Akhtar, Muhammad Faisal Siddiqui, Naveed ur Rehman

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


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.

Original languageEnglish
Article number102896
JournalDigital Signal Processing: A Review Journal
Publication statusPublished - Jan 2021


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

ASJC Scopus subject areas

  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics
  • Electrical and Electronic Engineering
  • Artificial Intelligence
  • Applied Mathematics


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