A Statistical Approach to Signal Denoising Based on Data-driven Multiscale Representation

TL;DR

This paper introduces a data-driven signal denoising method using variational mode decomposition and Cramer Von Misses statistic, effectively separating noise from signal without prior noise distribution knowledge.

Contribution

It proposes a novel denoising approach leveraging VMD and CVM statistic to estimate and reject noise modes, improving robustness over classical methods.

Findings

Outperforms state-of-the-art denoising techniques

Effectively segregates noise into specific modes

Works without prior noise distribution knowledge

Abstract

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.