  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.
