The most important limitation of the proposed VMD is
with boundary effects, and sudden signal onset in general.
This is strongly related to the use of an L2-based smoothness
term, that overly penalizes jumps at the domain borders and
within; conversely, this is also reflected by implicit periodicity
assumptions when optimizing in Fourier domain, and by the
narrow-band violation caused by discontinuous envelopes in
such AM-FM signals. Another point that critics might high-
light, is the required explicit (manual) selection of the number
of active modes in the decomposition, like in EWT but as
opposed to EMD. Current work addresses these shortcomings,
and we are also working on suitable extensions to signals on
domains of dimension greater than one.