M3-4206
Candidate
Heming Wang | Applied Math, University of Waterloo
Title
A Novel Diffusion-based Empirical Mode Decomposition Algorithm for Signal and Image Analysis
Abstract
In
the
area
of
signal
analysis
and
processing,
the
Fourier
transform
and
wavelet
transform
are
widely
applied.
Empirical
Mode
Decomposition(EMD)
was
proposed
as
an
alternative
frequency
analysis
tool.
Although
shown
to
be
effective
when
analyzing
non-stationary
signals,
the
algorithmic
nature
of
EMD
makes
the
theoretical
analysis
and
formulation
difficult.
Futhermore,
it
has
some
limitations
that
affect
its
performance.
In
this
thesis,
we
introduce
some
methods
to
extend
or
modify
EMD,
in
an
effort
to
provide
a
rigorous
mathematical
basis
for
it,
and
to
overcome
its
shortcomings.
We
propose
a
novel
diffusion-based
EMD
algorithm
that
replaces
the
interpolation
process
by
a
diffusion
equation,
and
directly
construct
the
mean
curve
(surface)
of
a
signal
(image).
We
show
that
the
new
method
simplifies
the
mathematical
analysis,
and
provides
a
solid
theory
that
interprets
the
EMD
mechanism.
In
addition,
we
apply
the
new
method
to
the
1D
and
2D
signal
analysis
showing
its
possible
applications
in
audio
and
image
signal
processing.
Finally,
numerical
experiments
for
synthetic
and
real
signals
(both
1D
and
2D)
are
presented.
Simulation
results
demonstrate
that
our
new
algorithm
can
overcome
some
of
the
shortcomings
of
EMD,
and
require
much
less
computation
time.