III.- MISSING DATA SCENARIO
VIDEO 2, VIDEO
3.
If parts of the spectrogram are corrupted
or missing like in figure 5 a) we can "fill in" those values
by considering the correspondent parts
of variables X as hidden, and propagating continuous
"belief" messages from and to the hidden
nodes, we use again belief propagation. The posteriors
of the continuous hidden nodes is approximated
using gaussian distributions. The missing values
are then "filled in" with the means
of their posterior distributions. Check the full sequence of
iterations on Video 2.
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Figure 5
a) Original Occluded Signal
b) Filled in signal after 5 iterations
c) Filled in signal after 10 iterations
d) Filled in signal after 20 iterations
e) Filled in signal after 30 iterations
f) Filled in signal after 40 iterations
The video presents the missing data application
using a single layer model. This time four panels are
used. Panel 1 is first used to defined
the missing regions, once the "Fill In" button is pressed the
missing regions are estimated with the
"filled in" values. Panel 2, as before, shows the local
likelihood potentials.When
the observation of a particular time-frequency bin is missed, no reliable
local likelihood potential can be estimated,
and therefore any local "belief" regarding the identity
of the correct transformation can be
transmitted to the correspondent transformation node. Then,
we set the correspondent messages from
the local likelihood potentials to the transformation nodes
as uniform. The transformation posteriors
(Panel 3) are estimated as before using the "new" local
likelihood potentials, therefore the
transformation posteriors on the "missing" regions are driven
entirely by the transformation "beliefs"
of their reliable neighbors. We keep the transformation
posteriors fixed and then we start propagating
the continuous messages and the missing values begin
to be filled. Once
we have some "meaningful" information on the missing regions we start to
calculate the local potentials on the
missing regions using the "filled in" values and the
transformation posteriors are frequently
reestimated. Panel 4 shows the original signal for
comparison purposes only.
VIDEO 2.- Missing Data Application.
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ACTIVE THE VIDEO !
This is one is similar to the previous
one, it also shows the "fill in" application with a single
layer. The purpose of this video is
to illustrate that belief propagation is not "magic", and
that when a single missing region is
too big, the reliable neighbors are too far apart to propagate
the right transformations "beliefs"
to their missing neighbors. However the perceptual
results obtained are significantly better
than the signal with "missing regions".
VIDEO 3.- Missing Data Application. Severe Case
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