Databases Reference
In-Depth Information
Rate
Rate
R
2
R
1
Distortion
Distortion
F I GU R E 14 . 28
Two rate distortion functions.
happens if we do not. Consider the two rate distortion functions shown in Figure
14.28
.
Suppose the points marked
x
on the rate distortion functions correspond to the selected rates.
Obviously, the slopes, and hence the values of
λ
, are different in the two cases. Because of
the differences in the slope, an increase by
R
in the rate
R
1
will result in a much larger
decrease in the distortion than the increase in distortion if we decreased
R
2
by
R
. Because
the total distortion is the sum of the individual distortions, we can therefore reduce the overall
distortions by increasing
R
1
and decreasing
R
2
. We will be able to keep doing this until the
slope corresponding to the rates is the same in both cases. Thus, the answer to our second
question is that we want to use the same value of
for all the subbands.
Given a set of rate distortion functions and a value of
λ
, we automatically get a set of
rates
R
k
. We can then compute the average and check if it satisfies our constraint on the total
number of bits we can spend. If it does not, we modify the value of
λ
λ
until we get a set of rates
that satisfies our rate constraint.
However, generally we do not have rate distortion functions available. In these cases we
use whatever is available. For some cases we might have
operational
rate distortion curves
available. By “operational” we mean performance curves for particular types of encoders
operating on specific types of sources. For example, if we know we are going to be using
pdf
-optimized nonuniform quantizers with entropy coding, we can estimate the distribution
of the subband and use the performance curve for
pdf
-optimized nonuniform quantizers for
that distribution. We might only have the performance of the particular encoding scheme for
a limited number of rates. In this case we need to have some way of obtaining the slope from
a few points. We could estimate this numerically from these points. Or we could fit the points
to a curve and estimate the slope from the curve. In these cases we might not be able to get
exactly the average rate we wanted.
Finally, we have been talking about a situation where the number of samples in each
subband is exactly the same, and therefore the total rate is simply the sum of the individual
