Databases Reference
In-Depth Information
If the problem with the encoding of the image decomposed by the Johnston filter is
an insufficient number of bits for encoding the low-low band, why not simply assign both
bits to the low-low band? The problem is that the bit allocation scheme assigned a bit to
the high-low band because there was a significant amount of information in that band. If
both bits were assigned to the low-low band, we would have no bits left for use in encod-
ing the high-low band, and we would end up throwing away information necessary for the
reconstruction.
The issue of energy compaction becomes a very important factor in reconstruction quality.
Filters that allow for more energy compaction permit the allocation of bits to a smaller number
of subbands. This in turn results in a better reconstruction.
The coding schemes used in this example were DPCM and scalar quantization, the tech-
niques generally preferred in subband coding. The advantage provided by subband coding
is readily apparent if we compare the result shown in Figure
14.33
to results in the previous
chapters where we used either DPCM or scalar quantization without prior decomposition.
It would appear that the subband approach lends itself naturally to vector quantization.
After decomposing an image into subbands, we could design separate codebooks for each
subband to reflect the characteristics of that particular subband. The only problemwith this idea
is that the low-lowsubband generally requires a large number of bits per pixel. Aswementioned
in Chapter 10, it is generally not feasible to operate the nonstructured vector quantizers at high
rates. Therefore, when vector quantizers are used, they are generally used only for encoding
the higher frequency bands. This may change as vector quantization algorithms that operate
at higher rates are developed.
14.13 Summary
In this chapter we introduced another approach to the decomposition of signals. In subband
coding we decompose the source output into components. Each of these components can
then be encoded using one of the techniques described in the previous chapters. The general
subband encoding procedure can be summarized as follows:
Select a set of filters for decomposing the source. We have provided a number of filters
in this chapter. Many more filters can be obtained from the published literature (we give
some references below).
Using the filters, obtain the subband signals
{
y
k
,
n
}
:
N
−
1
y
k
,
n
=
h
k
,
i
x
n
−
i
(119)
i
=
0
where
{
h
k
,
n
}
are the coefficients of the
k
th filter.
