Databases Reference
In-Depth Information
Theremay be some vector inputs that can bewell represented by fewer stages than others. A
multistage vector quantizer with a variable number of stages can be implemented by extending
the idea of recursively indexed scalar quantization to vectors. It is not possible to do this
directly because there are some fundamental differences between scalar and vector quantizers.
The input to a scalar quantizer is assumed to be
iid
. On the other hand, the vector quantizer can
be viewed as a pattern-matching algorithm [
162
]. The input is assumed to be one of a number
of different patterns. The scalar quantizer is used after the redundancy has been removed from
the source sequence, while the vector quantizer takes advantage of the redundancy in the data.
With these differences in mind, the recursively indexed vector quantizer (RIVQ) can be
described as a two-stage process. The first stage performs the normal pattern-matching func-
tion, while the second stage recursively quantizes the residual if the magnitude of the residual
is greater than some prespecified threshold. The codebook of the second stage is ordered so
that the magnitude of the codebook entries is a nondecreasing function of its index. We then
choose an index
I
that will determine the mode in which the RIVQ operates.
The quantization rule
Q
, for a given input value
x
, is as follows:
Quantize
x
with the first-stage quantizer
Q
1
.
If the residual
x
−
Q
1
(
x
)
is below a specified threshold, then
Q
1
(
x
)
is the nearest
output level.
Otherwise, generate
x
1
=
and quantize using the second-stage quantizer
Q
2
.
Check if the index
J
1
of the output is below the index
I
.Ifso,
x
−
Q
1
(
x
)
Q
(
x
)
=
Q
1
(
x
)
+
Q
2
(
x
1
)
If not, form
x
2
=
x
1
−
Q
(
x
1
)
and do the same for
x
2
as we did for
x
1
.
This process is repeated until for some
m
, the index
J
m
falls below the index
I
, in which
case
x
will be quantized to
Q
(
x
)
=
Q
1
(
x
)
+
Q
2
(
x
1
)
+···+
Q
2
(
x
M
)
Thus, the RIVQ operates in two modes: when the index
J
of the quantized input falls below
a given index
I
and when the index
J
falls above the index
I
.
Details on the design and performance of the recursively indexed vector quantizer can be
found in [
163
,
164
].
10.7.5 Adaptive Vector Quantization
While LBG vector quantizers function by using the structure in the source output, this reliance
on the use of the structure can also be a drawback when the characteristics of the source change
