Databases Reference
In-Depth Information
0
1
1
0
0
1
Sign bit
msb
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
2
−5
−2 5
6
29
−20
F I GU R E 16 . 15
Embedded coding of quantization values 2,
−
5,
−
25, 6, 29,
and
−
20.
16.5.4 Quantization
The coefficients are quantized using a midtread quantizer in which the step-sizes are uni-
form except for the middle step size, which is twice the size. The quantization index can be
generated as
,v))
|
a
b
(
,v)
|
b
u
q
b
(
u
,v)
=
sign
(
a
b
(
u
b
where
a
b
(
u
,v)
is the coefficient at location
(
u
,v)
in subband
b
,
b
is the step size, and
q
b
(
u
,v)
is the quantization index. The reconstructed value
a
b
(
ˆ
u
,v)
can be obtained from the
quantization index by
a
b
(
ˆ
u
,v)
=
(
q
b
(
u
,v)
+
δ
b
)
where
and is usually taken to be 0.5 [
220
]. The
quantized values are encoded in an embedded manner as shown in Figure
16.15
.
The assumption implicit in the example in Figure
16.15
is that the highest resolution or
depth is five. The value of
δ
b
can take on a value in the interval
[
0
,
1
)
b
is 1. The encoder scans the most significant bit of each quantized
value, then the next most significant bit, and so on. When a quantized value first becomes
significant, the encoder encodes a sign bit. Truncating the bitstream is effectively equivalent
to multiplying the step size by 2
discard
where
discard
is the number of bitplanes discarded. In
this example, if we truncated the bitstream after the first two rows, we would obtain quantized
values of 0, 0,
−
24, 0, 24, and
−
16. As we are discarding three bitplanes these would be the
results one would expect with
b
=
8.
