Databases Reference
In-Depth Information
1.5
T
−
T
T
−1.5
T
F I GU R E 16 . 9
A three-level midtread quantizer.
2
log
2
c
max
T
0
=
(1)
This selection guarantees that the largest coefficient will lie in the interval
[
T
0
,
2
T
0
)
. In each
pass, the threshold
T
i
is reduced to half the value it had in the previous pass:
1
2
T
i
−
1
T
i
=
(2)
For a given value of
T
i
, we assign one of four possible labels to the coefficients:
significant
positive (sp), significant negative (sn), zerotree root (zr)
, and
isolated zero (iz)
.Ifweusea
fixed-length code, we need 2 bits to represent each of the labels. Note that when a coefficient
is labeled a zerotree root, we do not need to label its descendants. This assignment is referred
to as
significance map coding
.
We can view the significancemap coding in part as quantization using a three-level midtread
quantizer. This situation is shown in Figure
16.9
. The coefficients labeled
significant
are simply
those that fall in the outer levels of the quantizer and are assigned an initial reconstructed
value of 1
5
T
i
, depending on whether the coefficient is positive or negative. Note
that selecting
T
i
according to (
1
) and (
2
) guarantees the significant coefficients will lie in
the interval
.
5
T
i
or
−
1
.
. Once a determination of significance has been made, the significant
coefficients are included in a list for further refinement in the refinement or subordinate passes.
In the refinement pass, we determine whether the coefficient lies in the upper or lower half
of the interval
[
T
,
2
T
]
. In successive refinement passes, as the value of
T
is reduced, the
interval containing the significant coefficient is narrowed still further and the reconstruction is
updated accordingly. An easy way to perform the refinement is to take the difference between
the coefficient value and its reconstruction and quantize it using a two-level quantizer with
reconstruction values
[
T
,
2
T
]
±
T
/
4. This quantized value is then added on to the current reconstruction
value as a correction term.
