Information Technology Reference
In-Depth Information
Unlike the above description, which defines the wavelet transform as a se-
quence of filtering and subsampling operations, the JPEG 2000 standard specifies
its supported wavelet transforms in terms of their lifting implementation [19]. A
lifting implementation of the wavelet transform allows in-place execution, re-
quires less computations and allows for reversible operation, which is needed for
lossless compression. Two different transforms are supported, i.e. the irreversible
CDF 9/7 transform and the reversible CDF 5/3 transform [20, 21]. Lossless com-
pression requires the use of the reversible CDF 5/3 transform. For lossy compres-
sion, the CDF 9/7 transform is typically preferred.
After the transform, the resulting set of coefficients is divided into code-blocks
C
which are typically chosen to be 32 by 32 or 64 by 64 coefficients in size.
Each of these code-blocks is thereafter independently coded using embedded bit-
plane coding. This means that the wavelet coefficients
()
≤< are coded
in a bit-plane by bit-plane manner by successive comparison to a series of dyadi-
cally decreasing thresholds of the form
ci
,0
i N
()
2
p
T
=
. A wavelet coefficient
cj
is
p
called significant with respect to a threshold
T
if its absolute value is larger than
or equal to this threshold.
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q
TpqM
,
<≤
q
TpqM
,
<≤
Fig. 6
Application of the different coding passes in JPEG 2000
Encoding starts with the most significant bit-plane
M
and its corresponding
threshold
(
)
(
( )
⎢
⎥
2
M
=
⎢
⎣ ⎦
. Bit-plane
p
of the wavelet
coefficients in each block is encoded using a succession of three coding passes.
First, the significance propagation pass codes the significance of the coefficients
which (
i
) were not significant with respect to any of the previous thresholds
,
T
=
, with
M
log
ma
iN
c i
2
0
≤<
and (
ii
) are adjacent to at least one other coefficient which was al-
ready significant with respect to one of the previous thresholds
q
Tpq M
<≤
.
Additionally, when a coefficient becomes significant with respect to
T
, its sign is
also coded. In the magnitude refinement pass, all coefficients that were significant
with respect to one of the previous thresholds
q
Tpq M
,
<≤
q
Tpq M
,
<≤
are refined by
