Digital Signal Processing Reference
In-Depth Information
j = 3
j = 2
j = 1
(a)
(b)
(c)
FIGURE 10.9
(a) The pyramid representation of dyadic image blocks. (b) Wavelet subtree. (c) 2D HMT.
In particular, wavelet-domain HMT was used to obtain the statistical multi-
scale characterization regarding the likelihood function
f
y
(
n
)
|
x
(
n
)
=
. Using
the Haar DWT of the best spatial localizability, an image can be recursively
divided into four subimages of the same size
J
times and represented in a
pyramid of
J
scales, as shown in Figure 10.9a. We denote a dyadic block at
scale
n
as
y
(
n
)
. Given a set of Haar wavelet coefficients
w
and a set of HMT
model parameters
(
c
)
, the dyadic block
y
(
n
)
θ
is associated with three wavelet
LH
,
HL
,
HH
subtrees
. The three wavelet subtrees are rooted in the tree
wavelet coefficients of the same location and from three subbands at scale
n
.
Regarding the model likelihood in Equation 10.29, the computation
f
{T
T
T
}
y
n
(
|
θ)
is a realization of the HMT model
θ
and is obtained by
f
T
(
n
)
LH
f
T
(
n
)
HL
f
T
(
n
)
HH
,
y
(
n
)
|
θ)
=
LH
HL
HH
(
|
θ
|
θ
|
θ
f
(10.30)
where it is assumed that three wavelet subbands are independent and each
component in Equation 10.30 can be computed based on the closed formula
in Reference 1.
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