Digital Signal Processing Reference
In-Depth Information
According to the above visual model, JND threshold should be calculated for each
coefficient. In HL subband block coefficients greater than their corresponding JND
are visible and are chosen. In LH and HH subband coefficients greater than their cor-
responding JND multiply by 1.2 are selected [13]. In this way it can allocate more bits
to the area that human eyes are sensitive and do not allocate bit to the invisible area.
Moreover the perceptual distortion metric between the original coefficient and the
recovered coefficient is introduced in the proposed algorithm. It can be defined as
1
β
e
(, ,,)
ξθ
ξθ
i j
β
D
=
|
|
(, ,,)
(4)
Fnn
(,)
t
i j
12
JND
(,,,)
ξθ
ij F
∈
Where
F
(
n
1
,
n
2
) denotes the area in the spatial domain that is centered at location
(
n
1
,
n
2
), ( ,
ξθ and
F
is the set of
DWT coefficients whose values affect the
F
(
n
1
,
n
2
) reconstruction.
Then the perceptual rate-distortion cost
J
p
is
e
ξθ
, ,
i j
)
is the quantization error at location ( ,
, ,
ij
)
J
=
D
+
λ
×
R
(5)
p
Fn n
(,)
12
where the output rate
R
can be approximated by the theoretical first-order entropy.
1
=−
HX A
(|
)
PA
()
Px A
(|
l g (|
Px A
)
(6)
i
i
i
2
i
=
0
x
∈
A
i
where
A
is the superset[1]. From Eqn.(5), it can be seen that the human vision charac-
teristics is considered in the rate distortion optimization. Then the PRDOTCQ
algorithm can allocate more bits to the area that human eyes are more sensitive and
allocate less bits to the area that human eyes are less sensitive.
With the above discussion, the PRDOTCQ algorithm can be divided into two parts.
Firstly, the transformed coefficients are classified according to JND threshold. Only
the coefficients greater than the threshold are retained. Then the perceptual weighted
rate-distortion cost is used to optimize the trellis path selection. For a fixed λ
PRDOTCQ algorithm takes the following main steps:
1. Calculate JND threshold for each DWT transformed coefficient.
2. For all of the transformed coefficients detect if the coefficient is retained by com-
paring the transformed coefficient with the JND threshold.
If the coefficient in HL subband block is less than the JND, the coefficient is not
selected.
If the coefficient in LH and HH subband is less than the corresponding JND mul-
tiply by 1.2 , the coefficient is not selected.
3. Suppose the total state number is
N
s
and Initialize the
N
s
total cost
J
tot
(
i
) to 0, 0 ≤
i
≤
N
s
-1.
4. Estimate the rate for the signals falling into the predefined window.
5. Examine if the current sample located in the predefined window. If no, calculate
the distortion cost as the original quantization method; else compute the perceptual
weighted rate-distortion cost for all the subsets according to Eqn.(5).
