Method of designing watermark in consideration of wiener attack and whitening filtered detection
View Patent ↗Disclosed a method of designing a watermark having the power spectral density optimized so that the detection performance can be improved by employing the whitening filtered detection after the Wiener attack. The power spectral density of the watermark is designed using an optimization method that can improve the entire detection performance by reflecting the gain of the whitening filter after the Wiener attack. A higher detection gain is obtained using the whitening filter after the Wiener attack, and the expected value of the difference between test statistics of the two hypotheses that the watermark exists and the watermark does not exist, respectively, is maximized to optimize the detection performance. Regarding the expected value of the difference between the test statistics as an objective function, the power spectral density of the watermark, which corresponds to a maximum differentiated value of the power spectral density of the watermark using the Lagrange multiplier method, is obtained.
1. A method of designing a watermark in consideration of the watermark being subjected to a Wiener attack and a whitening filtered detection, the method comprising the steps of:
defining an expected value of the difference between test statistics of two hypotheses where the watermark exists and where the watermark does not exist, respectively, as an objective function of the method;
calculating the objective function of the method for improving the detection performance by an equation using the power spectral density of an original signal and the power spectral density of the watermark; and
obtaining an optimized power spectral density of the watermark from the objective function using a Lagrange multiplier method.
2. The method as claimed in claim 1 , wherein the expected value of the difference of the test statistics is defined by the equation E[T 1 (y)−T 0 (y)], and is used as the objective function of the optimization method for improving the detection performance,
where
T
1
(
y
)
=
(
x
+
w
-
h
*
(
x
+
w
)
)
T
R
x
-
1
w
is the test statistic of the hypothesis where the watermark exists, and
T
0
(
y
)
=
(
x
-
h
*
x
)
T
R
x
-
1
w
is the test statistic of the hypothesis where the watermark does not exist.
3. The method as claimed in claim 1 , wherein the objective function is calculated by the equation
1
2
π
∫
-
π
π
Φ
w
(
Ω
)
Φ
x
(
Ω
)
+
Φ
w
(
Ω
)
ⅆ
Ω
,
where Φ x (Ω) is the power spectral density of the original signal, Φ w (Ω) is the power spectral density of the watermark, and Ω is a frequency within the range of [−π, π).
4. The method as claimed in claim 1 , wherein the power spectral density of the optimized watermark obtained from the objective function is calculated by the equation
Φ
w
(
Ω
)
=
-
Φ
x
(
Ω
)
+
Φ
x
(
Ω
)
1
2
π
∫
-
π
π
Φ
x
(
Ω
)
ⅆ
Ω
(
σ
x
2
+
σ
w
2
)
,
where σ x 2 is the variance of the original signal, and σ w 2 is the variance of the watermark.
5. A method of detecting a watermark, comprising:
designing the watermark, comprising:
defining an expected value of the difference between test statistics of two hypotheses where the watermark exists and where the watermark does not exist, respectively, as an objective function of the method;
calculating the objective function of the method for improving the detection performance by an equation using the power spectral density of an original signal and the power spectral density of the watermark; and
obtaining an optimized power spectral density of the watermark from the objective function using a Lagrange multiplier method; and
filtering the watermark from the original signal to detect the watermark.
6. The method as claimed in claim 5 , wherein the step of filtering the watermark further comprising filtering the watermark using a whitening filter.
7. The method as claimed in claim 5 , wherein the expected value of the difference of the test statistics is defined by the equation E[T 1 (y)−T 0 (y)], and is used as the objective function of the optimization method for improving the detection performance,
where
T
1
(
y
)
=
(
x
+
w
-
h
*
(
x
+
w
)
)
T
R
x
-
1
w
is the test statistic of the hypothesis where the watermark exists, and
T
0
(
y
)
=
(
x
-
h
*
x
)
T
R
x
-
1
w
is the test statistic of the hypothesis where the watermark does not exist.
8. The method as claimed in claim 5 , wherein the objective function is calculated by the equation
1
2
π
∫
-
π
π
Φ
w
(
Ω
)
Φ
x
(
Ω
)
+
Φ
w
(
Ω
)
ⅆ
Ω
,
where Φ x (Ω) is the power spectral density of the original signal, Φ w (Ω) is the power spectral density of the watermark, and Ω is a frequency within the range of [−π, π).
9. The method as claimed in claim 5 , wherein the power spectral density of the optimized watermark obtained from the objective function is calculated by the equation
Φ
w
(
Ω
)
=
-
Φ
x
(
Ω
)
+
Φ
x
(
Ω
)
1
2
π
∫
-
π
π
Φ
x
(
Ω
)
ⅆ
Ω
(
σ
x
2
+
σ
w
2
)
,
where σ x 2 is the variance of the original signal, and σ w 2 is the variance of the watermark.
10. A method of detecting a watermark, comprising:
designing the watermark, comprising:
defining an expected value of the difference between test statistics of two hypotheses where the watermark exists and where the watermark does not exist, respectively, as an objective function of the method;
calculating the objective function of the method for improving the detection performance by an equation using the power spectral density of an original signal and the power spectral density of the watermark; and
obtaining an optimized power spectral density of the watermark from the objective function using a Lagrange multiplier method; and
subjecting the watermark to a Weiner attack; and
filtering the watermark from the original signal to detect the watermark.
11. The method as claimed in claim 10 , wherein the step of filtering the watermark further comprising filtering the watermark using a whitening filter.
12. The method as claimed in claim 10 , wherein the expected value of the difference of the test statistics is defined by the equation E[T 1 (y)−T 0 (y)], and is used as the objective function of the optimization method for improving the detection performance,
where
T
1
(
y
)
=
(
x
+
w
-
h
*
(
x
+
w
)
)
T
R
x
-
1
w
is the test statistic of the hypothesis where the watermark exists, and T 0 (y)=(x−h*x) T R x −1 w is the test statistic of the hypothesis where the watermark does not exist.
13. The method as claimed in claim 10 , wherein the objective function is calculated by the equation
1
2
π
∫
-
π
π
Φ
w
(
Ω
)
Φ
x
(
Ω
)
+
Φ
w
(
Ω
)
ⅆ
Ω
,
where Φ x (Ω) is the power spectral density of the original signal, Φ w (Ω) is the power spectral density of the watermark, and Ω is a frequency within the range of [−π, π).
14. The method as claimed in claim 10 , wherein the power spectral density of the optimized watermark obtained from the objective function is calculated by the equation
Φ
w
(
Ω
)
=
-
Φ
x
(
Ω
)
+
Φ
x
(
Ω
)
1
2
π
∫
-
π
π
Φ
x
(
Ω
)
ⅆ
Ω
(
σ
x
2
+
σ
w
2
)
,
where σ x 2 is the variance of the original signal, and σ w 2 is the variance of the watermark.