Information Technology Reference
In-Depth Information
between the watermarking performance and the host data energy. In addition, since
watermarked data may be subjected to channel noise or undergo compression coding,
spectrum equalization provides advantages that the additive interference can be con-
sidered as white Gaussian noise.
Similar to the single-bit scheme, multi-bit watermarking uses more than one PN
sequence, each representing one bit in the watermark. To be embedded into
N
coeffi-
cients in the host, a meaningful watermark is first converted into an
L
S
-bit binary array
W
, each bit taking +1 or
1. In most cases,
N
is significantly greater than
L
S
, therefore
L
S
nearly independent PN sequences, each
N
bits long, can be found:
−
N
−
1
=
∑
S
,
S
S
(
j
)
S
(
j
)
≈
0
u
,
v
=
0
1
,
L
−
1
u
≠
v
.
(4)
u
v
u
v
j
=
0
Multiplied by
W
(
i
), these sequences are superimposed to produce the embedded mark:
L
−
1
∑
I
'
=
I
+
α
W
(
i
)
S
,
(5)
S
i
k
=
0
where
α
S
is the strength of watermarking based on single-bit-per-sequence scheme. In
watermark extraction, cross-correlation is calculated:
(6)
1
N
−
1
∑
.
ρ
=
I
'
j
)
S
(
j
)
i
i
N
j
=
0
The mutual influence tamongst different watermark bits is considered negligible due
to the approximate independence between the PN sequences as shown in Equation
(4).
By introducing spectral equalization, any additive interference can be modeled by a
zero mean i.i.d. Gaussian process with standard deviation
N
. According to the central
limit theorem, the output of the cross-correlation satisfies Gaussian distribution:
2
2
σ
N
σ
I
N
,
ρ
~
N
W
(
i
)
α
S
,
(7)
i
where
W
(
i
) is either
1. Thus, a decision criterion is obtained, and the embed-
ded watermark bits can be extracted:
+
1 or
−
1
ρ
≥
0
i
W
'
i
)
=
(8)
−
1
ρ
<
0
i
The error probability in extracting each bit is:
N
BER
=
1
−
Φ
α
.
(9)
S
S
2
2
σ
+
σ
I
N
If all transforms used in this scheme are orthogonal, the watermark energy in the
transform domain is equal to that in the time/space domain,
