International Journal of Security and Its Applications
Vol.9, No.1 (2015)
224 Copyright ⓒ 2015 SERSC
where length of the
i
y
signal is M, and
B
is a
2
BM
measurement matrix such that size of
the m is
NBM /
2
and M is the number of samples needed by the CS measurement for the
whole image. In this way,
has a block-diagonal structure as follow:
B
B
B
000
00
00
(4)
Therefore, the overall technique above was called block CS (BCS) [18].
4. The Watermarking Signal in CS Domain
4.1. The Generation of the CS-watermarking Signal
In the scheme presented, we divide firstly the original fingerprint watermark image into a
lot of non-overlapping blocks, in which blocking criteria of the image is jointly decided by
size of the watermarking signal and positioning accuracy of the watermarking as extraction
and recover purpose. Next, each block of the image is carried out by a sparse basis matrix in
which we use DCT as the sparse basis Ψ, and form various DCT coefficients blocks.
Simultaneously, measurement matrix
B
is deployed to sense these DCT coefficients
independently within each block. The process is simply random linear projection, and can be
achieved by inner product operation of corresponding two elements between Ψ and
B
. Here,
according to the CS principle in [16-17], selection of
B
is incoherent with Ψ. By
considering that the sparse basis Ψ is a type of DCT matrix in our method, we can solve the
constraint by designing an appropriate measurement matrix
B
. We will discuss the design of
B
in subsection 4.2. Finally, the watermarking signal is produced by combining the all
sampling values of measurement matrix
B
. The realization principle of the watermark signal
is shown in Figure 3.
In Figure 3, assume that an original gray watermark image is size of
21
NNN
, in
which
1
N
and
2
N
denote rows and columns ( both
1
N
and
2
N
are multiples of 8),
respectively. We segment the watermark image into nonoverlapping 8×8 pixel blocks, and
denote the pixels as
),( jix
k
, where
81,64/1 iNk
and
81 j
. Then, perform DCT
in kth block to yield the DCT coefficients
16
)12(
cos
16
)12(
cos),(
4
)()(
),(
8
1
8
1
vjui
jix
vCuC
vuC
i j
kk
(5)
Figure 3. Process of the CS-watermarking Signal
Original
watermark
image
Blocking 1
Blocking 2
Blocking k
BCS
BCS
1
y
Blocking
process
2
y
km
y
BCS
The CS-
watermarking
signal
wM
y
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