haii

1. 2012 International Symposium on Computer, Consumer and Control
A Novel Fractional Discrete Cosine Transform Based Reversible Watermarking for
Biomedical Image Applications
Lu-Ting Ko Jwu-E Chen Yaw-Shih Shieh Tze-Yun Sung*
Department of Electrical Engineering Department of Electronics Engineering
National Central University Chung Hua University
Chungli City 320-01, Taiwan Hsinchu City 300-12, Taiwan
e-mial: {985401007@cc, jechen@ee}.ncu.edu.tw e-mail: {ysdaniel, bobsung}@chu.edu.tw
Abstract—Digital watermarking is a good tool for healthcare [8]. The fractional discrete cosine transform (FDCT) [9-10],
information management systems. The well-known which is a generalized DCT, is yet more applicable in the
Quantization Index Modulation (QIM) based watermarking digital signal processing applications. In this paper, we
has its limitations as the host image will be destroyed; however, propose a novel algorithm called the fractional discrete
the recovery of biomedical image is essential to avoid cosine (FDCT) based watermarking for the healthcare
misdiagnosis. A transparent yet reversible watermarking information management applications. In addition, the
algorithm is required for biomedical image applications. In advantage of FDCT is to take account of the phenomena of
this paper, we propose a fractional discrete cosine transform image processing. The reminder of the paper proceeds as
(FDCT) based watermarking to exactly reconstruct the host
follows. In section II, the type-I fractional discrete cosine
image. Experimental results show that the FDCT based
transform is reviewed. Section III describes the half discrete
watermarking is preferable to the QIM based watermarking
for the biomedical image applications. cosine transform. The proposed FDCT based watermarking
and experimental results on various biomedical images are
Keywords- Quantization index modulation (QIM), fractional presented in section IV. The architecture of the half-DCT
discrete cosine transform (FDCT), reversible watermarking, based watermarking processor implemented by using FPGA
biomedical image applications, healthcare information (field programmable gate array) is given in section V.
management systems Conclusion can be found in section VI.
II. REVIEW OF TYPE-I FRACTIONAL DISCRETE COSINE
I. INTRODUCTION TRANSFORM
In the healthcare information systems nowadays, one of
For the sake of simplicity, let us take the 8-point,
the major challenges is a lack of complete access to patients’
type-I forward DCT as an example. The corresponding
health information. Ideally, a comprehensive healthcare
information system shall provide the biomedical records matrix can be expressed as follows [9-10],
including health insurance carriers, which are important for 2 ª § mnπ ·º
clinical decision making. There is sure to be a risk of C= «km kn cos¨ ¸» (1)
8 −1 ¬ © 8 − 1 ¹¼
misdiagnosis, delay of diagnosis and improper treatments in
case of insufficient biomedical information available [1]. where
Digital watermarking, which is a technique to embed ­ 1
° , m = 1 and m = 8
imperceptible, important data called watermark into the host km = ® 2 (2)
image, has been applied to the healthcare information ° 1 ,
¯ 1< m < 8
management systems [2-4]. However, it might cause the
distortion problem regarding the recovery of the original host ­ 1
° , n = 1 and n = 8
image. In order to protect the host image from being kn = ® 2 (3)
distorted, digital watermarking with legal and ethical ° 1 ,
¯ 1< n < 8
functionalities is desirable especially for the biomedical
images applications [6-7]. Specifically, any confidential data m = 1,2,3,...,8 and n = 1,2,3,...,8
such as patients’ diagnosis reports can be used as watermark It can be diagonalized by
and then embedded in the host image by using digital C = U ȁ UT (4)
watermarking with an authorized utilization. Thus, digital where U is an orthonormal matrix obtained from the
watermarking can be used to facilitate healthcare information eigenvectors of C , ȁ is a diagonal matrix composed of the
management systems.
Discrete Cosine Transform (DCT) has been adopted in corresponding eigenvalues -1 and 1. UT is the transpose
various international standards, e.g. JPEG, MPEG and H.264 matrix of U. Based on equation (4), the square of the DCT
_________________________________________________ matrix can be written as
*Corresponding author: Tze-Yun Sung, Dept. of Electronics Engineering,
Chung Hua University, Hsinchu City 300-12, Taiwan, bobsung@chu.edu.tw.
978-0-7695-4655-1/12 $26.00 © 2012 IEEE 36
DOI 10.1109/IS3C.2012.19

2. C2 = C ⋅ C CI C R = 0 (23)
= U ȁ UT U ȁ UT (5) Form equations (20) ~ (23), we have
2 T
C R z = C R x + jC R y (24)
=Uȁ U
Similarly, we have C I z = C I y + jC I x (25)
α
C =Uȁ U α T
(6) Thus, x and y can be obtained from z as follows.
where ȁ is a diagonal matrix composed of the x = (CR + CI )−1 (Re{CR z} + Im{C I z}) (26)
corresponding eigenvalues λa = e j (θ n + 2πq n ) a α is a real
n y = (C R + CI ) (Re{CI z} + Im{CR z})
−1
(27)
fraction, n = 1,2,3,...,8 , θ1,θ 2 ,θ3 ,θ 4 = π and θ5 ,θ 6 ,θ7 ,θ8 = 0 ,
IV.THE PROPOSED FRACTIONAL DISCRETE COSINE
qn is an element of generating sequence (GS) TRANSFORM BASED WATERMARKING
q = (q1, q2 ,...., q8 ) , and qn is an integer for 0 ≤ qn ≤ 7 . Both transparency and recovery of the host image are
required for the biomedical applications. As the
III. HALF DISCRETE COSINE TRANSFORM conventional Quantization Index Modulation (QIM) [7]
The half-DCT, i.e. the FDCT with α = 1 2 is obtained based watermarking is irreversible, we propose a novel
FDCT based algorithm for reversible watermarking.
by
C = U ȁ1 / 2 UT (7) A. Quantization Index Modulation
The matrix, z , obtained by combining the 8-point half-DCT Figure 1 depicts the conventional QIM based
of x and y is defined as watermarking [7]. In which, W , K , S , V and QV denote
z = C1x − C1y the watermark, the secret key, the coded watermark, the host
(8)
= C1x + C2 y image and the watermarked image, respectively. For the
where sake of simplicity, let us consider monochromatic images
C1 = U ȁ1 / 2 UT (9) with 256 grey levels, and the size of the watermark is one
fourth of that of the host image. The secret key is used to
C 2 = −C1
(10) map the binary representation of the watermark onto the
= − U ȁ1 / 2 UT host image, for example, Figure 2 depicts the binary
U is the orthonormal matrix given by representation of a watermark pixel that is mapped onto a
U = [u1, u 2 ,....,un ] (11) 4 × 4 segment using a given secret key.
K q
­1, m = n
u muT = ®
n (12)
¯0, m ≠ n W
S
QV
Let U n be defined as
U n = u n uT
n (13) V
we have Figure 1. The conventional QIM based watermarking
U mU n = (u muT )(u nuT )
m n b0 0 b2 b3
­U = u nuT , m = n
° (14) 0 b1 0 0
=® n n b7 b6 b5 b4 b3b2 b1b0
→
b4 0 b5 0
°
¯ 0, m ≠ n The binary representa tion of a watermark pixel
0 b7 b6 0
It is noted that C1 and C 2 can be rewritten as
The secret key K used for mapping onto a 4x4 segment
C1 = U ȁ1/ 2 UT Figure 2. The secret key K used for mapping the watermark onto the host
(15) image
= C R + jC I
C2 = −U ȁ1 / 2 UT The operation of the QIM block, in which the grey
(16)
= C I + jC R levels of the host image, V , ranging between 2c ⋅ q and
where (2c + 1) ⋅ q will be quantized into (2c + 1) ⋅ q if the
CR = U1 + U 2 + U3 + U 4 (17) corresponding pixels of the coded watermark, S , are bit 1;
CI = U5 + U6 + U7 + U8 (18) otherwise they are quantized into 2c ⋅ q if the corresponding
Thus pixels are bit 0. For the grey levels of V that are between
z = (CR + jC I )x + (CI + jCR )y (19) (2c + 1) ⋅ q and (2c + 2) ⋅ q , they will be quantized into
According to equations (14), (17) and (18), we have (2c + 1) ⋅ q or (2c + 2) ⋅ q depending on the corresponding
C RC R = C R (20) pixels of S being bit 1 or 0, respectively. Note that q
C I CI = C I (21)
C RC I = 0 (22)
37

3. V
255
denotes the quantization step, 0 ≤ c , and c is an
2⋅q
T
HVR HVRR
integer number. HVRI
It is noted that the watermarked image, QV , can be HVR
written as QV
­(2c + 1)q ; if V (i, j ) ∈ ((2c + 0.5)q, (2c + 1.5)q], S (i, j ) = 1 (28) HVI
QV (i, j ) = ®
¯(2c)q ; if V (i, j ) ∈ ((2c − 0.5)q, (2c + 0.5)q ], S (i, j ) = 0 HVIT HVIR
V HVII
where (i, j) denotes the position index of pixels, and the
coded watermark, S , can be obtained by
­1 ; if QV (i, j ) ∈ ((2d + 0.5)q, (2d + 1.5)q ]
V
S (i, j ) = ® (29)
¯0 ; otherwise Figure 5. Data flow of 2-D half-DCT operations.
Together with the secret key, K , the watermark, W , can be
exactly extracted from the watermarked image, QV , as
shown in Figure 3.
q K V HVR
S Secret Key
QV Inverse QIM W
Decoder
QV HVI
Figure 3. Extraction of the watermark, W , from the watermarked image,
QV , based on the conventional QIM scheme
B. Proposed FDCT based watermarking Figure 6. Data flow of the 1-D half-DCT operation.
According to equation (19), the half-DCT can be used The original host image, V, and watermark, W, can be
to combine two real valued signals into a single, complex exactly reconstructed from the watermarked images:
valued signal. Let x and y in equation (19) be the host image HVRR , HVRI , HVIR and HVII as shown in Figures 7 and 8.
and the watermark, respectively, and z be the watermarked S
image. The watermark and host image can be extracted from
z by using equations (26) and (27). Figure 4 depicts the HVRR
QV
proposed FDCT based watermarking, where W, V, S, QV, W
HVRI
HVRR , HVRI , HV and HV are the watermark, the host
IR II
HVIR
image, the secret key, the QIM watermarked image, and the V
watermarked images, RR, RI, IR and II, respectively. The 2- HVII
D half-DCT consists of three 1-D half-DCT and two
Figure 7. The proposed inverse FDCT based watermarking for image
transpose operations as shown in Figure 5, where HVR and extraction
HVI are the intermediate watermarked images for real, R, V
and imaginary, I, parts, respectively. According to equation
(19), the 1-D half-DCT consists of two matrix HVRR T
HVR
multiplications as shown in Figure 6, where CR and CI are HVRI HVR
the half-DCT coefficient matrices for equations (17) and QV
(18), respectively.
HVIR HVI
HVIT
V
HVII
W QV HVRR
V
S HVRI
Figure 8. Data flow of the 2-D inverse half-DCT
HVIR
V
HVII
Figure 4. The proposed FDCT based watermarking
Figure 9. The host images (Spine, Chest, Fetus and Head) and watermark
image (Lena)
38

4. 55
C. Experimental Results on Biomedical Images QIM watermarked image
FDCT watermarked image RR
FDCT watermarked image RI
FDCT watermarked image IR
50
FDCT watermarked image II
The proposed FDCT based watermarking algorithm 45
has been evaluated on various biomedical test 256× 256 40
PSNR(dB)
images with 256 grey levels, namely Spine, Chest, Fetus 35
and Head obtained by magnetic resonance image (MRI), X- 30
ray, ultrasound and computed tomography (CT), 25
respectively, as shown in Figure 9 are used as host images 20
3 6 9 12 15 18 21 24 27 30
[7]. The 64× 64 Lena image as shown in Figure 9 with 256 QIM quantization step
grey levels is used as watermarks [7]. Figure 13. The PSNR of the watermarked image of Head (CT) at various
Figures 10~13 show the PSNR of the QIM QIM quantization steps
watermarked image and FDCT watermarked images RR, RI,
IR and II of Spine (MRI), Chest (X-ray), Fetus (ultrasonic) V. CONCLUSION
and Head (CT) at various QIM quantization steps q. It is
noted that the FDCT watermarked images are more In this paper, a novel algorithm called the FDCT based
transparent than conventional QIM watermarked images, reversible watermarking has been proposed for biomedical
and the block effect of the FDCT based watermarking is image watermarking. The transparency of the watermarked
eliminated. image can be increased by taking advantage of the proposed
watermarking. As the host image can be exactly
reconstructed, it is suitable especially for the biomedical
55
QIM watermarked image
FDCT watermarked image RR
FDCT watermarked image RI
image applications. In addition, the elimination of block
FDCT watermarked image IR
effect avoids to detect QIM coded watermarked image. Thus,
50
FDCT watermarked image II
45
the FDCT based reversible watermarking is preferable to
40
facilitate data management in healthcare information
PSNR(dB)
35
management systems.
30
25
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