Reversible Image Watermarking for Health Informatics Systems
Using Distortion Compensation in Wavelet Domain
Hamidreza Zarrabi, Mohsen Hajabdollahi, S.M.Reza Soroushmehr,
Nader Karimi, Shadrokh Samavi, Kayvan Najarian


Abstract— Reversible image watermarking guaranties
restoration of both original cover and watermark logo from the
watermarked image. Capacity and distortion of the image
under reversible watermarking are two important parameters.
In this study a reversible watermarking is investigated with
focusing on increasing the embedding capacity and reducing
the distortion in medical images. Integer wavelet transform is
used for embedding where in each iteration, one watermark bit
is embedded in one transform coefficient. We devise a novel
approach that when a coefficient is modified in an iteration, the
produced distortion is compensated in the next iteration. This
distortion compensation method would result in low distortion
rate. The proposed method is tested on four types of medical
images including MRI of brain, cardiac MRI, MRI of breast,
and intestinal polyp images. Using a one-level wavelet
transform, maximum capacity of 1.5 BPP is obtained.
Experimental results demonstrate that the proposed method is
superior to the state-of-the-art works in terms of capacity and
distortion.

I. INTRODUCTION
Medical image analysis is extensively used to help
physicians in medical applications and improves their
diagnostic capabilities. Transmission of the medical
information through a public network such as internet or
computer network may be leaded to the security problems
such as, modification and unauthorized access. In this regard,
many researches were performed to address these problems
and provided solutions for content authentication. Although
digital
image
watermarking
has
addressed
the
aforementioned problems but medical image watermarking
causes original image modification and distortion. Small
distortion in medical images may have negative impact on
physician diagnostic hence the original image content must
be preserved. In recent years reversible watermarking has
been introduced as an effective way to restore both the
original image and watermark information. In this manner,
physician diagnostic process and treatment are not affected,
H.R Zarrabi, M. Hajabdollahi, and N. Karimi are with the Department of
Electrical and Computer Engineering, Isfahan University of Technology,
Isfahan 84156-83111, Iran.
S.M.R. Soroushmehr is with the Department of Computational Medicine
and Bioinformatics and Michigan Center for Integrative Research in Critical
Care, University of Michigan, Ann Arbor, MI, U.S.A.
S. Samavi is with the Department of Electrical and Computer Engineering,
Isfahan University of Technology, Isfahan 84156-83111, Iran. He is also
with the Department of Emergency Medicine, University of Michigan, Ann
Arbor, MI, U.S.A.
K. Najarian is with the Department of Computational Medicine and
Bioinformatics; Department of Emergency Medicine; and the Michigan
Center for Integrative Research in Critical Care, University of Michigan,
Ann Arbor, MI, U.S.A.
.

and patient privacies are kept. Reversible image
watermarking can be considered as an essential part of health
information system (HIS).
Recently, reversible watermarking has attracted a lot of
attention in the research community. In many recent studies
watermarking using transform domain, focused on the
wavelet transform to reach better robustness. For example in
[1], Haar discrete wavelet transform was used for reversible
watermarking. In [2], difference expansion based reversible
watermarking in Haar discrete wavelet domain was used.
Kumar et al. employed singular value decomposition based
reversible watermarking in discrete wavelet transform [3]. In
[4], 4th level of discrete wavelet transform using a
quantization function was used for embedding. Watermark
information was encoded by BCH encoding to reach more
security. Selvam et al. [5] firstly used integer wavelet
transform to generate a transformed image and then they
applied discrete gould transform in transformed coefficients
and reached a capacity of 0.25 per pixel. In [6], CohenDaubechies-Fauraue integer wavelet transform was used. In
order to prevent the overflow/underflow, histogram was
firstly pre-processed, and then additional information was
created. Companding was applied to compression and
decompression of the transformed coefficients. Since in
companding process, there was a probability of distortion, so,
additional information was created.
Some of the previous studies have investigated the
problem of the reversible watermarking with other
transformation and techniques. In [7], mean value of
transformed coefficients was utilized by slantlet for
embedding. In order to increase the security, watermarking
was transformed to Arnold domain and overflow/underflow
was prevented by post-processing. In [8], initial using
adaptive threshold detector algorithm, region of interest and
non-region of interest was separated automatically. Then,
embedding in each region separately was implemented using
bin histogram. In [9], [10] and [11], reversible image
watermarking based on Prediction Error Expansion was
proposed. In [9], diagonal neighbors were considered as
embedding locations, when overflow/underflow was
occurred. In [12], histogram shifting was applied directly on
pixels or prediction error, dynamically. In [13], two
intelligent techniques including “Genetic algorithm” and
“particle swarm optimization” were utilized for watermarking
with interpolation error expansion. In [14], intermediate
significant bit substitution was used as watermark embedding
process. A fragile watermark was embedded for tamper
detection. Watermark bits were encrypted before embedding
in order to increase the security.

Reversible watermarking can be useful in case of
encrypted images. Hence in [15], probabilistic properties of
Paillier cryptosystem was used for encrypted images. In [16],
block histogram shifting was used for encrypted image.

Integer Wavelet Transform

Selection of Sub- bands

In this paper, a novel reversible watermarking method for
medical images in telemedicine applications is proposed.
Integer wavelet domain is utilized and watermark bits are
embedded in each sub-band in two iterations. In the first
iteration, coefficients are modified by embedding. In the
second iteration, coefficients are modified in such a way that
to be close to the original values. In this manner it is possible
to have 2 bit embedding without any modifications. In other
words, coefficient modification in the first iteration is
compensated in the second iteration.

Cover image
Compensation (Algorithm1)
Watermark Logo
Embedding by Subroutine-1 in
Selected Sub- bands

Embedding by Subroutine-2 in
Selected Sub-bands

Watermarked image
Inverse Integer Wavelet
Transform

The rest of this paper is organized as follows. In Section
II, proposed reversible watermarking based on integer
wavelet transform is presented. Section III is dedicated to the
experimental results. Finally in Section IV, our concluding
remarks are presented.

&

Side information

Figure 1. Block diagram of the embedding Procedure

II. PROPOSED METHOD
In recent studies, discrete wavelet transform is
extensively used as transformed domain based reversible
image watermarking. In discrete wavelet transform, pixels
are converted in form of integer values to the floating point
one. Due to changing the coefficient values in embedding
phase in form of truncation, preservation of original integer
value cannot be guaranteed. To address this problem, in the
proposed reversible image watermarking, integer to integer
wavelet transform is exploited. The proposed method consists
of two embedding and extraction phases. In the proposed
algorithm, wavelet coefficients are converted to a binary map
by:
𝑥
𝑄(𝑥) = 𝑚𝑜𝑑 (⌊ ⌋ , 2)
2

Post processing on pixels with
overflow or underflow

(1)

where “𝑚𝑜𝑑” is a function for calculating the remainder and

⌊. ⌋ is a floor function. According to the watermark bit and

corresponding binary map, original coefficient value is
changed by a constant value. This process may produce the
same value for different coefficients and causes ambiguity
during reconstruction of the original image. To avoid this
ambiguity, tracker key is produced as side information and
makes the algorithm reversible. In the followings, embedding
and extraction phases are presented respectively.

A. Embedding phase
An overview of the proposed embedding phase is
presented in Fig. 1. System inputs are cover image and
watermark logo and outputs are watermarked image and
tracking key. At first, cover image is transformed by onelevel integer wavelet transform and four wavelet sub-bands
including LL, LH, HL and HH are calculated. LL sub-band
has high sensitivity to human visual system and embedding
in low frequency sub-band can be leaded to the perceptual
distortion. So, according to the capacity requirements, three
number of high frequency sab-bands (LH, HL, and HH) are
selected for embedding. The number of watermark bits for
embedding is divided in to the two equal parts for each
selected embedding sub-band. Embedding phase has two
iterations and in the first iteration, each bit of the first part is

embedded in a coefficient. In the second iteration, second
part of the watermark is embedded in the previously
embedded coefficients.
Embedding algorithm for two iterations is explained in
Algorithm1. Embedded image in wavelet domain is
transformed back to the spatial domain with inverse integer
wavelet transform. Embedding process may lead to a value
outside of the acceptable range of the image values which are
underflow in the case of pixels with value smaller than 0 and
overflow in value greater than 255. For these cases, pixel
values are truncated and their locations as well as their
original values are considered as side information. Suppose
that 𝑐(𝑢, 𝑣) is wavelet coefficient, 𝑡𝑘𝑒𝑦(𝑖) 𝑖 = 1, … is length
of watermark as side information, 𝑤 is watermark, 𝑐 𝑤 (u, v)
is watermarked coefficient. Embedding algorithm
(Algorithm1) is as follow.
Algorithm1 : Embedding
1: Calculate 𝑄(𝑐(𝑢, 𝑣)) by equation (1)
2:

If 𝑸(𝒄(𝒖, 𝒗)) == 𝟏

3:

𝑡𝑘𝑒𝑦(𝑖) = 1

4:

In first iteration, apply subroutine 1 as follow

5:

If 𝑤(𝑖) = 0 then 𝑐 𝑤 (u, v) = c(u, v) + 2

6:

Else 𝑐 𝑤 (u, v) = c(u, v)

7:

In second iteration, apply subroutine 2 as follow

8:

If 𝑤(𝑖) = 0 then 𝑐 𝑤 (u, v) = c(u, v) − 2

9:

Else 𝑐 𝑤 (u, v) = c(u, v)

10:

Else If 𝑸(𝒄(𝒖, 𝒗)) == 𝟎

11:

𝑡𝑘𝑒𝑦(𝑖) = 0

12:

In first iteration, apply subroutine 1 as follow

13:

If 𝑤(𝑖) = 1 then 𝑐 𝑤 (𝑢, 𝑣) = 𝑐(𝑢, 𝑣) + 2

14:

Else 𝑐 𝑤 (𝑢, 𝑣) = 𝑐(𝑢, 𝑣)

15:

In second iteration, apply subroutine 2 as follow

16:

If 𝑤(𝑖) = 1 then 𝑐 𝑤 (𝑢, 𝑣) = 𝑐(𝑢, 𝑣) − 2

17:

Else 𝑐 𝑤 (𝑢, 𝑣) = 𝑐(𝑢, 𝑣)

Watermark information is embedded by iteration 2 in
such a way that the variations due to iteration 1 are
compensated. Embedding process has three advantages. First,
the number of modified coefficients is small which can be
leaded to the low perceptual distortion. Second, variation on
coefficients duo to in iteration 1, can be compensated in
iteration 2. Third, by the ability of embedding in each subband (LH, HL, HH), it is possible to increase the embedding
capacity. Hence the maximum capacity is 1.5 BPP. Also by
using simple methods such as duplicating, more robustness
can be obtained.
B. Extraction phase
Overview of the proposed extraction phase is presented in
Fig. 2. Inputs are watermarked image as well as tracking key
and outputs are recovered original image and extracted
watermark logo. At first, as a pre-processing stage we apply
the side information including overflow or underflow and
retrieve spatial domain version of the watermarked image.
After the pre-processin, integer wavelet transform is applied
on watermarked image and four sub-bands are obtained.
Watermark information is extracted from the embedded subbands in two iterations by compensation algorithm. In each
iteration, one bit is extracted from each wavelet coefficient.
The order in which watermark information is extracted is
inverse of the order in which it is embedded. So embedded
watermark in the second iteration is extracted in the first
iteration. Finally the original image is recovered by inverse
integer wavelet transform. For extraction phase, suppose that
𝑐 𝑤 (𝑢, 𝑣) is coefficient value, 𝑡𝑘𝑒𝑦(𝑖) 𝑖 = 1, … is length of
watermark as side information, 𝑤 𝑒 is as extracted watermark
and 𝑐 𝑟 (𝑢, 𝑣) is recovered coefficient. The extraction
algorithm (Algorithm2) of the proposed watermarking
procedure is as follow.
Algorithm 2: Extraction
1: Calculate 𝑄(𝑐 𝑤 (𝑢, 𝑣)) by equation (1)
2:

𝑤 𝑒 = 𝑄(𝑐 𝑤 (𝑢, 𝑣))

3:

If 𝒕𝒌𝒆𝒚(𝒊) = 𝟏 then

4:

In first iteration, apply subroutine 1 as follow

5:

If (𝑐 𝑤 (𝑢, 𝑣))=0 then 𝑐 𝑟 (𝑢, 𝑣) = 𝑐 𝑤 (𝑢, 𝑣) + 2

6:

Else 𝑐 𝑟 (𝑢, 𝑣) = 𝑐 𝑤 (𝑢, 𝑣)

7:

In second iteration , apply subroutine 2 as follow

8:

If 𝑄(𝑐 𝑤 (𝑢, 𝑣))=0 then 𝑐 𝑟 (𝑢, 𝑣) = 𝑐 𝑤 (𝑢, 𝑣) − 2

9:

Else 𝑐 𝑟 (𝑢, 𝑣) = 𝑐 𝑤 (𝑢, 𝑣)

10: Else If 𝒕𝒌𝒆𝒚(𝒊) = 𝟎 then
11:

In first iteration, apply subroutine 1 as follow

12:

If 𝑄(𝑐 𝑤 (𝑢, 𝑣))=1 then 𝑐 𝑟 (𝑢, 𝑣) = 𝑐 𝑤 (𝑢, 𝑣) + 2

13:

Else 𝑐 𝑟 (𝑢, 𝑣) = 𝑐 𝑤 (𝑢, 𝑣)

14:

Figure 2. Block diagram of the extraction procedure.

Sample images from four medical datasets are illustrated in
Fig. 3. All images have been resized to be 512×512. Input
watermark is a binary image, consisting equal number of
ones and zeros (49% ones and 51% zeros).
In Table 1, capacity-distortion results of the proposed
method in case of four medical images are provided. Brain
MRI, cardiac MRI, intestinal polyp and breast MRI are
including 80, 70, 100 and 100 images which the average
results of each dataset are as Table 1. Simulation results show
the maximum capacity of 1.5 BPP with low distortion is
obtained. Also it is observed from Table 1 that increasing the
capacity from 0.1 to 1.5 BPP does not affect the visual
quality significantly.
For comparison of the proposed method with other
related methods, an experiment is performed in case of Lena
image. A capacity-PSNR chart is illustrated in Fig. 4. It is
observed that our method, for the same capacity, has better
PSNR compared to the other six comparable methods. Also,
visual quality after relatively high amount of embedding is
acceptable. It is important to note that in the proposed
algorithm, more capacity can be obtained by more
transformation levels or iterations. Finally in order to
evaluate the visual quality of the watermarked images, in Fig.
5 the original and the watermarked images are shown. In Fig.
5b, a sample watermark logo is shown for embedding. Fig. 5c
shows watermarked image with capacity of 1.5 BPP. Fig. 5
shows that the watermarked images are not visually different
from the original ones.

In second iteration, apply subroutine 2 as follow

15:

If 𝑄(𝑐 𝑤 (𝑢, 𝑣))=1 then 𝑐 𝑟 (𝑢, 𝑣) = 𝑐 𝑤 (𝑢, 𝑣) − 2

16:

Else 𝑐 𝑟 (𝑢, 𝑣) = 𝑐 𝑤 (𝑢, 𝑣)

III. EXPERIMENTAL RESULTS
Performance of the proposed method is tested on four
grayscale medical image datasets including brain MRI [17],
cardiac MRI [18], intestinal polyp [19] and breast MRI [20].

Figure .3 (a) Brain MRI, (b) Cardiac MRI, (c) Intestinal Polyp,
(d) Breast MRI

TABLE 1. Average capacity (BPP) vs. distortion (PSNR) for four medical image
datasets.

PSNR(dB)
Capacity
(BPP)
0.1
0.2
0.3
0.7
1
1.3
1.4
1.5

Brain
MRI
58.92
55.65
53.80
50.17
48.60
47.46
47.12
43.83

Cardiac
MRI
58.74
55.71
53.97
50.33
48.81
47.65
47.32
47.03

Intestinal
Polyps
58.13
55.12
53.36
49.68
48.13
46.98
46.66
46.36

Breast
MRI
59.52
56.54
54.72
51.08
49.53
48.40
48.06
47.75

performed in two iterations with a compensation method. It
was possible for modified coefficients in the first iteration, to
recover its original value in the second iteration. One bit was
embedded on each iteration, hence maximum capacity of 1.5
BPP was obtained. Simulation results demonstrated that the
proposed reversible image watermarking provided suitable
capacity-distortion in comparison with the other methods.
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[1]
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Figure 4. Comparison of capacity-distortion of proposed method with six
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[8]
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[14]

[15]
a) Original image

b) Logo image

c) Watermarked
image

Figure 5. Visual quality of watermarked images using the proposed
embedding method.

IV. CONCLUSION
Novel reversible image watermarking method was
presented in medical images based on integer wavelet
transform. Improving distortion and embedding capacity was
considered in the proposed method. Embedded process was

[16]
[17]
[18]
[19]
[20]

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