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Research Article
An Image Steganography Method Hiding Secret
Data into Coefficients of Integer Wavelet Transform
Using Pixel Value Differencing Approach
Avinash K. Gulve1and Madhuri S. Joshi2
1Government College of Engineering, Aurangabad, Maharashtra 431 005, India
2Jawaharlal Nehru College of Engineering, Aurangabad, Maharashtra 431 005, India
Correspondence should be addressed to Avinash K. Gulve; akgulve@geca.ac.in
Received November ; Accepted December
Academic Editor: Gen Qi Xu
Copyright © A. K. Gulve and M. S. Joshi. is is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
e image steganography systems use either the spatial domain or the frequency domain to hide the secret information. e
proposed technique uses spatial domain technique to hide secret information in the frequency domain. e cover image is
transformed using integer wavelet transform to obtain four subbands: LL, LH, HL, and HH. en, the PVD approach is used to hide
the secret information in the wavelet coecients of all the four subbands. For improving the security of the hidden information,
the proposed method rst modies the dierence between two wavelet coecients of a pair and then uses the modied dierence
to hide the information. is makes extraction of secret data from the stego image dicult even if the steganography method fails.
e result shows that the proposed technique outperforms other PVD based techniques in terms of security of secret information
and hiding capacity of cover image.
1. Introduction
Now a day, it is easy to share the information which is in
the form of text, image, audio, or video using the Internet
as the communication channel. Since Internet is an open
channelofcommunication,thereisalwaysathreatofstealing
the information. erefore, it is becoming more important
toadoptsecuritymeasuressothattheinformationcanbe
protected from being stolen by malicious user. e security
measures include cryptography, steganography, and coding.
Steganography involves hiding secret information in a multi-
media object such as image, audio, or video in such a way that
its existence in these documents cannot be noticed. Digital
images are preferred for hiding the secret information. It is
relatively easy to place information in digital images because
of the availability of sucient redundant area where valuable
information could be placed in an imperceptive way. It is
possible to use images, either in the spatial domain or in the
frequency domain, to hide secret information. In the spatial
domain, the pixel values are used for hiding the secret
information and, in the frequency domain, the wavelet
coecients are used for hiding the secret information.
e organization of the paper is as follows. A review of
necessary background of IWT and PVD based steganography
is presented in this section. In Section ,theproposed
method is discussed. In Section , the results are discussed
while the paper is concluded in Section .
In the PVD method, as suggested by Wu et al. [,], a
gray-valued cover image is partitioned into nonoverlapping
blocks composed with two consecutive pixels, 𝑖and 𝑖+1.For
each block, dierence value 𝑖is calculated by subtracting
𝑖from 𝑖+1. Since the pixel value ranges from to , the
dierence value also ranges from − to . erefore, |𝑖|
ranges from to . e block is in smooth area if the
dierence value |𝑖|is small; otherwise, it is in sharply edged
area. A range table is designed with contiguous ranges (𝑘
where =1,2,3,...,)andthetablerangeisfromto.
e lower and upper boundaries of 𝑘are denoted by 𝑘and
𝑘,respectively.Hence,𝑘∈[𝑘,𝑘].ewidth𝑘of 𝑘is
calculated as 𝑘=𝑘−𝑘+.iswidth𝑘is used to estimate
Hindawi Publishing Corporation
Mathematical Problems in Engineering
Volume 2015, Article ID 684824, 11 pages
http://dx.doi.org/10.1155/2015/684824
Mathematical Problems in Engineering
thenumberofbits𝑖(where 𝑖=log2𝑘)ofsecretmessage
that can be hidden using the dierence of two consecutive
pixels. Aer hiding 𝑖bits using the dierence 𝑖,newvalues
are assigned to 𝑖and 𝑖+1.enewdierence
𝑖is calculated
by subtracting 𝑖from 𝑖+1.enewdierence
𝑖stands for
the secret data hidden in the pair. During extraction, the stego
image is partitioned into nonoverlapping blocks composed
with two consecutive pixels, 𝑖and 𝑖+1.en,thedierence
value
𝑖foreachpairoftwoconsecutivepixels𝑖and 𝑖+1 is
calculated. Next, |
𝑖|is used to locate the suitable range 𝑘.
e decimal equivalent of the secret information hidden in
the block is given by |
𝑖|−𝑘which is then transformed into
abinarysequencewith𝑖bits.
In order to improve the capacity of hiding secret data
and to provide an imperceptible stego image quality, a novel
steganographic method based on least-signicant-bit (LSB)
replacement and pixel-value dierencing (PVD) method is
presented by Wu et al. []. e range table is divided into
lower level (smooth area) and higher level (edged area). In
the smooth area, bits of the secret data is hidden by LSB
method while, in the higher level, secret data is hidden using
the PVD method.
To improve the hiding capacity of the cover image and
quality of the stego image, another enhanced method is
introduced based on the PVD method by Chang et al. [,,].
In this method, data is hidden in vertical and diagonal edges
along with the horizontal edges. e cover image is divided
into the blocks of × pixels. Considering and to be the
pixel locations, each × block includes four pixels (𝑥,𝑦),
(𝑥+1,𝑦),(𝑥,𝑦+1),and(𝑥+1,𝑦+1).Pixel(𝑥,𝑦) is grouped with
the remaining three pixels in the block to form three pixel
pairs. ese three pairs are named 0,1,and2where
0=(
(𝑥,𝑦),(𝑥+1,𝑦)),1=(
(𝑥,𝑦),(𝑥,𝑦+1)),and2=
((𝑥,𝑦),(𝑥+1,𝑦+1)), respectively. Aer embedding the secret
information in each pair using PVD approach, values of two
pixels in each pair get modied. us, the original dierence
value 𝑖is modied to a new dierence value
𝑖.enew
pixel values in each pair are dierent from their original ones.
at is, three dierent values are obtained for the pixel (𝑥,𝑦).
However, pixel (𝑥,𝑦) can have only one value. erefore,
one of the
𝑖is selected as the reference pair to oset the
remaining two pixel values. at is, two pixel values of the
reference pair are used to adjust the pixel values of other
two pairs and construct a new × block. e embedded
secret data is unaected because new dierence values,
𝑖,
are unaltered. During extraction, the dierence value
𝑖is
used to extract the hidden information. |
𝑖|is used to locate
the suitable range 𝑘. e decimal equivalent of the secret
information hidden in the pair is given by |
𝑖|−𝑘which is
then transformed into a binary sequence with 𝑖bits.
Gulve and Joshi []haveproposedasteganography
method to improve the security of the secret information
using ve-pixel pair dierencing approach. e cover image is
partitioned into blocks of ×pixelstoformvepixelpairs.
e secret data is embedded in the pairs using the dierence
value of pixels in that pair. Instead of hiding bits in the
pair using the dierence value, bits ≤are hidden in the
pair where is the average of bits that can be hidden in each
pairoftheblock.us,incaseoffailureofthesteganography
system, it becomes dicult to estimate exact number of bits
hidden in each pair of the block. Another level of security
for the secret information is introduced by converting the
secret information in its gray code form. For each pair in the
block, the method converts bits of secret information in the
gray code form and then embeds these bits in that pair. us,
the security of the secret information is improved without
involving the overhead of encryption and decryption. Gulve
and Joshi [] have proposed a steganography method to
improve the security of the secret data embedded in the
image. e cover image is divided in the blocks of ×
pixels to form ve pairs. e location of the common pixel is
decided using the image data. For this reason, data of last few
rowsareused.Sincethecommonpixelischangedrandomly
basedontheimagedata,itisdiculttoextractthesecretdata
from stego image even if the steganography method fails.
Integer wavelet transform maps an integer data set into
another integer data set. Calderbank et al. [] have explained
the working of integer wavelet transform. Haar wavelet
transform, in its unnormalized version involving pair wise
averages and dierences, is written as
1,𝑛 =0,2𝑛 +0,2𝑛+1
21,𝑛 =0,2𝑛+1 −0,2𝑛.()
Its inverse is given by
0,2𝑛 =1,𝑛 +1,𝑛
20,2𝑛+1 =1,𝑛 −1,𝑛
2.()
Because of division by two, this is not integer transform.
e integer version can be built by omitting division by two
in 1,𝑛 andcalculatingthesuminsteadoftheaverage.isis
called transform []. Consider the following example:
1,𝑛 =0,2𝑛 +0,2𝑛+1
2
1,𝑛 =0,2𝑛+1 −0,2𝑛.()
It is possible to dene 1,𝑛 as above because the sum and
dierenceoftwointegersareeitherevenorodd.us,itis
safe to omit last bit of sum since it is similar to last bit of
dierence. e transform []isinvertibleanditisgivenby
0,2𝑛 =1,𝑛 −1,𝑛
2
0,2𝑛+1 =1,𝑛 +1,𝑛 +1
2.()
A dierent way of writing Haar transform using “liing”
steps leads to natural generalizations. It is possible to write
Haar and transform using liing schemes [].
First, compute the dierence and, then, use the dierence
in second step to compute the average:
1,𝑛 =0,2𝑛+1 −0,2𝑛 1,𝑛 =0,2𝑛 +1,𝑛
2.()
e inverse transform can be calculated in two steps.
First, recover the even samples from the average and dier-
ence, and recover the odd samples from even and dierence
[]. It is given by the following equations:
0,2𝑛 =1,𝑛 −1,𝑛
20,2𝑛+1 =1,𝑛 +0,2𝑛.()
Mathematical Problems in Engineering
It is possible to write integer transform by truncating the
division:
1,𝑛 =0,2𝑛+1 −0,2𝑛 1,𝑛 =0,2𝑛 +1,𝑛
2. ()
Liingcanbeusedtocomputetheinversetransform.e
equations follow from reversing the order and changing the
sign of the forward transform []:
0,2𝑛 =1,𝑛 −1,𝑛
2
0,2𝑛+1 =1,𝑛 +0,2𝑛.()
Ramalingam et al. []haveelaboratedtheprocessof
separating four subbands using Haar IWT. e rst stage
IWT is given by
H=𝑜−𝑒,
L=𝑒+H
2, ()
where 𝑜represents pixels in odd column and 𝑒represents
pixels in even column. In the next stage, the IWT coecients
are calculated using high pass and low pass lter banks. is
process creates four subbands: low-low (LL), low-high (LH),
high-low (HL), and high-high (HH). e second stage IWT
is given by
LH =Lodd −Leven,
LL =Leven +LH
2,
HH =Hodd −Heven,
HH =Heven +HL
2,
()
where Hodd represents H band’s odd row, Lodd represents L
band’s odd row, Heven represents H band’s even row, and Leven
represents L band’s even row [].
Ghasemietal.[,] have proposed a novel steganogra-
phy scheme based on integer wavelet transform and genetic
algorithm. e scheme embeds data in integer wavelet
transform coecients by using a mapping function based
on genetic algorithm. e methods use wavelet transform
coecients to embed secret data into the four subbands
of two-dimensional wavelet transform. Genetic algorithm is
used to nd the mapping function. A chromosome is encoded
as an array of genes containing permutations to
thatpointtopixelnumbersineachblock.OPAPisusedto
minimize the error between cover and stego image.
Xuan et al. []havesuggestedalosslessdatahiding
method for digital images using integer wavelet transform
and threshold embedding technique. CDF (.) integer
wavelet transform is used to obtain the wavelet coecients.
Histogram modication is applied to prevent possible under-
ow/overow of pixel values. A predened threshold value
isusedtoembeddatainthewaveletcoecients.
El Safy et al. [] have suggested an adaptive stegano-
graphic model which combines adaptive hiding capacity
function that hides secret data in the integer wavelet coef-
cients of the cover image with the optimum pixel adjust-
ment (OPA) algorithm. Histogram modication is applied
to prevent possible underow/overow of pixel values. e
cover image is divided into ×nonoverlappingblocks.
Each block is transformed using D Haar integer wavelet
transformtoobtainfoursubbands:LLI,LHI,HLI,and
HHI. Hiding capacity of each coecient is determined and
the data is embedded in the coecients. A pseudorandom
number generation function is used to select the wavelet
coecients for increasing the security of the hidden data.
e OPA algorithm is applied aer embedding secret message
to minimize the embedding error. e extraction procedure
is a blind process since it requires only the secret key from
the receiver. e secret key is used to identify the wavelet
coecients. Secret message bits are extracted from each
selected wavelet coecient.
Archana et al. [] have proposed a method for hiding
secret information in the discrete wavelet transform coe-
cients using GA and OPAP algorithm to provide optimum
hidingcapacity.efoursubbandsLL,HL,LH,andHHare
used for hiding the data. Hiding capacity function is modied
by using dierent ranges for k for the LH, HL, and HH
subbandswhereitsvaluesrangefromto.elengthLof
message bits to be hidden in wavelet coecient is determined
by using hiding capacity function.
Al-Asmari et al. []haveproposedamethodusingdis-
crete wavelet transform and pixel value dierencing approach
tohidetheinformation.Usingthediscretewavelettransform,
thecoverimageisdecomposedtoobtainthefoursubbands
(LL, HL, LH, and HH). en, the LSB method is used to
hide secret information in the LL subband by hiding two bits
of secret information in each coecient. e PVD approach
is used to hide the information in the remaining three
subbands. For hiding the information, two consecutive pixels
in the vertical direction are grouped to form a pair. e
method gives high performance in terms of capacity, human
visual quality, and PSNR.
2. Proposed Method
e proposed method hides secret information in the gray
scale images. It uses spatial domain technique to hide secret
information in the frequency domain. In the frequency
domain, the image is decomposed into four subbands using
integer wavelet transform and then the spatial domain
techniqueisusedtohidesecretinformationinthewavelet
coecients of the four subbands.
e cover image is transformed using D Haar integer
wavelet transform to obtain four subbands: LL, LH, HL, and
HH. e proposed method embeds data in the coecients of
four subbands by using the pixel value dierencing approach.
2.1. Preprocessing. e gray scale image is read as a D array
of size [,]. Histogram modication [–]isappliedto
prevent the possible overow/underow of pixel values. is
problem occurs when the pixel values of the cover image are
closetoor,becausetheymayexceedorfallbelow
Mathematical Problems in Engineering
LL HL
LH HH
F : Arrangements of wavelet coecients.
F : e image lena.ti aer performing Harr transform.
during inverse integer wavelet transform. e problem can be
solved by mapping the lowest gray scale levels to the value
and the highest gray scale levels to the value . If the
pixel values exceed the boundaries during the inverse wavelet
transform, the image is not suitable for hiding secret data.
e image is transformed using D Haar wavelet transform
to obtain four subbands: LL, LH, HL, and HH of size [/,
/] each. All the four subbands are used to hide the secret
information. e D array of size [,] is again constructed
by arranging the four subbands as shown in Figure .
Figure shows the arrangement of four subbands of the
image lena.ti aer transforming it using D Harr integer
wavelet transform.
A D array obtained by arranging the wavelet coecients
of four subbands is shown as follows:
112230150⋅⋅⋅−45−120 80
130159172⋅⋅⋅−37 −89 −72
⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅⋅
−30−59−72⋅⋅⋅−37 −89 −72. ()
e dierence operation in Haar transform may cause some
of the wavelet coecients in HL, LH, and HH subbands to
have negative values.
Sincesomeofthewaveletcoecientshavenegative
values, the D array shown in () cannot be used for hid-
ing secret information using the pixel value dierencing
approach. Hence, absolute values are used for the coecient
with negative values to create a new D array with positive
elements as follows:
112230150⋅⋅⋅4512080
130159172⋅⋅⋅37 89 72
⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅⋅
30 59 72 ⋅⋅⋅37 89 72. ()
Aer hiding the secret information in the D array shown
in (), inverse wavelet transform is performed to obtain
the stego image. To obtain good quality of stego image, the
original sign of each wavelet coecient, as shown in (),is
required. Hence, the D array shown in () is used to create
asignmatrixofthesize[,]havingelementswithvalues
or−. e sign matrix so created is shown as follows:
1 1 1 ⋅⋅⋅−1−1 1
1 1 1 ⋅⋅⋅−1−1−1
⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅⋅
−1−1−1⋅⋅⋅−1−1−1. ()
e wavelet coecients having positive values are repre-
sented by whereas wavelet coecients having negative
values are represented by −inthesignmatrix.
2.2. Embedding Process. For hiding the data in the D array,
themethodsuggestedbyGulve[,]isused.Inthemethod
proposed by Chang [], a block of ×pixelsisusedtoform
pairs which are then used to hide the secret information. e
proposed method uses the block of × wavelet coecients.
e introduction of wavelet coecients in the ×block
forms two extra pairs. For a × image, it is possible to
form pairs using the approach suggested by Chang []
whereas, using the proposed approach, pairs can be
formed.Agreaternumberofpairsprovideextraspacefor
hiding the secret information. us, the proposed method
improves the hiding capacity of the cover image.
e dierence between two wavelet coecients in the pair
is used to hide the secret information. If the dierence value
is directly used to hide the information, it is easy to retrieve
the embedded information in case the steganography system
fails. To enhance the security of the secret information, the
proposed algorithm modies the dierence between the two
wavelet coecients in the pair and this modied dierence
is used to hide the secret information. is imposes extra
layer of security making harder extraction of original secret
information from stego image using the dierence values
directly [,].
e arrangement of wavelet coecients into nonover-
lapping blocks of × wavelet coecients is shown in
Figure .AsshowninFigure ,each× block includes six
wavelet coecients (𝑥,𝑦),(𝑥,𝑦+1),(𝑥,𝑦+2),(𝑥+1,𝑦),(𝑥+1,𝑦+1),
and (𝑥+1,𝑦+2),whereand are the locations of wavelet
coecients. Five pairs are formed by grouping the common
wavelet coecient PX1with the remaining ve wavelet
Mathematical Problems in Engineering
PX0
PX3
PX1
PX4
PX2
PX5
P(x,y) P(x,y+1) P(x,y+2)
P(x+1,y) P(x+1,y+1) P(x +1,y+2)
F : Pixel block.
coecients PX0,PX
2,PX
3,PX
4,andPX
5.evepairs𝑖
where =0,1,2,3,4are as shown below:
0=(𝑥,𝑦+1),(𝑥,𝑦),
1=(𝑥,𝑦+1),(𝑥,𝑦+2),
2=(𝑥,𝑦+1),(𝑥+1,𝑦),
3=(𝑥,𝑦+1),(𝑥+1,𝑦+1),
4=(𝑥,𝑦+1),(𝑥+1,𝑦+2).
()
e dierence value 𝑖is calculated for each pair 𝑖by
subtracting the common wavelet coecient PX1from the
other wavelet coecient in that pair. is dierence value is
used to identify the corresponding range 𝑘,𝑖 from the range
table .erangetableisdesignedwithranges[0–7],[8–15],
[16–31],[32–63],[64–127],and[128–255].ewidth𝑘,𝑖
of range 𝑘,𝑖 is used to determine the number of bits 𝑖(𝑖=
log2𝑘,𝑖) that can be hidden in each pair where =0,1,2,3,4.
is 𝑖is then used to calculate the average value ()of
number of bits possible to be hidden in each pair of the block.
e average value isusedtocalculatethereviseddierence
𝑖as 𝑖is remainder (𝑖/2𝑁)sothat𝑖≤2𝑁where 𝑖is
the original dierence. e oset dierence OD𝑖is calculated
as |𝑖|−|𝑖|foreachpairintheblock.ereviseddierence
|𝑖|is then used to determine the number of bits 𝑖for each
pair in the block. us, if the original dierence value |𝑖|
allows bits to be hidden in the pair; then the proposed
approach hides bits ≤in that pair [,].
Aer embedding 𝑖bits of the message in the pair, new
dierence
𝑖is calculated as OD𝑖+𝑘,𝑖 +where 𝑘,𝑖 represents
lower boundary of the range 𝑘,𝑖 in the range table and
represents the decimal equivalent of 𝑖message bits hidden in
that pair.
Embedding 𝑖bits in the pair modies the values of
both the wavelet coecients in the pair. e new values
of wavelet coecients in each pair are dierent from their
original values. Since new value is assigned to common
wavelet coecient PX1in each pair, ve dierent values are
obtained for the common wavelet coecient PX1.However,
the common wavelet coecient PX1can have only one value
in each bock. is requires values of other ve wavelet
coecients PX0,PX
2,PX
3,PX
4,andPX
5to be adjusted such
that the new dierence
𝑖remains unchanged. erefore,
the pair, having new values of wavelet coecients close to
their original values, is selected as the reference pair. To nd
the reference pair, the dierence between 𝑖and
𝑖is
calculated. Small value of ||indicates that the new dierence
value
𝑖is close to the original dierence value 𝑖.us,
for the pair with minimum ||,thenewvaluesofwavelet
coecients are close to their original values. So the pair with
minimum ||is selected as the reference pair. e values of
the two wavelet coecients in the reference pair are used to
adjust the values of wavelet coecients in other pairs and
construct a new 2×3block. e embedded secret information
in newly constructed block is unaected because dierence
values for the pairs are unaltered [,].
During the extraction process, average value ()is
calculated using the same process adopted during embedding
of the secret message. e average value is used to calculate
the revised dierence
𝑖as
𝑖is remainder (𝑖/2𝑁). Suit-
able range 𝑘,𝑖 is identied using this revised dierence. e
secret message is extracted in the decimal form by subtracting
𝑘from |
𝑖|. Secret message is then converted into a binary
stream with 𝑖(𝑖=log
2𝑘,𝑖)bits[,].
e process of hiding secret information in the cover
image is described below [,].
() Create the D array as shown in () by preprocessing
the gray scale cover image.
() Partition the array into nonoverlapping blocks of 2×3
wavelet coecients and group wavelet coecient PX1
with the remaining wavelet coecients in the block to
form ve pairs.
() Calculate the dierence values 𝑖for the ve pairs in
each block: 0=(𝑥,𝑦) −(𝑥,𝑦+1),
1=(𝑥,𝑦+2) −(𝑥,𝑦+1),
2=(𝑥+1,𝑦) −(𝑥,𝑦+1),
3=(𝑥+1,𝑦+1) −(𝑥,𝑦+1),
4=(𝑥+1,𝑦+2) −(𝑥,𝑦+1).
()
() Use |𝑖|where =0,1,2,3,4to locate suitable range
𝑘in the designed range table. Use this range to
calculatenumberofbits𝑖that can be hidden in each
pair 𝑖. en, calculate the average bits using
avg =∑4
𝑖=0 𝑖
5. ()
() Calculate the revised dierence |𝑖|where =
0,1,2,3,4as 𝑖is remainder (𝑖/2avg )sothat𝑖<=
2avg.
() Calculate the dierence OD𝑖as OD𝑖=|𝑖|−|𝑖|for
each pair.
() Use |𝑖|where =0,1,2,3,4to locate suitable range
𝑘in the designed range table.
Mathematical Problems in Engineering
() Compute the number of bits 𝑖that can be embedded
in each pair using the corresponding range given by
𝑘.evalue𝑖can be estimated from the width 𝑘
of 𝑘,whichisgivenby𝑖=log
2𝑘where width 𝑘=
𝑘−𝑘+1and 𝑘and 𝑘are upper and lower boundaries
of the range 𝑘.
() Read 𝑖bits from the binary secret data.
() Calculate the new dierence value
𝑖given by
𝑖=OD𝑖+𝑘,𝑖 +𝑖,if 𝑖≥0,
𝑖=−OD𝑖+𝑘,𝑖 +𝑖, if 𝑖<0. ()
() Modify the values of wavelet coecients in the pair
𝑖using
𝑛,
𝑛+1=𝑛−2,𝑛+1 +2, ()
where 𝑛and 𝑛+1 represent two wavelet coecients
in the pair 𝑖and is obtained by subtracting 𝑖
from
𝑖.
() Select the pair with minimum ||as the optimal
reference pair and use this pair to adjust the values of
wavelet coecients of the other four pairs. e value
of the common wavelet coecient is given by
𝑛of
the reference pair. Modify value of another wavelet
coecient
𝑛+1 of remaining four pairs such that
the new dierence
𝑖will remain unchanged. us,
newvaluesareassignedtoremainingfourwavelet
coecients in the block.
() Check the new values of wavelet coecients for fall-
o boundaries; that is, check whether all the values
are within the range from to . If not, modify the
values preserving the dierence between the values of
two wavelet coecients of each pair in the block.
(a) Find out the smallest of all the wavelet coe-
cients. If the smallest is less than then add
|smallest|in all the wavelet coecients in that
block.
(b) Find out the largest of all the wavelet coe-
cients. If the largest is greater than , subtract
largest − from all the wavelet coecients in
that block.
(c) If fall-o boundary problems still exist, the
cover image is not suitable for hiding secret
information.
() Now, reconstruct the block from all pairs with modi-
ed values of wavelet coecients.
() Repeat steps (2)through () until the secret informa-
tion is embedded in the cover image.
2.3. Postprocessing. Aer the embedding process is over,
original signs are assigned to the elements of D array using
the sign matrix created during preprocessing phase. is is
accomplished by one to one comparison of elements of D
array with the elements of D sign matrix. e D array is
then split to obtain the four subbands. Using inverse D Haar
integer wavelet transform, the four subbands are combined to
obtain the stego image of size [,].Allthepixelvaluesof
the stego image in the range from to indicate that secret
data is safely hidden and can be extracted accurately.
2.4. Extraction Process. e extraction process is blind. It
does not require the existence of cover image for extracting
hidden secret data from the stego image. e stego image is
preprocessed to obtain the D array as shown in ().e
process of extraction of secret information from the stego
image is described below [,].
() Create the D array as shown in () by preprocessing
the gray scale stego image.
() Partition the array into nonoverlapping blocks of ×
wavelet coecients and group wavelet coecient PX1
with the remaining wavelet coecients in the block to
form ve pairs. Keep the partition order the same as
that of the embedding.
() Calculate the dierence values 𝑖for the ve pairs in
each block: 0=(𝑥,𝑦) −(𝑥,𝑦+1),
1=(𝑥,𝑦+2) −(𝑥,𝑦+1),
2=(𝑥+1,𝑦) −(𝑥,𝑦+1),
3=(𝑥+1,𝑦+1) −(𝑥,𝑦+1),
4=(𝑥+1,𝑦+2) −(𝑥,𝑦+1).
()
() Use |𝑖|where =0,1,2,3,4to locate suitable range
𝑘in the designed range table. Use this range to
calculate number of bits, 𝑖, which is hidden in each
pair 𝑖. en, calculate the average bits using ().
() Calculate revised dierence |
𝑖|where
=0,1,2,3,4as
𝑖is remainder (𝑖/2avg )
() Use |
𝑖|where =0,1,2,3,4to locate suitable 𝑘in
the designed range table.
() Aer 𝑘is located, 𝑘is subtracted from |
𝑖|and
𝑖is obtained in decimal form. A binary sequence is
generated from
𝑖with 𝑖bits where 𝑖=log
2𝑘.
Repeat steps (2)through () until embedded message is
extracted.
3. Results
A set of gray scale TIFF images is used for the experimenta-
tion.issetconsistsofstandardimagesaswellasimages
taken from the camera. e standard images are obtained
from the “the USC-SIPI image database (http://sipi.usc
.edu/database/)”. e images taken from Canon A camera
Mathematical Problems in Engineering
T : Comparison of hiding capacity (in bytes).
Cover image PVD method []TPVDmethod[]Gulve’smethod[]Proposedmethod
Capacity PSNR Capacity PSNR Capacity PSNR Capacity PSNR
Lena . . . .
Baboon . . . .
Peppers . . . .
Cover image
Lena.ti
(a)
Stego-image
Lenna.ti
(b)
Baboon.ti
Cover image
(c)
Baboon.ti
Stego-image
(d)
F : Cover and stego images.
in JPG format are converted into gray scale ti format. e
textlesareusedassecretdata.Sincetheproposedalgo-
rithm use PVD approach to hide information in wavelet
coecients, the data hiding capacity and PSNR values of
the proposed method are compared with PVD method [],
TPVD []method,andGulve’smethod[]. e comparison
is shown in Table . e proposed method provides increased
hiding capacity and improved PSNR values as compared
to PVD and TPVD method. Although the PSNR is less as
compared to Gulve’s [] method, there is an improvement in
the security of secret data.
e average payload of the proposed system is ∼. bpp.
e performance of the proposed method is analyzed using
PSNR, Universal Quality Index (), and Structural Similarity
Index Measure (SSIM). and SSIM are full reference image
quality assessment models and require the cover image to
be available [,]. Tab l e shows the PSNR values, MSE,
Universal Quality Index (), and Structural Similarity Index
Mathematical Problems in Engineering
0
500
1000
1500
2000
2500
3000
050 100 150 200 250
Cover image
Lenna.ti
(a)
0
500
1000
1500
2000
2500
3000
0 50 100 150 200 250
Stego image
Lenna.ti
(b)
0
500
1000
1500
2000
2500
3000
0 50 100 150 200 250
Cover image
Baboon.ti
(c)
0
500
1000
1500
2000
2500
3000
0 50 100 150 200 250
Stego image
Baboon.ti
(d)
F : Histograms of cover and stego images.
Measure (SSIM) for dierent images obtained using proposed
method.ePSNRvaluesareabovethethresholdofdB
[] even aer using more than % of the hiding capacity of
the cover image. Also Universal Quality Index ()values[]
and Structural Similarity Index Measure (SSIM) values []
are close to , which proves that the stego images are visually
indistinguishable from original cover images.
Figure shows the cover image and the corresponding
stegoimagesobtainedusingtheproposedmethod.Asthe
gures show, distortions resulted from embedding are imper-
ceptible to human vision.
Figure showsthehistogramofthecoverandstegoimage
obtained using the proposed method. From the gure, it can
be observed that the shape of the histogram is preserved.
e cover image data is subtracted from stego image
and plotted as histogram. Figure shows the pixel dierence
histogram. From the gure, it can be observed that there are
more numbers of bins which are close to as compared to
bins which are away from . Also the step pattern is not
observed in the gure. is conrms that the method is
robust against histogram analysis attack.
Histogram of cover image is represented as [0,1,...,
255]whereas histogram of stego image is represented as
[
0,
1,...,
255].echangeinhistogram[]ismeasured
by ℎ=255
𝑚=1
𝑚−𝑚.()
e proposed method can hide at least bits in each
pair considering the smallest width of the subrange to be .
Figure shows the comparison of the value of ℎof the
bit LSB replacement method and the proposed method with
dierent size of secret data embedded in the cover image,
Lena.ti. It can be observed that dierence in histogram for
theproposedmethodislessthanthatofbitLSBmethod.
Mathematical Problems in Engineering
0 5 10 15 20
0
0.5
1
1.5
2
2.5
3
Dierence values
Occurrence frequency
−20 −15 −10 −5
×104
Cover image
Lenna.ti
(a)
0 10 20 30
0
0.5
1
1.5
2
2.5
3
3.5
Dierence values
Occurrence frequency
−30 −20 −10
×104
Cover image
Baboon.ti
(b)
F : Dierence histogram.
T : Hiding capacity, PSNR, MSE, and index.
Cover
image
Resolutionofcover
image
Hiding
capacity
(Kb)
%of
hiding
capacity
Message
le size
(Kb)
PSNR MSE SSIM
Baboon × . . . . . . .
Lena × . . . . . . .
Elaine × . . . . . . .
Baboon × . . . . . . .
Lena × . . . . . . .
Tan k × . . . . . . .
Peppers × . . . . . . .
Barbara × . . . . . . .
Boat × . . . . . . .
Grass × . . . . . .
e output images are tested under the steganalysis
[]. It is observed from Figure that the dierence between
𝑀and −𝑀 and 𝑀and −𝑀 is very small. e rules 𝑀≅
−𝑀 and 𝑀≅−𝑀 are satised for the output images. is
proves that the proposed method is secure against attack.
4. Conclusion
In steganography, hiding capacity of cover image, quality of
stego image, and security of secret data are three important
factors. ere is always a trade-o between data hiding
capacity of cover image and security of secret data. e
proposed algorithm provides improvements in the data
hiding capacity as well as security of the secret data as
compared to PVD [] and TPVD [] methods. Although
Gulve’s [] method provides better PSNR values as compared
to proposed method, the proposed method improves security
of secret information. e secret information is securely
hidden in the coecients of integer wavelet transform. For
the implementation purpose, the four subbands obtained
aer decomposing the cover image by integer wavelet trans-
form are arranged as shown in Figure .Butitispossibleto
arrange the four subbands in ! = dierent ways thereby
improving the security of the steganography system since
the exact arrangement of four subbands will be known to
sender and receiver only. e algorithm revises the original
dierence between two wavelet coecients in the pair and
this revised dierence is used for hiding the data in that pair.
is makes estimation of exact number of bits hidden in the
pair dicult. Image steganography techniques hiding textual
information require % accuracy for successful retrieval of
hidden information from stego image. If the steganography
method fails, correct estimation of number of bits hidden for
some of the pairs will be a challenge for the invader. us,
Mathematical Problems in Engineering
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
10 20 30 40 50 60 70 80
Histogram dierence
Size of hidden message (KB)
LSB
Proposed
F : Histograms comparison of bit LSB substitution and
proposed method (Lena.ti).
0
0.1
0.2
0.3
0.4
10 20 30 40 50 60 70 79
Ratio of R, S
Message size (KB)
RMSM
R−M S−M
F : diagram.
one more level of security is imposed to secure the secret
information.
e PSNR values produced by the algorithm are close to
. which are well above the threshold of dB aer using
full hiding capacity of the cover image. is proves that the
stego images are of good quality. Results also show that the
dierence between cover image and stego image cannot be
noticed by human visual system (HVS).
Considering the fact that there is currently no steganogra-
phy system that can resist all the steganalysis attacks, the best
way to provide security to the secret data and to eliminate the
attack of comparing the original image with the stego image
is to freshly create an image and destroy it aer generating the
stego image.
Conflict of Interests
e authors declare that there is no conict of interests
regarding the publication of this paper.
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