Robust Image Adaptive Steganography using Integer Wavelets

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Robust Image Adaptive Steganography using Integer WaveletsK. B. Raja*, S. Sindhu*, T. D. Mahalakshmi*, S. Akshatha*, B. K. Nithin*, M. Sarvajith*,

K. R. Venugopal*, L. M. Patnaik***Department of Computer Science and Engineering

University Visvesvaraya College of Engineering, Bangalore University, Bangalore 560 001** Microprocessor Applications Laboratory, Indian Institute of Science, Bangalore 560 012

raja [email protected]

Abstract— Information-Theoretic Analysis for Parallel Gaus-sian Models of Images prescribe embedding the secret data in lowand mid frequency regions of image which have large energies.In this paper, we propose a novel steganographic scheme calledRobust Image Adaptive Steganography using Integer WaveletTransform(RIASIWT), which is a practical realization of theseprescriptions. Using this scheme we can hide large volumes ofdata without causing any perceptual degradation of the coverimage. The scheme embeds the payload in every non-overlapping4x4 blocks of the low frequency band of cover image, two pixelsat a time, one on either sides of the principal diagonal. Testsfor the similarity between the Condition Number of the coverimage and the stego image are done for further embedding.We also perform cover image adjustment before embedding thepayload in order to ensure lossless recovery. Embedding done inthe low frequency bands ensures robustness against attacks suchas compression and filtering. Experimental results show bettertrade off between Visual perceptivity and capacity compared tothe existing algorithms.

Index Terms— Steganography, Integer Wavelet Transforms,Wavelet Lifting, Cover Image Adjustment.

I. INTRODUCTION

Advancement in digital communication and networkinghave posed serious threats to secure data transmission. Thishas driven significant rise in interest among the computersecurity researchers in the field of information hiding.The early approach to secure communications was viadata encryption termed as Cryptography. Cryptographyconcentrates on designing methods to map the original datato some random looking data (encryption) and at the receiverside recovering the meaningful data (decryption). Informationhiding encompasses applications such as Steganography,Copyright protection for digital media and Data embedding .Steganography is the art and science of hiding informationinto a host data set such that its presence cannot be detected.

Generally, steganographic technique consists of two steps:(a) Identification of redundant information in cover object.(b) Replacing or altering the redundant bits to hide thesecret message. The redundant bits are chosen for theembedding process because, any changes made in thesebits do not corrupt the quality or integrity of the coverobject. Steganography finds extensive applications in covertcommunications, authentication, proof of ownership, customertracing, feature tagging and data embedding.

Many techniques have been devised to hide informationsuch that the changes made to the cover image areimperceptible to human vision. Common approaches include:(a) Least Significant Bit insertion, (b) Masking and Filtering,(c) Transform techniques. The simplest method for hidinga secret image is modifying the least significant bits of thepixels in the host image. The advantage of this method is itssimplicity but it is very weak in resisting even simple attackssuch as transforms, compression, etc. The masking andfiltering techniques analyze the image and hide information insignificant areas so that the hidden message is more a part ofthe image than being added noise in the image. The transformtechnique involves modulating the coefficients of the coverdata in the frequency domain. Image hiding techniques thatare implemented in frequency domain take advantage offeatures in human visual system for image hiding.

Common wavelet transforms often have floating pointcoefficients. Thus, when the input data consists of sequenceof integers (as in case of image), the resulting filteredoutput no longer consists of integers, which does not allowperfect reconstruction of the original image. As a result,the inverse wavelet transform becomes lossy. However, withthe introduction of Wavelet Transforms that map Integers toIntegers(IWT), the output can be completely characterizedby integers and exact decompression of the original data isachieved.

Contribution: In this paper, we propose a novel imageadaptive steganographic technique in the integer wavelettransform domain called as the Robust Image AdaptiveSteganography using Integer Wavelet Transform (RIASIWT).According to Information-Theoretic Prescriptions for ParallelGaussian models of images, data should be hidden in low andmid frequency ranges of the host image, which have largeenergies. However, we find that in order to hide large volumesof data with low perceptual distortion, it is essential to addlocal perceptual criteria regarding which host coefficientsto hide data in. A scheme for making such decision usingcondition numbers is provided. We also use cover adjustmentto prevent the over/under flow of the pixel values afterembedding the secret data.

The rest of the paper is organized as follows. In sectionII, we discuss about the related work, In section III we

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discuss about Background work, In section IV we present theRIASIWT model. The experimental results are presented insection V and concluded in section VI.

II. RELATED WORKS

A brief description of related works is presented in thissection.

Xinpeng Zhang et.al., [1] proposed a coding method fordigital steganography in which the amount of bit alterationsintroduced is significantly reduced, leading to lower distortionand enhanced security against steganalysis. This methodworks in a running manner thereby representing the secretbits by a series of consecutive cover bits. Flipping of onecover bit is used to insert several secret bits. However, aseach cover bit alteration is used to embed several consecutivesecret bits, the channel noise is fatal for secret data extractionbecause any cover bit error will cause several bit errors inthe extracted data.

Yu-Chee Tseng [2] proposes a scheme that can make thehiding effect quite invisible by taking into account the qualityof the image after hiding. It ensures that any bit that ismodified in the host image is adjacent to another bit that hasthe same value as former’s new value. Thus, the existenceof secret information in the host image is difficult to detect.Though the scheme is achieved by sacrificing some datahiding space, it offers a good data hiding ratio.

Ziang Liang [3] proposes a wavelet domain steganographicalgorithm based on redundancy evaluation, named as RES,for the JPEG2000 baseline system. The compatibilityand reversibility is ensured by considering the processof uniform quantization and rate distortion optimizedtruncation. Embedding point and its intensity is adjustedimage adaptively to enlarge the information hiding volume.However, the method is limited to lazy mode coding, becauseof the compatibility with the entropy coder of JPEG2000.The technique works well only with images with unevenbrightness and diverse texture activity.

Seki et.al., [4] developed an oblivious image steganographicscheme that requires no knowledge on data hiding positionswhen the data is extracted. This scheme offers to theusers, the flexibility of choosing positions to hide data. Itmodifies the coefficients to embed data image adaptivelyusing compression technology. Since it hides integer data inthe transformed coefficients after the quantization process ofimage compression, the hidden data is no longer distorted bythe rest of the compression process.

Niansheng Liu et.al., [5] developed a new image hidingscheme based on a chaotic sequence. Chaotic sequencesgenerated by chebyshev maps have good auto correlation andnoise like properties. When multiple information is hiddenin a digital image, every chaotic sequence is multiplied by a

corresponding digital signal of hidden grey image to obtaina spreading signal. The spreading signal is just a noise likesignal to an illegal user who does not know the chaoticsequence. So, he cannot extract the hidden information. Thespreading signal is added to the transform spectrum of theoriginal cover image based on discrete space-time transforms.

III. BACKGROUNDA. Lifting and Integer Wavelet Transform

Lifting is a flexible technique that has been used in severaldifferent settings for an easy construction and implementationof traditional wavelets and of second generation wavelets,such as spherical wavelets. Since we can write every wavelettransform using lifting, it follows that we can build an integerversion of every wavelet transform. In each lifting step wecan round-off the result of the filter right before addition orsubtraction [6] [7]. An integer dual lifting step thus becomes:

d(i)1,l = d

(i−1)1,l − b

∑

k

p(i)k s

(i−1)1,l−k + 1/2c (1)

while an integer primal lifting step is given by

s(i)1,l = s

(i−1)1,l − b

∑

k

u(i)k s

(i)1,l−k + 1/2c. (2)

This obviously results in an integer to integer transform.Because it is written using lifting steps, it is invertibleand the inverse immediately follows by flipping the signsand reversing the operations. This leads to the followingpseudo-code implementation of an invertible integer wavelettransform using lifting:

s(0)1,l = s0,2l (3)

d(0)1,l = s0,2l+1 (4)

for i=1 to M

∀l : d(i)1,l = d

(i−1)1,l − b

∑

k

p(i)k s

(i−1)1,l−k + 1/2c (5)

∀l : s(i)1,l = s

(i−1)1,l − b

∑

k

u(i)k d

(i)1,l−k + 1/2c (6)

The inverse transform is given by:for i=M to 1

∀l : s(i−1)1,l = s

(i)1,l − b

∑

k

u(i)k d

(i)1,l−k + 1/2c (7)

∀l : d(i−1)1,l = d

(i)1,l − b

∑

k

p(i)k s

(i−1)1,l−k + 1/2c (8)

s0,2l+1 = d(0)1,l (9)

s0,2l = s(0)1,l (10)

Now we rewrite the Haar transform using lifting. First wecompute the difference and then use the difference in thesecond step to compute the average:

d1,l = s0,2l+1 − s0,2l (11)

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s1,l = s0,2l + d1,l/2 (12)

This is same as Haar transform because s0,2l + d1,l/2 =s0,2l + s0,2l+1/2 − s0,2l/2 = s0,2l/2 + s0,2l+1/2

It is now clear that the inverse transform can be computedin two sequential steps. First, recover the even sample fromthe average and difference, and later recover the odd sampleusing the even and difference. The equation can be foundby reversing the order and changing the signs of the forwardtransform:

s0,2l = s1,l − d1,l/2 (13)

s0,2l+1 = d1,l + s0,2l (14)

as long as the transform is written using lifting, the inversetransform can be found immediately.

B. Condition NumberThe Condition Number is a measure of sensitivity of a

matrix for variation in its elements. Consider a 4x4 matrix,C.

C =

c1,1 c1,2 c1,3 c1,4

c2,1 c2,2 c2,3 c2,4

c3,1 c3,2 c3,3 c3,4

c4,1 c4,2 c4,3 c4,4

The Condition Number of this matrix is evaluated as,

κ(C) =‖ C ‖‖ C−1 ‖ (15)

where, C−1 is the inverse of the matrix CDifferent types of matrix norms are available. A few of themare given below.a)P Norms:

‖ C ‖p= (

m∑

i=1

n∑

j=1

| Ci,j |p)

1

p (16)

b)Frobenious Norms:

‖ C ‖F = Tr(CC∗)1

2 (17)

c)Spectral Norms:

‖ C ‖= (λmaxCC∗)1

2(18)

where, C∗ is the transpose of the complex conjugate of C.But in our case, the elements of the matrices are not complexquantities. Hence, C∗ can be written as CT .

C. Cover Image AdjustmentBefore embedding the secret image into the cover image, it

is necessary to apply a pre-processing step on the cover imageto preserve the overall invertibility of the transform. Theembedding process may modify a coefficient that correspondsto a saturated pixel color component in such a way that itmay exceed its maximum value (255). In such a case, thehigher values will be clipped and the secret message is lost.Hence, the original cover pixel components (C(i, j, k)) areadjusted according to the equations given below,

C ′(i, j, k) =

{

C(i, j, k) − (2N − 1) if C(i,j,k)=255C(i, j, k) otherwise

(19)where C ′(i, j, k)denotes the modified pixel component, i, jdenote the spatial coordinates of the pixel and k representsthe specific color component(red, blue, green). The valueof N denotes the number of bits to be embedded in eachcoefficient. Here, N=4.

IV. MODELIn this section we discuss the embedding and extraction

module of the RIASIWT algorithm.

A. RIASIWT SchemeThe data hiding technique employed in RIASIWT is

an attempt to hide information without introducing muchstatistical variations in the image.

Theorem:Embedding in the principal diagonal causes large variationin the condition number.

Proof : Consider a non-singular 4x4 matrix A.

A =

a1,1 a1,2 a1,3 a1,4

a2,1 a2,2 a2,3 a2,4

a3,1 a3,2 a3,3 a3,4

a4,1 a4,2 a4,3 a4,4

Let κ(A) be the Condition Number of the matrix A, thenby definition we have,

κ(A) =‖ A ‖‖ A−1 ‖ (20)

But from Equation(17), we have,

‖ A ‖= Tr(AAT )1

2 (21)

Let AAT = T.Therefore,

‖ A ‖=

4∑

i=1

Ti,i

1

2

(22)

Similarly,

4

A(3,3)

A(4,1) A(4,2) A(4,3) A(4,4)

A(3,4)A(3,2)A(3,1)

A(2,1) A(2,2) A(2,3) A(2,4)

A(1,4)A(1,3)A(1,2)A(1,1)

Fig. 1. Order in which embedding is done in each 4x4 matrix

‖ A−1 ‖= Tr(A−1(A−1)T ) (23)

κ(A) =

4∑

i=1

Ti,i

1

2 4∑

i=1

T ′

i,i

1

2

(24)

Thus from the above equation, it can be seen that conditionnumber is a direct function of the product of traces of thematrices. Hence embedding is not carried out in the principaldiagonal.

B. Embedding ModuleThe block diagram for RIASIWT embedding scheme

is shown in Figure 2. The payload is converted into onedimensional bit-stream. Before taking transform of the coverimage, we perform cover image adjustment on it to assurethat the reconstructed pixels of cover image after embeddingwould not exceed the maximum value (255), thereby, ensuringproper recovery of the secret message. However, as the coverimage is in true color format (i.e., it consists of three planesnamely Red, Blue and Green), transform is applied on eachplane separately. Taking Integer Wavelet Transform insteadof Discrete Wavelet Transform ensures lossless coding. Theapproximation band, P, obtained after applying IWT on thecover image, C, is divided into a number of non-overlappingblocks of size 4x4. Each of these 4x4 blocks become theentries of another matrix, D. If a cover image, C, of size512x512 is taken , after applying transformation, the size ofthe approximation band, P, will be 256x256 and the size ofmatrix D will be 64x64.

Thus, we can write,

D = [Ai,j ] i, j ∈ 1, 2, 3, ..., 64 (25)

where, each element of D is given as,

Ai,j =

a4i−3,4j−3 a4i−3,4j−2 a4i−3,4j−1 a4i−3,4j

a4i−2,4j−3 a4i−2,4j−2 a4i−2,4j−1 a4i−2,4j

a4i−1,4j−3 a4i−1,4j−2 a4i−1,4j−1 a4i−1,4j

a4i,4j−3 a4i,4j−2 a4i,4j−1 a4i,4j

or,Ai,j = [ak,l] k, l ∈ 1, 2, 3, 4 (26)

The payload is embedded in each of these 4x4 matrices,sparing the principal diagonal elements, as it is observedthat embedding in the principal diagonal would cause largevariations in the Condition Number. After embedding in everytwo pixels, one on either sides of the principal diagonal, wecheck the Condition Number of the matrix. This value iscompared with the Condition Number of the original matrix.Two different cases arise here,

Case1: If the percentage change between the ConditionNumber of matrix before embedding and the ConditionNumber of same matrix after embedding in two pixels (a(1,4)

and a(4,1)), does not exceed the predefined threshold, thenthe the embedding is continued in the next two pixels in theorder shown in Figure 1 .

Case2: If the Condition Number of the matrix afterembedding exceeds the Condition Number of original matrix,then the embedding is stopped. The two changed pixels arereplaced by there original values. Also, the total numberof pixels embedded in the matrix are recorded in positionmemory.

Let the embedded 4x4 matrix be,

A′ = A ± β (27)

where β is the variation caused by embedding process and isgiven as,

β =

0 α1,2 α1,3 α1,4

α2,1 0 α2,3 α2,4

α3,1 α3,2 0 α3,4

α4,1 α4,2 α4,3 0

Observe that the principal diagonal is all zeros as no changeis introduced in it. Let, D1 be the 64x64 matrix of the stegoimage given by,

D1 =

A′

1,1 A′

1,2 · · · A′

1,64

A′

2,1 A′

2,2 · · · A′

2,64

· · · · · ·· · · · · ·· · · · · ·

A′

64,1 A′

64,2 · · · A′

64,64

or,D1 = [A′

i,j ] (28)

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where, i, j ∈ 1, 2, ...., 64 and each A′

i,j , is the 4x4 embeddedmatrix. Substituting for each A′

i,j from Equation (27) inEquation (28), we get,

D1 =

A1,1 A1,2 · · · A1,64

A2,1 A2,2 · · · A2,64

· · · · · ·· · · · · ·· · · · · ·

A64,1 A64,2 · · · A64,64

±

β1,1 β1,2 · · · β1,64

β2,1 β2,2 · · · β2,64

· · · · · ·· · · · · ·· · · · · ·

β64,1 β64,2 · · · β64,64

D1 = D ± γ (29)

where γ is the 64x64 matrix in which each element is thechanged 4x4 matrix, βi,j and is given as,

γ =

β1,1 β1,2 · · · β1,64

β2,1 β2,2 · · · β2,64

· · · · · ·· · · · · ·· · · · · ·

β64,1 β64,2 · · · β64,64

κ(D1) =‖ D1 ‖‖ D−11 ‖ (30)

Substituting Equation (29) in Equation (30), we get,

κ(D1) =‖ (D ± γ) ‖‖ (D ± γ)−1 ‖ (31)

Taking p=2 in Equation (16) and using it to expand,‖ (D ± γ) ‖ in Equation (31),

‖ (D ± γ) ‖= [{

64∑

i=1

64∑

j=1

| Ai,j ± βi,j |2}1

2 ] (32)

or,

‖ (D ± γ) ‖= [{

64∑

i=1

64∑

j=1

| [ak,l]i,j ± [αk,l]i,j |2}1

2 ] (33)

Similarly for ‖ (D ± γ)−1 ‖ in Equation(31),

‖ (D ± γ)−1 ‖= [{

64∑

i=1

64∑

j=1

| (Ai,j ± βi,j)−1 |2}

1

2 ] (34)

or,

‖ (D±γ)−1 ‖= [{

64∑

i=1

64∑

j=1

| ([ak,l]i,j±[αk,l]i,j)−1 |2}

1

2 ] (35)

Only those matrices in which αk,l � ak,l are chosen forembedding. This is justified as the above condition willensure that the Eigen Value of the embedded matrix will notvary significantly, thus not varying the Condition Numbersignificantly as stated in Theorem.

Substituting the above condition in Equations (33) and(35),we get,

‖ (D ± γ) ‖≈ [{64∑

i=1

64∑

j=1

| [ak,l]i,j |2}1

2 ] (36)

‖ (D ± γ)−1 ‖≈ [{64∑

i=1

64∑

j=1

| ([ak,l]i,j)−1 |2}

1

2 ] (37)

thus we get,‖ (D ± γ) ‖≈‖ D ‖ (38)

and

‖ (D ± γ)−1 ‖≈‖ D−1 ‖ (39)

Substituting Equations (38) and (39) in (31),

κ(D1) ≈‖ (D) ‖‖ (D)−1 ‖ (40)

κ(D1) ≈ κ(D) (41)

Thus the Condition Number of the stego image isapproximately same as the Condition Number of thecover image, so that not much variation occurs in the stegoimage. This ensures that the statistical features of the coverimage are not altered significantly. The position memoryis embedded continuously into the approximation band ofanother color plane. For added security we use pseudo-randomnumber generator to randomly select the blocks. Thus, evenif the algorithm is known, one cannot extract the hidden datawithout knowing the key used for pseudo-random numbergenerator. Inverse IWT is taken after embedding is completedto obtain stego image.

C. Extraction ModuleThe extraction process is quite simple and the inverse of the

embedding operation. Figure 3 shows the block diagram forextraction of payload from the cover image. The stego imageis separated into different color planes and IWT is performed

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from Approximation Band

Color Plane Separation

One Dimensional Bit Stream

Inverse Integer Wavelet Transform

Extraction of 4x4 Blocks

RIASIWT

Payload

N=4

LiftingHaar

Cover Adjustment

Cover Image

Integer Wavelet Transform

Stego Image

Embedding Based on

Pseudo RandomNumber GeneratorKey

Position Memorization

Embed in Approximation band

Fig. 2. Block Diagram for Embedding the Payload in Cover Image usingRIASIWT algorithm

LiftingHaar

Stego Image

Approximation Band4x4 blocks of

Separation of Colour Planes

Retrieval Using RIASIWT

One−Dimensional bit streamof Payload

Payload

Position Memory

Approximation Band

Pseudo Random

Integer Wavelet Transform

Number Generator

Key

Fig. 3. Block diagram for Retrieval of Payload from Stego Image usingRIASIWT algorithm

on each plane. From the approximation band, the positionmemory is retrieved and later from another approximationband, the payload is retrieved by making use of the positionmemory. However, it is necessary that the decoder knows inwhich plane the position memory and payload are embedded.The key for the pseudo-random number generator must alsobe known, without which, the retrieved message is just arandom noise for the retriever. The necessity of knowledgeof the order in which the pixels are embedded adds to theextra security of the stego image. Thus, even if the algorithmis made public, it is not possible to retrieve the data withoutknowing the key and the embedding order.

TABLE I

Algorithm for Embedding: RIASIWT1) Take a color image of size 512x512 as an input and

perform cover image adjustment.2) Separate the color planes.3) Take IWT of one of the color planes.4) Divide the approximation band into non-overlapping

matrices of size 4x4.5) Find the Condition Number of each matrix.6) Embed two pixels of payload in two non-principal

diagonal elements of 4x4 matrix, one on either side ofthe principal diagonal.

7) Check the Condition Number of altered matrix.8) If the percentage change between the Condition Number

of original matrix obtained in step 5 and that of thechanged matrix obtained in step 7 is within the thresh-old, repeat step 6 and step 7, else switch to step 9.

9) Repeat step 5 to step 8 for each 4x4 matrix and recordthe number of pixels embedded in each matrix into anarray (position memory).

10) Embed the array obtained in step 9 into the approxima-tion band of another color plane of the cover image.

11) Take the inverse transform using IIWT.12) Combine the three color planes into a single color

image.

D. Algorithm

Problem definition:Consider a cover image and a payload, the objectives are to

• Embed the payload into the cover image using IntegerWavelet Transform.

• The stego image should be robust and secure againstattacks.

• The stego image must have minimum perceptualdegradation i.e., maximum PSNR.

Assumptions:

• Embedding is carried out only in the non-singular ma-tricies.

• A change in the intensity value of the pixel by ±15 orless is imperceptible to human vision.

• Cover image and Payload are JPEG images. The Coverimage is a color image of size 512x512.

The RIASIWT algorithm for embedding is given in Table I.Cover image is adjusted against overflow and converted intowavelet domain using IWT. The payload is converted into onedimensional bit stream and embedded in 4x4 non overlappingblocks of approximation band of the cover image to derivethe stego data. The stego data is converted into spatial domainstego-image using Inverse IWT.

The RIASIWT algorithm for retrieval is given in Table II.The payload is retrieved at the destination using the reverseprocess of RIASIWT embedding.

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TABLE II

Algorithm for retrieval: RIASIWT1) Input stego image and separate the color planes.2) Apply Integer Wavelet Transform.3) Retrieve the position memory from the approximation

band of corresponding color plane.4) Divide the approximation band into non-overlapping

matrices of size 4x4.5) Start extracting the payload in the order in which it

is embedded. Use position memory to know the exactnumber of pixels embedded in each matrix.

6) Convert the extracted one dimensional array of payloadinto an image.

Fig. 4. Test Image Set: Bouquet, Lena, Flowers, Mandril, Mountain, Redparrot, Pepper, Saturn, Tigers

Fig. 5. Cover image(Flowers) and Original payload(Parrots)

Fig. 6. Stego image(Flowers) and Retrieved payload(Parrots)

Fig. 7. Stego images generated by RIASIWT algorithm for differentthresholds,T =0, 15, 30, 50

8

9

10

11

12

13

14

15

16

17

0 10 20 30 40 50

Capacit

y in 100

0 Pixel

s

Threshold

PepperMandril

Fig. 8. Relationship of the Capacity versus the threshold obtained for highresolution(Pepper) and low resolution (Mandril) image.

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Payload Size DWT DWT IWT IWT(in pixels) PSNR MSE PSNR MSE

128x128 44.51 2.29 45.03 2.04150x150 43.91 2.64 44.34 2.38200x200 42.53 3.62 42.85 3.37256x256 41.10 5.04 41.32 4.79

TABLE IIICOMPARISON OF DWT AND IWT WITH PARROTS AS THE PAYLOAD AND

SATURN(512X512) AS COVER IMAGE

Threshold Payload PSNR MSE EntropyPercentage size (pixels) Change

0 8251 45.01 1.96 0.00041 8443 45.06 2.02 0.00042 8521 45.01 1.89 0.00043 8713 44.93 2.08 0.00054 8873 44.89 2.10 0.00055 8943 44.84 2.13 0.0006

10 9639 44.49 2.31 0.000715 10,451 44.22 2.45 0.000720 11,145 44.03 2.56 0.000725 12,103 43.74 2.74 0.000930 13,073 43.41 2.96 0.000935 14,259 43.06 3.21 0.000840 14,813 42.87 3.37 0.001245 15,851 42.60 3.56 0.001150 17,193 42.33 3.79 0.0013

TABLE IVEXPERIMENTAL RESULTS: PAYLOAD(PARROTS), COVER

IMAGE(FLOWERS)

V. EXPERIMENTAL RESULTS AND PERFORMANCEANALYSIS

We tested our algorithm on a test image set shown inFigure 4, which includes some of the common imagesused in steganography. The scheme provided excellentresults in all the cases. The algorithm was simulated usingMATLAB. Figure 5 shows the cover image and payloadbefore embedding. The stego image obtained after embeddingthe payload using RIASIWT algorithm and the retrievedpayload from the stego image are shown in Figure 6. It isobserved that the cover image and stego image as well asthe original payload and the retrieved payload are similar.We now show that, using the proposed algorithm, one canhide large volumes of data with high robustness and minimalperceptual degradation. We use PSNR as an objective metricto qualify the quality of the stego image. Table IV shows thenumber of pixels embedded in the cover image for differentpercentage threshold. It is observed that as the thresholdincreases, the capacity increases remarkably with slightdecrease in PSNR. The entropy variation remains almost zerotill the threshold reaches the value, 40. At threshold equal to40, the entropy variation slightly increases. The MSE valuesare also acceptable. Figure 7 shows the different stego imagesobtained after embedding with different thresholds viz. 0, 15,30 and 50. It is observed that the stego image in all the casesis very similar to the original cover image. However, minutechanges can be observed in the low intensity regions of the

stego image for threshold equal to 50. A comparison betweenIWT and DWT has been made in Table III to show that IWTcan perform better and lossless than DWT. It is observed thatthe PSNR and MSE of the images have improved remarkablyafter employing IWT.

The Graph in Figure 8 shows the comparison betweenthe performance of RIASIWT algorithm on a low resolutionimage (Mandril) and a high resolution image (Pepper). Forlow values of threshold, T, the algorithm embeds almostsame volume of payload in both the images. However,beyond the threshold 10, there is a significant rise in thepayload volume in the low resolution image. It is alsoobserved that at threshold 30, the given payload of size16,384 pixels gets completely embedded in Mandril whereasPepper can accommodate only about 12,250 pixels of payload.

VI. CONCLUSIONSA robust steganographic technique to embed high volumes

of data in the integer wavelet domain has been proposed.The scheme uses the Condition Number of the blocks of thestego image as an objective metric to decide the amount ofinformation to be hidden in the corresponding blocks of coverimage. Embedding done in non-principal diagonal coefficientsof the low frequency band ensures better robustness. Thealgorithm offers excellent performance without any errorcorrection codes. It can hide high volumes of informationcompared to many existing robust and secure data hidingtechniques and yet retain better values of PSNR and MSE.However, the algorithm requires hiding of the positionmemory along with the payload in the stego image whichmay be a drawback in certain cases. This when avoided canincrease the capacity to a higher value.

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