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Kumar and Muttoo, J Comput Eng Inf Technol 2013, 2:2http://dx.doi.org/10.4172/2324-9307.1000105 Journal of Computer

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Image Steganography Based on Wavelet FamiliesSushil Kumar1* and S. K. Muttoo2

AbstractWavelet transforms are considered to be an ideal domain for image compression and transmission. The new generation still image compression standard JPEG2000 uses the bi-orthogonal CDF 5/3 wavelet (also called the CDF (2, 2) wavelet) for lossless compression and a CDF 9/7 wavelet for lossy compression. There are several known wavelet families such as Daubechies, Coiflet, Symlet, CDF, etc. The problem of selecting a suitable wavelet for signal and image processing has always challenged the researchers. The conventional wavelet filters often have floating point coefficients and couldn’t realize the lossless reconstruction. The second generation wavelet transforms are based on lifting scheme and they map integers to integers. Thus they realize the lossless compression of image data with minimal memory usage and low computational complexity. For image steganography, the researchers have used mainly Integer Wavelet Transforms, viz., Haar Wavelet or CDF (2, 2).There are research papers investigating different wavelets and finding a suitable wavelet for image compression or image denoising, but the research on investigating wavelet families for the steganography is still an open problem. In this paper, we analyze some of the wavelets available in Matlab ver 8.0 using the modified LSB technique for the embedding of secret message in the transform domain. In the first stage, we obtain the secret message by encoding the original message with self-synchronizing codes, T-codes. In the pre-processing stage, we apply the hard thresholding to the high bands obtained by applying the wavelet transform to the original cover and obtain the noisy regions for hiding the message. The embedding technique used is modified LSB, as it is simple and fast, in the high bands of the transformed image. From experimental results, it is observed that the distortion is not visible through the naked eyes, though mathematically, it can be easily detectable through histogram analysis. The results show that Haar wavelets are best for the imperceptibility and security of image as compare to other wavelets.

KeywordsSteganography; Wavelet; PSNR; SSIM; KlDiv

IntroductionThe wavelet research community has presented several wavelet

families, such as Daubechies, Coiflet, Symlet, Haar, Cohen-Daubechies-Feauvea (CDF) etc. each with different shape and lengths of mother wavelet leading to different wavelet filters with different properties [1,2]. Grgic et al. [1] have shown the scaling and wavelet functions from each wavelet families with their filter lengths in figure

*Corresponding author: Sushil Kumar, Department of Mathematics, Rajdhani College, University of Delhi, New Delhi, India, Tel: +91-1125930752 ; Fax: +91-11-25116988; E-mail: skazad@rajdhani.du.ac.in

Received: February 15, 2013 Accepted: March 29, 2013 Published: April 23, 2013

5, page 688. Choosing the right wavelet for a specific application has been an open question due to lack of sufficient understanding. A Haar wavelet is the simplest type of wavelet. It is fast and is memory efficient, since it can be calculated in place without a temporary array. It is also exactly reversible without the edge effects that are a problem with other wavelet transforms [3,4]. Sylvia et al. [5] have described a steganography implementation using the insignificant coefficients of a fast transform of an image for data hiding. On the basis of performance of their method using different transforms, they observed that Haar wavelet transform is the best choice over the FFT, DCT and Hadamard transform. Daubechies wavelets are a family of orthogonal wavelets defining a discrete wavelet transforms and characterized by a maximal number of vanishing moments for some given support. A wavelet is said to have “N-vanishing moments” if it has this property on polynomials up to degree N-1.The Symlet and Coiflet wavelet come from Daubechies wavelet, but are both symmetric. Meyer wavelets are also symmetric but no fast algorithm is available for its wavelet transform [6]. The CDF wavelets are historically the first family of bi-orthogonal wavelets, which were made popular by Ingrid Daubechies. The JPEG 2000compression standard uses the biorthogonal CDF 5/3 wavelet (also called CDF (2, 2) wavelet) for lossless compression and a CDF 9/7 wavelet for lossy compression. Shakhakarmi [7] has shown highest SNR and lowest MSE in Biorthogonal-2.4, higher MSE in Haar WLT except FFT-2 and DCT, DB-2 and Bior-2.4 provide the highest Entropy and Haar and Sym-8 provide best PSNR. He has further found that the 2D image compression performance is significantly 93.00% in DB-4, 93.68% in bior-4.4, 93.18% in Sym-4 and 92.20% in Coif-2 during the multiscale analysis. The details on wavelet families and their associated properties can be found at the site Mathworks [8]. We summarize the characteristics of some of wavelets used in Table 1.

Among all the filters, Integer Wavelet Transforms (IWTs), i.e., the transforms that map integers to integers such as S-transform, Haar transform and CDF (2, 2) transform, have been widely used by the researchers for data hiding in images [9-17]. Xuan et al. [17] proposed a reversible data hiding method based on wavelet spread spectrum and histogram modification. They have mentioned that various wavelet families can be applied to their scheme, but found CDF (2, 2) to be a better candidate than other wavelet families in terms of embedding capacity and visual quality of embedded images since IWT’s can reconstruct the original cover without distortion. Another

Wavelet

Compact-ly sup-ported

orthogo-nal

Com-pactly

support-ed bi-or-thogonal

Symme-try

Fast Computa-

tion

Vanish-ing

MomentsFilters

Bior<Nr.Nd> No Yes Yes Yes Arbitrary FIR

Coif<N> Yes No Near Yes Arbitrary FIRDb<N> Yes No No Yes Arbitrary FIRHaar Yes No Yes Yes Two FIR

Meyer No No Yes No Infinite FIRSym<N> Yes No Near Yes Arbitrary FIR

Table 1: The characteristics of wavelet families.

Citation: Kumar S, Muttoo SK (2013) Image Steganography Based on Wavelet Families. J Comput Eng Inf Technol 2:2.

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reason for this was given to overcome the problem that even if the input signal/cover object is of integer values, the output of wavelet filters (i.e., the coefficients of the approximation and detail sub-bands) are floating point values, and some modifications (including the machine precision) to these values cause quantization errors at the reconstruction stage, resulting into a non-perfect reconstruction [18,19,10,12]. Further, IWT is inferior in capturing edge details of the image [20].To take care of this problem, we use the following (approximation) reversible formula to convert the coefficient values of detail sub-bands obtained of wavelet families:

( )( ) ( ) _ / .*x int floor abs x T sign x= (i)

( ) ( )( )_ _ .* _ .5 * x rec sign x int abs x int T= + (ii)

The value of T is used to map the floating point representation of transform coefficients to integers. This is an approximation method and the error between original cover image values and the resulting values obtained of (i) depends on the choice of T. For uniform data, it is seen that when T reduced from 0.9 to 0.1, the error reduces approximately from 0.8 to 0.05. It is observed that more the value of T more is the space available for hiding data. On the other hand, larger the value of T, lower is the value of PSNR (peak signal noise ratio) observed. Thus, the best choice of T would then be the value that provides larger space for hiding the message with minimal error.

In this paper we compare different wavelet families for the image steganography based on Modified LSB technique and find out which wavelet is more suitable from them. It is known thatLSB embedding is likely to be modified, and destroyed, by further compression, filtering, or a less than perfect format or size conversion [21]. Thus, we have proposed a modified or randomized LSB technique that uses a randomized permutation function to permute the coefficients of detail sub-bands obtained from the cover image before embedding the secret message using LSB technique. We note here that the proposed embedding technique, however, is still vulnerable to replacing the LSB’s with a constant but it proves to be a simple and fairly powerful tool for steganography at the expense of its low fidelity in secret communications. Since we expect no intentional attacks, for sake of its simplicity, we use the modified LSB technique for data hiding. Further, we use self-synchronizing variable length codes, viz., T-codes, introduced by Titchener [22] for obtaining the secret message from the original message. The research on T-codes by Gunther [23] proves that T-codes resynchronize the variable-length coded data after the data loss of within one to three words. It has been shown by P. Reddy [24] that T-codes exhibit better synchronization properties when compared to Huffman codes. Kumar S et al. [13] have used T-codes for encoding the original message before embedding in the wavelet-like transforms and complex wavelet transform. Their results shows better imperceptibility and embedding rate than the existing DWT based methods.

We present a review on the attributes of steganography techniques in the under the heading ‘Steganographic Techniques’. Under the heading ‘Proposed First Algorithm, we propose the first algorithm on different orthogonal wavelets. The experimental results are given under the heading ‘Experimental Results for Algo 1’. Under the heading ‘Proposed Second Algorithm’ , we present another algorithm based on Haar and CDF9/7 and their experimental results are discussed under the heading ‘Expermental Results for Algo 3’. Finally, the conclusion and the future scope are discussed under the heading ‘Conclusions’.

Steganographic TechniquesMany research articles [25-30,3] can be found in the literature

on the data hiding or steganography techniques. There are two basic steganographic methods: Image domain methods (i.e., Least Significant Bit (LSB)) and Transform-Based methods. Transform based steganography is potentially more resistance to loss from image manipulation and vulnerable to attacks as mentioned in [31]. According to Tolba et al. [14], we may also classify the data hiding into two main categories: High bit-rate data hiding and low bit-rate data hiding. High bit-rate methods are not immune to image modifications. They can be made more robust through the use of error-correction coding but at the expense of data rate. However, for some authors, robustness should not be considered as an attribute of steganography as it is then difficult to differentiate it from watermarking. The three main attributes of steganography are Imperceptibility, Payload Capacity and Security [10,11,14,21]. In Table 2, we give the meaning of these characteristics. In Table 3 we present the comparison between LSB and transform techniques base on these requirements.

The solution to a problem of designing a high capacity data embedded system based on DWT is provided by many research scholars [32-35,11]. Researchers mainly concentrated on hiding data in gray-scale images and color images. It is generally considered that gray-scale images are more suitable than color images for hiding data because the disturbance of correlations between color components may easily reveal the trace of embedding. Therefore, we have focused on gray-scale images for proposed image steganography technique. To measure the different requirements of image steganography, the following three metrics are widely used:

Measure of imperceptibility

The most prominent measure for calculating the difference between the original image and the stego-image (or the reproduced image) is PSNR (Peaked Signal to Noise Ratio). This aspect measures how much difference (distortion) was caused by data hiding in the original cover, where the higher the stego-image quality, the more invisible the hidden message. We can judge the stego-image quality by using Peak Signal to Noise Ratio (PSNR). The PSNR for an image of size NxN is given as follows:

Characteristics Meaning

Imperceptibility(or invisibility) Inability of an attacker to distinguish between cover object and steganographic object.

Security Complexion of extraction procedure not to extract the hidden data, easily

Payload Capacity measure of amount of information that can be stored in the cover object

Table 2: The characteristics of Stegaongraphy.

Domain Impercepti-bility

Embedding Payload Security

Robust-ness

against common statistical

attacks

Robust-ness

against image

processing operations

LSB High High Low Low LowTransform High Medium High Medium Medium

Table 3: A comparison between LSB and transform domain based Image Steganography Techniques.

Citation: Kumar S, Muttoo SK (2013) Image Steganography Based on Wavelet Families. J Comput Eng Inf Technol 2:2.

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( ) ( )

( ) ( )

2

2

10 10 255 / ,

1 / * – ’ ,

PSNR log MSE dB

MSE N N xij x ij

=

= ∑ ∑

The MSE is the Mean Square Error, xij stands for the image pixel value in the cover image and x’ij is for the pixel value at position (i, j) in the image after inserting secret message. When values of MSE are below 0 dB, it means the noise power is larger than the signal. For identical images, the PSNR is infinite. A high value of PSNR means better image quality (less distortion). Generally, when the PSNR is 40 dB or larger, then the 2-images are virtually indistinguishable by human observer [36].

The Matlab code segment for finding the PSNR after adding Gaussian noise to stego-image, GPSNR, used in the paper, is as follows:

( )( )

( )( ) ( )( )( )( ) ( )

( )( )

’ ’;1 ,1 ;

2 ,2 ;

, ' ',0.0001 ;

. ^ 2 / 1* 2 ;

20* 10 255 / ;

im stego imageN size im

N size im

stgauss imnoise im gaussian

gmse sum sum double im double stgauss N N

GPSNR log sqrt gmse

= −

=

=

=

= −

=

For finding PSNR after adding Salt-n-Pepper noise in stego-image, the code segment used is:

2

( , ,0.005);( (( ( ) ( )). )) / ( 1* 2);

20* 10(255 / ( ));

stSnP imnoise im salt n pepperSnPmse sum sum double im double stSnp N NSnPPSNR log sqrt SnPmse

′ ′= − −

= −=

Measure of structural similarity

The structural similarity (SSIM) was suggested by Wang et al. [31]. It is composed of three values: Luminance comparison; Contrast comparison; and Structural comparison. These components are normalized such that they are 1.0 for identical images. The SSIM index is the product of these three components (raised by an exponent, if required). The formula for this measure is given by

( ) ( )( )

1 2

2 2 2 21 2

2 ( ,

)

(

)

σ

σ σ

+ +=

+ + + +x y xy

x y x y

µ µ C CSSIM E F

µ µ C C

where µx , µy , σx, σy , and σxy local statistics parameters of the two images E and F and C1 , C2 are constants used to avoid division by zero.

Measure of security

The Kullback-Liebler Divergence (KLDiv) or relative entropy is a measure of distance between two probability distributions. Let random variable X and Y denote the cover image and stego image respectively, and let px and qy represent the probability mass functions (pmfs) of x and y respectively. The KLDiv between the two probability mass functions (pmfs), px and qy, is defined as:

( ) ( ) ( )( ( || ) [ /g GD px qy px g log px g qy gε= ∑

where g εG≈{0, 1, 2, ..., 255}is the pixel value in gray scale images.

The stego system is considered perfectly secure in the Cachin’s sense [9] if ( || ) 0D px qy = . It is called ε-secure, if ( | .) |D px qy ε≤

For the design of embedding schemes that can evade statistical

steganalysis while hiding at high rates, and achieve robustness against attacks, zero K-L divergence between the cover and the stego signal distributions is proposed by Solanki et al. [30] as the provable security. We note that the relative entropy provides only a security measure against steganalysis.

Proposed First AlgorithmIn this section we investigate different orthogonal wavelet filters

for image steganography based on randomized LSB method. We implement these algorithms in Matlab 8.0. The Embedding algorithm 3.1, the embedding process of the proposed algorithm based on different orthogonal wavelets as given in Table 3 is summarized.

Algo 1: Embedding

Input: Message, M, cover image, Cover, an 8-bit grayscale image, of size 256 X 256,thresholding value, T (used to map floating values to integers),and random-key, k.

Output: stego-image, I’

Step1: First, the cover image is pre-processed to protect from overflow and underflow by reducing the intensity value 255 to 254 and 0 to 1.

Step 2: The cover image is then transformed using wavelet filters using the matlab code

[C, S] = wavedec2(‘Cover’,N,’sym20’),

where N is the level of decomposition.

Step 3: Obtain the row vectors A, H, V, D from C where A = approximation coefficients, H = horizontal detail coefficients, V = vertical detail coefficients and D = diagonal detail coefficients

Step 4: The coefficients of H, V and D are approximated to integer values using the formula

x = floor (abs(x/T)).*sign(x), …… (*)

where the threshold, T=0.9.

Step 5: The secret message is obtained by encoding the original message with SSVLC, viz., T-codes. This also generates a encoded-key, which will be required later by receiver for decoding the secret message.

Step 6: The frequency coefficients of middle and high sub-bands, H, V and D are mapped into integer values using threshold T=0.9 using the formula (*) as given in step 4.

Step 7: The coefficients of sub-bands, A, V and D are permuted randomly using a random-key, k, and obtain new sub-bands A’, V’ and D’

Step 8: Embed the secret message in the middle and high frequency bands, A’, V’ and D’ using the LSB method.

Step 9: The coefficients of A’, V’ and D’ are then readjusted by the reverse operation of Step4,viz.,

x = sign(x).* (abs(x)+.5) * T

Step 10: Finally, the stego-image is obtained by applying the matlab code:

y=waverec2(C,S,’sym20’);

Citation: Kumar S, Muttoo SK (2013) Image Steganography Based on Wavelet Families. J Comput Eng Inf Technol 2:2.

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{Vector C is organized as:C = [A(N)| H(N)| V(N)| D (N) | ..H(N-1) | V(N-1) | D(N-1) | ...| H(1) | V(1) | D(1) ],where A, H, V, D, are row vectors such that: A = approximation coefficients, H = Horizontal detail coefficients, V = Vertical detail coefficients, D = Diagonal detail coefficients and each vector is the vector column-wise storage of a matrix.}

The process of extraction is just the reverse process of embedding and is summarized below:

Algo 2: Extraction

Input: stego-image, y, random-key, k, encoded- key, K

Output: original message, M

Step 1: Apply Wavelet filters to the stego-image,y to obtain sub-bands, A, V, and D as shown in Step2 of embedding.

Step 2: Permute the coefficients of sub-bands A, V and D using the random- key, k to obtain the sub-bands A’’,

D’’and HH’’.

Step 3: Extract the secret data, M’, from sub-bands using inverse operation of LSB technique.

Step 4: Recover the original message, M, by applying T-decoding using the encoded- key, K

Experimental Results for Algo 1For testing our algorithm 3.1 we have used 256 x 256 pixels

images. In the Table 3, GPSNR and SnPPSNR are the PSNR values obtained of stego-images after adding the Gaussian and Salt and Pepper noise with densities 0.001, 0.005, and 0.0001. The Figure 1 shows that the PSNR values decreases as the message size increases. It is observed that Haar wavelet outperforms than the other wavelets. The experimental results are summarized in the Table 4.

From Table 4, we observe that all wavelet families used in the proposed algorithm have acceptable PSNR values, SSIM values are near to 1, and maximum KLDiv values are near to zero. However, Haar Wavelet shows the best result in comparison to other wavelets. Further, we obtain the values of PSNR after adding Gaussian and Salt-n-Pepper noise of densities 0.01, 0.005 and 0.0001. We observe that the data hiding scheme based on MLSB is not robust, as expected.

In the Figure 2 we show the values of SSIM with respect to BPP and observe that Haar wavelet performs better than the other wavelets when compared in terms of SIMM as the embedding capacity increases.

Statistical steganalysis

In the literature we find different methods [38,27,28] for statistical steganalysis which are also exploited to design improved steganographic systems. Cachin [9] has proposed an appropriate

bior2.2coif4db8dmeyhaarsym8

50.5

50

49.5

49

48.5

48

47.5

470 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

BPP

PSN

R

Figure 1: PSNR vs message-size for some wavelets.

Wavelet PSNR SSIM MAX(KLDIV)

GPSNR(0.001,0.005,0.0001)

SnPPSNR(0.001,0.005, 0.0001)

Bior2.2/Bior2.4 47.408586/47.487810

0.990718/0.990870

0.000069/0.000074 5.7517, 5.7518, 5.7517 5.7541, 5.7540, 5.7541

Coif4 48.139825 0.991780 0.000069 5.7517, 5.7518, 5.7517 5.7541, 5.7540, 5.7541

Db2/Db8 48.466794/48.263149 0.992049/0.991933 0.000067/0.000068 5.7518, 5.7518, 5.7517 5.7541, 5.7540, 5.7541

Dmey 48.442661 0.992333 0.000065 5.7517, 5.7518, 5.7517 5.7541, 5.7540, 5.7542

Haar 49.557103 0.993614 0.000048 5.7517, 5.7518, 5.7517 5.7541, 5.7540, 5.7541

Sym8 48.056754 0.991643 0.000072 5.7517, 5.7518, 5.7517 5.7541, 5.7540, 5.7541

Sym20 48.175164 0.991867 0.000069 5.7517, 5.7518, 5.7517 5.7541, 5.7540, 5.7542

Db20 48.832998 0.993058 0.000054 5.7517, 5.7518, 5.7517 5.7541, 5.7540, 5.7542

Table 4: Comparative study of wavelet families (embedding capacity= 1000 ASCII characters).

Citation: Kumar S, Muttoo SK (2013) Image Steganography Based on Wavelet Families. J Comput Eng Inf Technol 2:2.

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BPP

0.995

0.9945

0.994

0.9935

0.993

0.9925

0.992

0.9915

0.991

0.99060 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

SSIM

bior2.2coif4db8dmeyhaarsym8

Figure 2: SIMM vs BPP for some wavelets.

BPP

7.5

7

6.5

6

5.5

5

4.5

4

3.50 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

max

(<_D

iv)

bior2.2coif4db8dmeyhaarsym8

x 10-5

Figure 3: Maximum KLDiv vs BPP: MLSB using wavelet family.

information-theoretic model and defined a formal security notion which is basically the relative entropy (KLDiv) between the cover data and the steganographic data. If KLDiv is zero, the steganographic system is called perfectly secure. In Figure 3, we show that the results of maximum KLDiv values obtained are of different wavelet families based on the proposed MLSB data hiding technique increases as the bit-per-pixel (BPP) values increases. From Table 4 and Figure 3, we observe that the KLDiv values are near to zero for all wavelet families, but Haar wavelet has the least value. Thus, Haar wavelet is better option than the others for provable security.

Histogram analysis

It may be noted as mentioned in [27] that the embedding distortion can be large, even if KLDiv is zero. Thus the embedding distortion should be as small as possible to achieve a secure steganographic system. In this paper, we, therefore, give histogram analysis as the method to measure the embedding distortion of data hiding scheme. In the Figure 4, we observe that the histograms of stego-image obtained from different wavelets for the image ‘lena.jpg’ after embedding the secret message of capacity 1000 bytes are almost similar.

From the experimental results of histogram, we observe that there is not much embedding distortion seen when the embedding capacity is 1000 ASCII characters for all the wavelet families used in the proposed algorithm. It is further observed that the embedding distortion in case of Haar Wavelet remains undetectable by histogram even if embedding capacity increases.

Proposed Second AlgorithmWe now present the second algorithm 5.1 that compares the

Integer Haar wavelet with the bi-orthogonal wavelet used in JPEG 2000, viz., CDF9/7 for the image steganography based on Modified LSB method.

Algo 3: Embedding

Input: Message, M, cover image, I, an 8-bit grayscale image, of size 256 X 256 and random-key, k.

Output: stego-image, I’

Step 1: First, obtain the secret data, M’, with encoded key, K, by applying best T-codes as a source encoder to the given input message, M.

Citation: Kumar S, Muttoo SK (2013) Image Steganography Based on Wavelet Families. J Comput Eng Inf Technol 2:2.

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Lena.jpg

Db8

Sym8 Db20 Sym20

Dmey Haar

Bior2.2 Coif4

Figure 4: Histograms of stego-images of ‘Lena.jpg’ for different wavelets.

Step 2: Apply pre-processing to I, to prevent possible “overflow” during embedding, i.e., replacing the gray scale values 0 to 1 and 255 to 254 of cover image.

Step 3: Decompose the cover image, I, into 4 sub bands, viz., HH, HL, LH and LL, by applying Integer Haar wavelet and CDF9/7 wavelet.

Step 4: The frequency coefficients of middle and high sub-bands, HH, HL and LH obtained through CDF9/7 are converted into integer values using threshold T=0.9 using the formula (*) as given in step 4 of algorithm 2.1.

Step 5: Permute the coefficients of sub-bands, HL, LH and HH randomly using a random-key, k, and obtain sub-bands LH’, HL’ and HH’.

Step 6: Embed the secret message in the middle and high frequency bands, LH’, HL’ and HH’ using LSB embedding technique.

Step 7: Apply the inverse of step4 to adjust the coefficients values and then obtain the stego sub-bands LH, HL and HH respectively, applying inverse operation of random permutation.

Step 8: Form the embedded image, E, of size 256 X 256by merging the stego sub-bands with low sub-band LL

Step 9: Obtain stego-image, I’ by taking the inverse Haar transform/ inverse CDF9/7 transform of E.

Algo 4: Extraction

Input: stego-image, I’, stego-key, k, encoded key, K

Output: original message, M

Step 1: Apply Haar/ CDF97 transform to the stego image to obtain 4 sub-bands, LL, HL, LH and LL

Step 2: Permute the coefficients of sub-bands HL, LH and HH using the stego- key, k to obtain the sub-bands HL’, LH’ and HH’.

Step 3: Extract the secret data, M’, from the middle and high frequency sub-bands by inverse modified LSB technique.

Step 4: Recover the original message, M, by applying T-decoding using the encoding key, K.

Experimental results for Algo 3In Table 5, we give the testing results of algorithm 5.1 based on

Haar wavelet and CDF9/7 wavelet for PSNR, MSE, SSIM and KLDiv performed on images of different formats such as, .jpg, .png, .tiff, and .bmp. These results are depicted in Figures 5 to 8. From Table 5, we observe that MSE values for Haar Wavelet based method are near to zero whereas for CDF9/7 wavelet they are more than 1 for different image formats. This shows that Haar wavelet based method has insignificant noise added. This is also reflected in the corresponding

Citation: Kumar S, Muttoo SK (2013) Image Steganography Based on Wavelet Families. J Comput Eng Inf Technol 2:2.

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ImagesCdf97 Wavelet Haar Wavelet

PSNR MSE SSIM Max.KLDiv PSNR MSE SSIM Max. KLDiv

c3.jpg 45.8924 1.674327 0.988455 0.000168 59.91015 0.066384 0.999524 0.000005

Tulips.jpg 45.86663 1.684291 0.99085 0.002119 59.82667 0.067673 0.999596 0.000089

Tooth1.jpg 45.26791 1.933258 0.980648 0.010391 59.95889 0.065643 0.999326 0.001464

New7.tif 45.56233 1.806539 0.987289 0.000693 60.23629 0.061582 0.999588 0.00003

New8.tif 46.78406 1.36356 0.996835 0.003357 60.38726 0.059478 0.999875 0.00047

New11.tif 46.24295 1.544491 0.990818 0.179342 60.05969 0.064137 0.999654 0.061294

New12.tif 45.55518 1.809514 0.983321 0.273993 59.95242 0.065741 0.999399 0.051537

C2.bmp 45.69508 1.752153 0.981776 0.000602 59.51143 0.072767 0.999196 0.000019

Baboo.bmp 46.83504 1.347649 0.995949 0.000159 60.39242 0.059407 0.999844 0.000006

C1.png 45.67597 1.759881 0.990762 0.000091 60.31166 0.060522 0.999684 0.000003

Zoneplate.png 46.95685 1.310374 0.999885 0.000062 60.46518 0.05842 0.999995 0.000049

Peppers.png/.jpg 45.32199 1.909332 0.985991 0.000322 60.04342 0.064378 0.999527 0.000012

Table 5: PSNR of stego-images (message-size= 1000 bytes).

70605040302010

0

Images

PSN

R

c3.jp

g

Tulip

s.jpg

Tooth1.jp

g

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New8.tif

New11.tif

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Figure 5: PSNR values of Haar(red lines) and cdf (blue lines) methods for different images.

2.52

1.51

0.50

Images

MSE

c3.jp

g

Tulip

s.jpg

Tooth1.jp

g

New7.tif

New8.tif

New11.tif

New12.tif

C2.bmp

Baboo.bmp

C1.png

Zoneplate.png

Peppers.png

Figure 6: MSE values of Haar(red lines) and cdf (blue lines) methods for different images.

1.0051

0.9950.99

0.9850.98

0.9750.97

Images

SIM

M

c3.jp

g

Tulips.jp

g

Tooth1.jpg

New7.tif

New8.tif

New11.tif

New12.tif

C2.bmp

Baboo.bmp

C1.png

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Peppers.png

Figure 7: SIMM values of Haar(red lines) and cdf (blue lines) methods for different images.

0.30.25

0.20.15

0.10.05

0

Images

Max

. KLD

iv

c3.jp

g

Tulip

s.jpg

Tooth1.jp

g

New7.tif

New8.tif

New11.tif

New12.tif

C2.bmp

Baboo.bmpC1.png

Zoneplate.png

Peppers.png

Figure 8: Max. KLDiv values of Haar (red lines) and cdf (blue lines) methods for different images.

PSNR values. CDF9/7 does not show high maximum KLDiv values for New11.tif and New12.tif images (i.e., not near to zero), though for rest of the images they can be said to be near zero. In Haar based method, almost all the image formats give the KLDiv maximum value near to zero. The SSIM values are also better in case of Haar wavelet than the CDF9/7.

From Figures 5 to 7, we observe that Haar wavelet is best option

in terms of imperceptibility (PSNR), noise tolerance (MSE), and structural similarity (SSIM).

From Figure 8, we observe that Haar wavelet and CDF9/7 both provides provable security for .jpg, .bmp and .png images as the

Citation: Kumar S, Muttoo SK (2013) Image Steganography Based on Wavelet Families. J Comput Eng Inf Technol 2:2.

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doi:http://dx.doi.org/10.4172/2324-9307.1000105

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Image Original Haar Based Method CDF9/7 Based Method

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maximum KLDiv values are near to zero, whereas Haar wavelet is better than CDF9/7 for .tif images for provable security.

Histogram analysis

In the Figure 9, we show the histograms of stego-images for some image formats for Haar and CDF9/7 wavelets obtained from MLSB steganography method with embedding capacity=1000 bytes. It can be observed that Integer Haar transform based method shows no distortion statistically even after embedding the message in the cover image, whereas CDF9/7 which is a lossy compression (the frequency coefficients are floating numbers required to be converted to integers- approximation required while embedding) shows some distortion statistically.

ConclusionWe have investigated orthogonal and biorthogonal wavelet

families for image steganography based on modified/randomized LSB method. We have performed experiments in Matlab 8.0 and comparison of wavelet families is done through the imperceptibility measure, PSNR, Structural Similarity measure, SIMM and provable security measure, provable security measure, KLDiv. It is found that Haar wavelet is better than other wavelets and hence the best choice for image steganography based on modified LSB method. One of the

major reasons of Haar transform showing better results than other wavelets perhaps is that Haar wavelet is exactly reversible without the edge effects that are problems with other wavelet transforms. In this paper our aim was to compare different wavelet families in terms of imperceptibility, embedding capacity, undetectability and security of the steganographic system. The proposed method MLSB is found to be non-robust to Gaussian and Salt-n-Pepper noise. Though robustness is not the important requirement, but one may require that the steganographic method is at least robust to channel communication noise. It is also well known that if one wants to embed high payload then either transparency may be lost or stego-system may not remain robust to common attacks or the message may become detectable by the eavesdropper [38].The proposed method can be applied easily by anyone as it is one of the simplest methods. However this method is proved to be detectable easily [39,38], there is no need to worry even if it is used by “bad guys” for hiding things because it is a highly secured scheme. Our future research will focus on designing a steganography system which can provide high imperceptibility, high security, high embedding capacity and also robustness against at least common statistical attacks. References

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Citation: Kumar S, Muttoo SK (2013) Image Steganography Based on Wavelet Families. J Comput Eng Inf Technol 2:2.

• Page 9 of 9 •

doi:http://dx.doi.org/10.4172/2324-9307.1000105

Volume 2 • Issue 2 • 1000105

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Author Affiliations Top1Department of Mathematics, Rajdhani College, University of Delhi, New Delhi, India2Department of Computer Science, University of Delhi, Delhi, India