Introduction


Steganography is the art and science of writing secret data in such a way that no one, except the sender and intended recipient, knows of the existence of the data. The information-hiding process in a steganographic system starts by identifying a cover medium’s redundant bits those that can be modified without destroying that medium’s integrity. The embedding process creates a stego medium by replacing these redundant bits with data from the hidden message. The cover medium can be text, image, audio, video, and multimedia . Steganography finds extensive applications in covert communications, authentication, proof of ownership, customer tracing, feature tagging and data embedding.

Modern steganography’s goal is to keep its mere presence undetectable, but steganographic systems ,because of their invasive nature leave behind detectable traces in the cover medium. Even if secret content is not revealed, the existence of it is: modifying the cover medium changes its statistical properties, so eavesdroppers can detect the distortions in the resulting stego medium’s statistical properties. The process of finding these distortions is called statistical steganalysis..

Three different aspects in information-hiding systems contend with each other: capacity, security, and robustness. Capacity refers to the amount of information that can be hidden in the cover medium, security to an eavesdropper’s inability to detect hidden information, and robustness to the amount of modification the stego medium can withstand before an adversary can destroy the hidden information.

Many techniques have been devised to hide information such that the changes made to the cover image are imperceptible to human vision. Common approaches include (a) Least Significant Bit insertion, (b) Masking and Filtering, © Transform techniques. The simplest method for hiding a secret image is modifying the least significant bits of the pixels in the host image. The advantage of this method is its simplicity but it is very weak in resisting even simple attacks such as transforms, compression, etc. The masking and filtering techniques analyze the image and hide information in significant areas so that the hidden message is more a part of the image than being added noise in the image. The transform technique involves modulating the coefficients of the cover data in the frequency domain. Image hiding techniques that are implemented in frequency domain take advantage of features in human visual system for image hiding.











Modern Steganographic Communication


Literature Review


Recently, many data hiding algorithms have been devised in both spatial and transform domains but those implemented in spatial domain is not robust. High robustness is achieved in transform domain. Many works in data hiding have been done in DCT and DWT but not much have been worked out in contourlet domain. Some works on watermarking in non-sampled contourlet domain have been done.

One method proposed by K.B. Raja hides data in the low and mid frequencies of the image. Data was hidden on either sides of the principal diagonal. Large amounts of data could be hidden and hiding in the low frequency regions ensures robustness against JPEG compression attacks. Integer Wavelet Transform is used for perfect reconstruction of the data from the embedded image.

One method proposed by Hedieh Sajedi and Mansour Jamzad presents a new adaptive a new adaptive steganographic scheme based on contourlet transform that provides large embedding capacity. The contourlet coefficients with larger magnitude that correspond to the edges are selected for embedding.This method is superior to a similar wavelet based approach.
In another method proposed by Nisha Mary Mathew and K. A. Navas a novel blind reversible data hiding algorithm in medical images based on non sub sampled contourlet transform is proposed. It has the advantages of high capacity, imperceptibility and robustness.

The advantages of contourlet transform over other transforms (wavelet & DCT)have been discussed by Minh N Do & Vetterli.

Contourlet transform

The Contourlet transform was proposed by M. N. Do and M. Vetterli The contourlet transform provides a multiscale and multi-directional representation of an image.It consists of a double filter bank structure for obtaining sparse expansions for typical images having smooth contours. In this double filter bank, the Laplacian pyramid (LP) is first used to capture the point discontinuities, and then followed by a directional filter bank (DFB) to page link point discontinuities into linear structures. The required number of directions can be specified by the user. Since contourlets gives more edges, it is more suitable for data hiding applications as more data can be hidden in the high frequency regions without perceptually distorting the original image.. The overall results is an image expansion using basic elements like contour segments, and, thus, are named contourlets.

Contourlet possesses the important properties of directionality and anisotropy which wavelets do not possess and so contourlet outperforms wavelets in many image processing applications .When compared with wavelets contourlets offer a much richer set of directions and shapes, and, thus, they are more effective in capturing smooth contours and geometric structures in images.Manipulating the values of coefficients in contourlet domain has less effect in the quality of image than in wavelet domain.




Contourlet filter bank


Embedding and extraction of data in Contourlet domain

The structure of a steganography scheme in contourlet domain is as shown in figure.










An image is decomposed with a one level contourlet transform. Then the embedding method determines the regions of the subbands in which the data can be embedded. It also determines higher contourlet coefficients in these regions that can be used for embedding.The data is embedded in to the cover image using proper algorithm.Then inverse Contourlet Decomposition is done to create the stego image.

At the destination the stego image received is subjected to contourlet decomposition.Then employing suitable decoding algorithm the embedded data is extracted.The same key used by the sender is used by the recipient.

Simulation


clear all;
clc;
x=imread('peppers','png');
disp( 'Displaying the input image...');
clf;
imagesc(x, [0, 255]);
title( 'Input image' ) ;
axis image off;
colormap('gray');
input( 'Press Enter key to continue...' ) ;
disp( ' ' );
nlevels = [1] ;
pfilter = 'pkva' ;
nfilter = 'pkva' ;
y = pdfbdec( double(x), pfilter, nfilter, nlevels );
disp('Displaying the contourlet coefficients...') ;
imcoeff = showpdfb( y ) ;
disp(y);
title('Contourlet coefficients');
input('Press Enter key to continue...' ) ;
disp(' ');
a=y;
b=a{1,2}{1,1};
c=b;
k=input('enter length');
input ('enter the data')
for u=1:k
g(u)=input('');
end
l=0;
for m=1:256
for n=1:2:512

l=l+1;


if (l>k)
break;
end

if (g(l)==1)
if b(m,n)<b(m,n+1)
temp=b(m,n);
b(m,n)=b(m,n+1);
b(m,n+1)=temp;
end
else
if b(m,n)>b(m,n+1)
temp=b(m,n);
b(m,n)=b(m,n+1);
b(m,n+1)=temp
end
end
end
end
a{1,2}{1,1}=b;
c = pdfbrec( a, pfilter, nfilter ) ;
disp('Displaying the reconstructed image...') ;
disp('It should be a perfect reconstruction' ) ;
disp(' ') ;
subplot(1,2,1), imagesc( x, [0, 255] );
title('Original image' ) ;
axis image off;
subplot(1,2,2), imagesc( c, [0, 255] );
title('Reconstructed image' ) ;
axis image off;
mse = sum( sum( (c - double(x)).^2 ) );
mse = mse / prod(size(x));
disp( sprintf('The mean square error is: %f', mse ) );
disp(' ');
d = pdfbdec( double©, pfilter, nfilter, nlevels );
e=d{1,2}{1,1};


q=0;
for o=1:256
for p=1:2:512

q=q+1;
if (q>k)
break;
end
if e(o,p)<e(o,p+1)
f(q)=0;
else
f(q)=1;

end


end
end
disp (f)

Experimental results

To evaluate the performance of the proposed steganographic method experiments performed using 512x512 gray scale images.All the simulations are done using MATLAB.The image was decomposed by using contourlet transform and a low pass image and many band pass images obtained.When using the low pass band large volume of data can be embedded with high robustness .High volume of data can also be embedded.But the mean square error increases considerably when the payload increases.
Payload (in bits ) Band selected Mean squa

When moving to high frequency bands the robustness of the data is reducing.But in high frequency bands the mean square error is less,so security will be high.

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