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International Journal of Electrical and Ele ctronics Engineering Research (IJEEER) ISSN(P): 2250-155X; ISSN(E): 2278-943X Vol. 4, Issue 2, Apr 2014, 125-130 Š TJPRC Pvt. Ltd.

STEGANOGRAPHY USING KARHUNEN-LOEVE TRANSFORM AND OPTIMUM PIXEL ADJUSTMENT RIZWAN S ALVI & SAVITA B HOSALE Depart ment of Electronics and Telecommun ication Eng ineering, M GM CET, Nav i Mu mbai, Maharashtra, India

ABSTRACT This paper proposes a novel technique for steganography by using Karhunen -Loeve transform (KLT) and Optimu m Pixel Adjustment (OPA ) procedure. Steganography is the practice of concealing messages or informat ion within another non-secret data. There are various methods and techniques proposed tp implement it. This paper uses KLT because of its superiority over other transforms such as DCT and DFT. KLT provides the image compression and for hiding the data in the image, a simp le LSB approach of Optimu m Pixel Adjustment (OPA) procedure is used. The paper starts with discussing steganography, KLT and OPA. To implement the paper MATLAB is used because of its large database of built-in algorithms for image processing applications. In the end we take into consideration its advantages and disadvantages with an example.

KEYWORDS: Comp ression, Karhunen-Loeve Transform (KLT), Optimu m Pixel Adjustment (OPA) Procedure, Steganography

INTRODUCTION Steganography is the art of passing information in a manner that the very existence of the message is unknown. The goal of Steganography is to avoid drawing suspicion to the transmission of a hidden message. If suspicion is raised, then this goal is defeated. Steganography encompasses methods of transmitting secret messages through innocuous cover carriers in such a manner that the very existence of the emb edded messages is undetectable. Creative methods have been devised in the hiding process to reduce the visible detection of the embedded messages. The main requirements that steganography techniques must satisfy is the integrity of the hidden information after it has been embedded inside the stego object must be correct. The stego object must remain unchanged or almost unchanged to the naked eye [1]. Karhunen-Loeve transform (KLT) is the unitary transform that diagonalizes the covariance or correlation matrix of a discrete random sequence. This decorrelation property is desirable because processing of any one of coefficient in the KLT do main has no direct bearings on other. In general, the KLT is considered to pack the most energy in the least number of coefficients. Minimize the MSE between the original and reconstructed signal for a given number of coefficients. Achieve the minimu m rate distortion function, among all unitary transforms. Decorrelate the signal in the transform domain. Further in the paper the discussion is about how compression is also important to reduce the message size so that message will hide easily and speedily. Then hide the message in carrier image and then by simp le procedure of LSB algorith m and recover back from carrier image. There is also a discussion about OPA procedure. In the end we will conclude with advantages and disadvantages about the technique.


Rizwan S Alvi & Savita Bhosale

RELATED WORK In [1] there is a discussion regarding steganography as an art of hiding data. There is also a comparison done on various methods of steganography theoretically. Issues regarding of various techniques are also highlighted. In [2] analysis of Discrete cosine transform (DCT) or Karhunen-Loeve transform has been carried out. And comparison for the compression result is made, the losses are significant for DCT whereas the losses in energy is slight for the KLT. The article [3] deals with the issues like rate distortion performance and co mplexit ies while co mputing linear transforms. It then provides with guidance related to the above mentioned issues relating to Karhunen -Loeve transform. In this paper [4] a description regarding KL transform is given and the decorrelation property of the transform is explained. And that KLT can be used for hid ing can is explained. This paper [5] discuss about how concealing capacity can be enhanced and by using Optimu m Pixel Adjustment(OPA) how the error d ifference between the cover image and the stego image can be minimised. This paper gives the idea about how steganography can be achieved using Least Significant Bit algorith m although it uses a entirely different frame-work [6]. In [7] a KLT-based method of increasing the concealing capacity and the robustness of the concealed image in the RGB spectrum is described. The KLT is applied on the RGB co mponents, while the concealment is obtained in Discrete Fourier Transform (DFT) domain. In [8] and [9] applications are presented using Karhunen-Loeve transform and with a claim of highlighting the potent of stegno image.

KARHUNEN-LOEVE TRANSFORM Karhunen-Loeve transform (KLT) is a also known as Eigenvector transform that diagonalizes the covariance or the correlation matrix of a d iscrete random sequence. This decorrelation property is needed for processing (quantization, coding etc) of any one coefficient in the KLT do main wh ich has no direct relation on the others. Also, it will be shown that why it is considered as an optimal t ransform among all discrete transforms based on various points. It is used rarely as it is statistically dependent on the sequence i.e. when the statistics undergo any change so as the KLT. Because of this dependency on signal, mostly there are no fast algorithm for this transform. Though, KLT has been used widely in evaluating the performance of other transforms. It also motivated researchers to develop transforms that are signal independent but also have fast algorithms and their performance reaches to that of KLT. Th is chapter defines how KLT can be used to provide compression. Segmentation is also done prior to compression. Segmentation enhances the concealing capacity and execution time. Consider an original message image in the form of matrix representation, let it be represented by Q.


Also it is represented in the pixel in RGB format.

Impact Factor (JCC): 5.9638

Index Copernicus Value (ICV): 3.0


Ste ganography Using Karhunen-Loeve Transform and Optimum Pixel Adjustment


Let div ide that matrix Q’ into the segments then Q* will be the first of these segments.


Where &

= =



= &j

Also calculate the sample vector mean Mean Vector =


And with the help of this result calculate covariance mat rix. Co-variance matrix is given as z= 1/n-1



Later on calculate eigen values and eigenvectors of covariance matrix and these eigenvectors will make a orthogonal matrix V = [v 1 v 2…..v 3c], also V.VT = VT .V = I3c [10] Also, VT

= Ʌ, where Ʌ is diagonal matrix.

The value of each eigen value is proportional to the quantity of energy stored by the corresponding vector [11]


The eigenvectors of V are arranged in descending order of eigen values. And then we find the projection matrix which leads to a particular co mpression rate depending on size of the segment.

MESSAGE HIDING AND OPA The informat ion will be h idden in the Least Significant Bit (LSB) of the carrier image. There are many approaches available for hid ing the data within an image. One of the simple least significant bit submission approaches is “Optimu m Pixel Adjustment Procedure”. The simp le algorithm for OPA exp lains the procedure of hiding the sample text in an image.


Rizwan S Alvi & Savita Bhosale

Step 1: A few least significant bits (LSB) are substituted with in data to be hidden. Step 2: The pixels are arranged in a manner of placing the hidden bits before the pixel of each cover image to minimize the errors. Step 3: Let n LSBs be substituted in each pixel. Step 4: Let d = decimal value of the pixel after the substitution.d1 = decimal value of last n bits of the pixel. d2 = decimal value of n bits hidden in that pixel. Step 5: If (d1~d 2) <= (2^n)/ 2 then no adjustment is made in that pixel. Else Step 6: If (d1<d2) d = d –2^n. If (d1>d2) d = d + 2^n. This “d” is converted to binary and written back to pixel this method of substitution is simple and easy to retrieve the data and the image quality better so that it provides good security.


Consider a carrier message such that its size will be greater than the message image and it will be in three dimensions.

Consider a message such that it will also be in RGB format and segments of that will be considered for better concealing capacity and execution time.

Co mpression will take p lace through KLT.

For hid ing of the message, the points discussed in IV will be considered.

Message recovery procedure will be opposite of hiding procedure. The next step is to undo the linear transformations used. The resulted projection mat rix and reduced eigen vector matrix are just approximat ions of their orig inal counter parts. By co mbining these recovered segments, we obtain an approximation of the orig inal hidden message.

Impact Factor (JCC): 5.9638

Index Copernicus Value (ICV): 3.0


Ste ganography Using Karhunen-Loeve Transform and Optimum Pixel Adjustment


Figure 1: Demonstrating how the Ai m of Steganography is Achi ved Depending on the size of the images used, there will be different values to these parameter. They are carrier error, message error, hid ing time, recover t ime, etc. this is as shown in following table. Table 1: List of the Parameters PARAMETERS Co mpression rate (%) Hid ing time (sec) Recovering time (sec) Message error (%) Carrier error (%)

IMAGE S ET 0.50 3.566 1.60 1.05 0.689

CONCLUSIONS The paper explains successfully the use of KLT and OPA in stegnography. The property of compression of KLT and OPA procedure is used and executed in the example considered. Parameters like execution time, concealing capacity, compression rate, robustness, stego image and recovered message quality (to quantify th is parameter, there is a calculation of Carrier Error and Message Error is done). If more number of LSB’s are used for hiding purpose there may be amore percentage of carrier error. The algorith m’s concurrent nature suggests practical use on mult i-core architecture. By analysing theory and parameter discussed the conclusion can be drawn that KLT and OPA can be used to develop a better stegnographic technique.


Shashikala Channalli, Ajay Jadhav, Singhad College of Engg, Pune International Journal on Computer Science and Engineering Vo l.1(3), 2009, 137-141.


S. G. Hoggar, “Mathemat ics of Digital Images”, Cambridge Un iversity Press, 2006, ISBN-13 9780521780292.


Rizwan S Alvi & Savita Bhosale


Candik M., Brechlerova D., “Digital watermarking in dig ital imag es”, Security Technology, 2008. ICCST 2008. 42nd Annual IEEE International Carnahan Conference on, 13-16 Oct. 2008, pp.43-46, ISBN: 978-1-4244-1816-9.


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Stanescu, D, Stratulat, M, Ciubotaru, B,.Ch iciudean, D, Cioarga, R, Borca, “Digital Watermarking using Karhunen-Loeve transform”, 4th International Sy mposium on Applied Co mputational Intelligence and Informatics, 2007. SACI '07, 18May 2007, pp. 187-190, Timisoara, Ro mania, ISBN: 1-4244-1234X.


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Impact Factor (JCC): 5.9638

Index Copernicus Value (ICV): 3.0

14 rizwan avi ijeeer  

This paper proposes a novel technique for steganography by using Karhunen -Loeve transform (KLT) and Optimum Pixel Adjustment (OPA) procedur...

14 rizwan avi ijeeer  

This paper proposes a novel technique for steganography by using Karhunen -Loeve transform (KLT) and Optimum Pixel Adjustment (OPA) procedur...