Image Steganography Technique based on Singular Value Decomposition and Discrete Wavelet Transform

Website: www.ijeer.forexjournal.co.in Image Steganography Technique based on Singular Value Decomposition ░ ABSTRACT - Steganography is a technique of hiding information in digital media. In recent years plenty of work has been done in this domain, and the work can be compared on various parameters such as high robustness and large capacity to achieve a goal. This paper proposed the method of steganography in digital media using Singular Value Decomposition (SVD) and Discrete Wavelet Transform (DWT). The DWT is a frequency-domain technique comprising DWT which comparatively offers better robustness and high PSNR value of stego image over other techniques. The proposed method works well for information hiding against AWGN (additive white Gaussian noise) attack and fulfills the objective to achieve high robustness and high PSNR.


░1. INTRODUCTION
Steganography stands for secret writing in any medium most popularly digital images. This paper utilizes DWT and SVD for data hiding. With the application of SVD, any image can be decomposed into three matrices and the same image can be regenerated with the three matrices. If any of the three matrixes is not available in that case regeneration of the original image is not possible [1,2].use of SVD in this technique is to represent message image in term SVD matrix. The size of SVD matrices is very less so instead of sending a direct message-image, SVD coefficients are sent to the receiver side. The small size of the SVD coefficient makes the hiding process simple and improves the PSNR [3].

░ 2. MATHEMATICAL BACKGROUND
Proposed technique is using two mathematical tools singular value decomposition (SVD) and discrete wavelet transform (DWT).

Singular Value Decomposition (SVD)
SVD transform has many properties like singularity and orthogonality. The SVD of any rectangular matrix produces three unitary matrices U, V and S. U and V are having singular values whereas S singular values are diagonal [4].

An×p=Un×n Sn×p V T p×p
For example, a 3×3 matrix and its SVD decomposition are given below. It is visible that matrix A, U, V contains 9 elements but matrix S can be represented by principle diagonal elements because non-diagonal elements are zero. = So, instead of sending a complete message image proposed technique sending only the S matrix and complete message image could reconstruct using USV matrices. The image's distinctive information is represented by the singular value of the singular-value matrix. After matrix transformation, the diagonal members of the singular-value matrix are sorted from large to small, with the first diagonal element having a larger value than the others. Furthermore, when the image is somewhat disrupted, the diagonal elements of the singularvalue matrix acquired from singular-value decomposition do not vary appreciably, indicating that the singular-value decomposition of the matrix is rotation invariant. In this regard, adding the secret image after the image's singularvalue decomposition can boost the algorithm's anti-attack performance.

Discrete Wavelet Transform (DWT)
DWT is a very popular mathematical tool in the field of signal analysis, processing, data hiding, filtering, and compression. DWT is a lossless tool and the mother wavelet is an orthogonal set of basis functions which is either scaled or dilated versions of it. To decompose any image in low (LL) and high (HH) components DWT proved to be an important tool. The Low-frequency component contains more information and the high component contains less information. So, any change in a cover image due to data hiding in the HH component causes less distortion in the cover image. HH component of DWT matrix will hold the secret data [5]. DWT has several advantages, including the ability to withstand multiple attacks while maintaining the image's original quality and ensuring the integrity of secret information collected.

░ 3. LITERATURE REVIEW
Lots of research has been carried out in the field of Image Steganography. It's an emerging field of information hiding behind any digital media. This paper considers most of the research work based on SVD and DWT techniques. Some of the most popular papers are included here.
Ali Ahmed proposed a method based on LSB and Double XOR Operations. A technique that comprises LSB techniques is most simple and requires less time in execution. These techniques suffer in presence of noise, so frequency domain techniques are more suitable. Maximum PSNR achieved 55.67dB [6].
Franklin Tchakounte proposed the data hiding technique based on DCT and SVD. The first hiding step calculated the DC of the cover image by converting it into 8×8 non-overlapping blocks. On these non-overlapping matrixes SVD is applied which gives three matrices U, S, and V. Now secret data embedding is done in S matrix, and the same process is applied in reverse order to calculate the stego image. Result based on various parameters outperforms similar hiding procedures [7].
Yambem Jina Chanu1 proposed method used SVD for data hiding which first converts cover-image into non-overlapping 4×4 matrices. In this paper, SVD is applied on each nonoverlapping matrices and secret binary data embedded in S matrix. Which yields a modified S matrix to generate a stegoimage from inverse SVD? Experimental results show that procedure works very well in case of various attacks like compression, Gaussian noise [8].
Sandy et al. proposed a method for protecting human related information like thumb impressions. Fingerprint and secret images passed through SVD and DWT respectively. After selecting HH matrix again SVD was applied to it and SV's of the HH band with SVs of the secret image. Maximum PSNR and SSIM achieved in this method ranging in 54.38 dB and 0.9995 [9]. K Suresh Babu proposed a method based on JPEG compression and SVD decomposition. The first payload is compressed to a certain level to reduce the size of the payload. Cover image decomposed in SVs. Payload is made hidden in SV coefficients. Any change in the SV coefficient causes less effect on the cover image which increases PANR and high capacity [10].
Singh et al. proposed an integrated method to enhance a perceptual quality by using SVD and IWT into two parts, first is embedding and then recovery. The cover image is decomposed by IWT and embedding is being done on SVD matrix into into Low frequency component (LL) component. The proposed method achieves high robustness against the geometric attack and image processing attack [14]. Lakshmi Sirisa proposed a secure data hiding techniques into digital images with an aims to achieve high robustness by using decomposition DWT and SVD methods algorithm to achieve. DWT is used to decompose the cover image and secret data into four sub-bands that is LL, HL, LH and, HH then SVD decomposition is being used on secret data to generate S, U and V sub-bands. After embedding the proposed method produce three stego-images as in result of high PSNR [15].
In this paper, further sections contain the proposed method and experimental results.

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░ 4. PROPOSED ALGORITHM AND METHODS
The hiding process takes the message image and cover image as input and produces a stego image. If message image size is small, it generates less imperceptibility effect on the cover image that leads to better PSNR and high robustness.

Data Embedding Algorithm
The embedding steps are summarized in the following points and shown in a block diagram Step 1-Select a message and cover image Step 2-Calculate SVD of message image and 2D DWT of cover image respectively Step 3-SVD gives USV matrices and DWT gives LL, LH, HL, HH matrices Step 4-Hide S Matrix in HH Matrix Step 5-Send U, V matrices at the receiver end which is key in this technique Step 6-Send Stego image through a channel to the receiver side

Data Extracting Algorithm
To retrieve the secret data the extracting steps summarized in the following points are shown in block diagram.

Figure 4. Data Extraction Algorithm
Step 1-Calculate DWT of stego image which decompose it in sub bands (LL, LH, HL, HH) Step 2-Select HH matrix and extract S matrix from it Step 3-Select U, V from key Step 4-Make complete set of U, S, V matrices Step 5-Take inverse SVD on USV matrices which gives a message image Bluesea Moon Nature

░ 5. ACKNOWLEDGMENT
This research is part of PhD work in the field of image steganography without any funding support/grant.