Digital Image Steganography Scheme Based on DWT and SVD

Article history: Received 3 March 2020 Accepted 1 November 2020 In this work, a grayscale image steganography scheme is proposed using a discrete wavelet transform (DWT) and singular value decomposition (SVD). In this scheme, 2-level DWT is applied to a cover image to obtain the high frequency band HL2 which is utilized to embed a secret grayscale image based on the SVD technique. The robustness and the imperceptibility of the proposed steganography algorithm are controlled by a scaling factor for obtaining an acceptable trade-off between them. Peak signal to noise ratio (PSNR) and Structural Similarity Index Measure (SSIM) are used for assessing the efficiency of the proposed approach. Experimental results demonstrate that the proposed scheme still holds its validity under different known attacks such as noise addition, filtering, cropping and JPEG compression.


Introduction
With the increasing development in the use of digital multimedia in computer networks and the internet, computerized information such as (audio, image, text, and video) can now be created, distributed, and transmitted through the internet or other networks quickly and simply. Therefore, digital multimedia can be illegally copied, changed, and effortlessly distributed. So, the transmission of information via the internet may be risky and insecure. For resolving this challenge, many approaches of information security have been suggested. The most common and closely related are steganography and cryptography, which are mainly utilized to protect data from harmful activity or unwanted parties [1].
The main difference between steganography and cryptography is to keep the message secret. In the cryptography technique, the message is encrypted in such a way that it is visible and can only be understood by the intended person. In the *Corresponding author. E-mail address: fadelkad2@gmail.com DOI: 10.24237/djes.2020.13402 case of steganography, the fact that the message exists is concealed by hiding it into other digital media. Steganography is a method of embedding secret information into data carrier in such a way that the existence of the secret message is not noticeable. Hence, steganography technique provides an additional layer of protection to data transfer as compared with cryptography technique. Generally, the quality of the steganography scheme is determined by two challenging factors: robustness and imperceptibility. The robustness factor measures the ability of the steganography scheme to resist digital signal processing operations and other intentional attacks while preserving the integrity of the hidden information. Whereas, imperceptibility means the ability of steganography scheme to hide the secret information so that it is unnoticed by human detects without distortion the quality of the data carrier. These two factors are conflict with each other, where increasing imperceptibility means reducing robustness and vice versa. Therefore, there is a need to develop a steganography method that provides an acceptable trade-off between imperceptibility and robustness [2,3].
In general, image steganography techniques are divided into two main parts: spatial domain and frequency domain. In the spatial domain, the secret information is embedded into the carrier image by modifying the pixel value directly such as in the Least Significant Bit (LSB) algorithm [4]. Where as in the frequency domain, the carrier image is firstly converted into the frequency domain then the secret information is embedded into the coefficients of carrier image. Discrete Wavelet Transform (DWT) [5] and Discrete Cosine Transform (DCT) [6] are the most commonly used algorithms in the frequency domain. These transformation techniques are more efficient than spatial domain techniques for achieving imperceptibility and robustness as clarified by several surveys [7,8,9]. Hence, the frequency domain is used for the proposed scheme.

Discrete wavelet transform
DWT is one of the most powerful mathematical tools used in digital image applications that decomposes an image hierarchically into sub-images. For two dimensional applications, DWT is applied in the horizontal direction followed by the vertical direction. Hence, an input image is firstly divided into two sub-bands: high frequency and low frequency bands by applying high pass (H) and low pass (L) filters horizontally. Then, each sub-band is divided again into two sub-bands by applying high pass and low pass filters vertically. As a result, four sub-bands are produced called: approximation (LL), vertical (LH), horizontal (HL), and diagonal (HH) as shown in figure 1. The low frequency component of the decomposed image is represented by the approximation (LL) band that contains the most significant features of the image. Whereas, the high frequency component is represented by the other three bands (LH, HL, and HH) that contain edge and image details. The high frequency components are commonly utilized for image hiding techniques because the Human Visual System (HVS) is less sensitive to changes in image details [10,11]. Hence, the horizontal sub-band HL is employed in this work for secret image hiding to optimize both imperceptibility and robustness requirements at the same time.

Singular value decomposition
SVD is one of the most useful matrix factorization methods which can be used to decompose a matrix into its eigenvalues and eigenvectors based on linear algebra. It has been successfully applied in various fields of digital image processing such as pattern analysis, image compression, watermarking, noise removal, and image steganography due to its high stability analysis against several image processing operations. In SVD, an image A with a size of M×N can be decomposed into three matrices namely U, S, V such that [12]: where U and V represent the left and the right orthogonal matrices with a size of m×m and n×n respectively, S represents the diagonal matrix with a size of m×n and the superscript T indicates the transpose operator. The columns of the matrices U and V are called left singular vectors and right singular vectors respectively which specify the geometry of image. While the elements of S are known as singular values that specify the luminance of the image [13]. The use of SVD in the field of image steganography improves the imperceptibility and robustness requirements based on two properties of SVD. The first one is any small alteration made to an image will not change significantly it's singular values. The second one is a few singular values specifies a large part of an image signal so fewer cover image values will be changed [14].

Proposed work
In this work, two different transformation techniques DWT and SVD are utilized to improve the performance of the proposed steganography scheme. The proposed scheme is divided into two main parts, secret image embedding process and secret image extraction process as shown in Figures 2 and 3. The secret image embedding and extraction algorithms are clarified below.

Embedding algorithm
Step 1: Reading the original host image and the secret image .
Step 2: obtaining the HL2 band by applying two level 2D-DWT as follows: Step 3: Applying SVD to the selected HL2 band and to get the singular value matrix as: Step 4: obtaining the singular value of the secret image as: Step 5: Getting the singular value of stego image as follows: ′ = + * where, α is the scaling factor which is discussed in section 5.
Step 6: obtaining the modified HL2' by combining the modified singular value ′ with the original and matrices of HL2 band as: Step 7: Getting the stego image ′ by performing two level inverse 2D-DWT as:  ( 1) Step3: Decomposing the selected HL2 by performing SVD as: Step4: Getting the singular values of the secret image by using the following formula: Step5: Extracting the secret image by combining the extracted singular value with orthogonal matrices and as follows:

Experimental results and simulation
The efficiency of steganography techniques is commonly estimated according to the imperceptibility of the stego image to human observers and the robustness of the inserted secret image under external attacks as well as the common signal processing operations. In order to evaluate the robustness of the proposed method, Structural Similarity Index Measure (SSIM) is utilized to measure the similarity degree between the original secret image and the extracted one. This metric is commonly used to estimate the quality of the restored images due to its correlation with the quality perception of the human.
The maximum value of SSIM is 1, which means that the extracted image and the restored image are precisely identical. SSIM value for two images f and g is calculated by the following equation [15]: where and represent the mean values and 2 and 2 represent the variance of the original and extracted image respectively. represent the covariance of the two images. The variables 1 and 2 are positive constants added to avoid a null denominator and defined as 1 = (0.01max ( )) 2 and 2 = (0.03max ( )) 2 . In order to evaluate the imperceptibility requirements for the proposed method, peak signal to noise ratio (PSNR) is used to measure the quality of the stego image. PSNR value is calculated as [16]: where MSE represent the mean square error of the original and stego image which is expressed as: The proposed scheme is simulated with MATLAB platform by using four widely known grayscale images are used which are Cameraman, House, and Boats as a cover image with the size of (512×512) in addition to Peppers image with the size of (64×64) as a secret image as shown in Figure 4. In the proposed scheme, the robustness and imperceptibility are controlled by adjusting the scaling factor (α) to give the desired trade-off between the robustness and imperceptibility. Where the lower value of α increases the perceptual quality of the stego image, but at the same time reduces the algorithm robustness level and vice versa as demonstrated visually in Figure  5 and quantitatively in table 1. Based on experiments, α=0.1 is selected and it can be changed depending on the image characteristics.  In Figure 6, the extracted Peppers images with the corresponding stage House images which are exposed to various well-known attacks. Table 2 presents a performance analysis of the proposed scheme based on SSIM and PSNR, the tested images are subjected to different attacks including median filtering, image cropping, speckle noise, salt & pepper noise, Gaussian noise, and JPEG compression with different quality factor (QF). Additionally, a comparison analysis of the proposed method with the steganography method in [17] is presented.

Conclusions
In this study, steganography algorithm for concealing a secret grayscale image based on DWT and SVD techniques is suggested. The imperceptibility level of the stego image is increased by embedding the secret image with the coefficients of high frequency wavelet HL2 of the cover image using SVD matrices. Furthermore, the robustness level is controlled by adjusting the scaling factor based on the desired level and the characteristics of the host image. The stego image is subjected to various attacks (speckle noise, salt and peppers noise, Gaussian noise, median filtering, cropping, and JPEG compression) for evaluating the proposed scheme. Experimental results and simulations show that the proposed algorithm based on DWT and SVD techniques has been able to meet robustness and imperceptibility requirements and makes a trade-off between them.