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Apr 21, 2018

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CHAPTER 8

REVERSIBLE IMAGE STEGANOGRAPHY BASED ON WAVELETS AND WAVELET-LIKE-TRANSFORM

So far we have focussed on evaluating the performance of algorithms of irreversible image steganography in the ECCs domain and Transform domain for the grayscale and color images. In this Chapter we shall cover the two type of reversible image steganographic algorithms using the Companding technique (also called Reversible Thresholding Method) based on SLT- Perceptual and Robust. We shall also give the comparative study of proposed algorithms with the corresponding modified wavelet based thresholding technique. 8.1. INTRODUCTION The reversible data hiding (RDH) technique enables cover image to be restored to their original form without any distortion after removing the hidden data from the stego-image. This technique is useful in many fields such as law enforcement, medical imagery, astronomical research, content authentication of multimedia data and so on.

A number of RDH techniques have been proposed. Awrangjeb (2003) classifies them into the following six types, viz., Lossless compression and encryption of Bit- planes, Reversible data hiding at Low Pixel-levels, Circular interpretation of Bijective Transformations based on integer Wavelet transform, High capacity based on difference expansion and RDH by histogram shifting. Yang et al (2010) divided the various RDH methods into four categories viz., Data Compression, Difference Expansion, Histogram Shifting and Integer Wavelet Transform. According to X. Zhang (2013), they can be classified into three types, viz., Lossless compression based methods, Difference expansion (DE) and Histogram modification (HM) methods. Yang and Lin (2012) discusses two kinds of RDH schemes which are

Perceptual quality schemes that provides a perceived high quality in stego-images with a high embedding rate and

Robustness-oriented schemes which are robust to image processing operations.

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In this Chapter, we propose both these schemes based on Slantlet and Complex Wavelet transforms in conjunction with AES. 8.1.1. Review of RDH schemes In this section we briefly summarize the different approaches proposed for RDH. RDH for fragile authentication Honsinger et al (2001) presented the lossless data hiding technique for fragile authentication that does not need much data to be embedded in a cover object. They used modulo-256 addition to embed the hash value of the original image for authentication, but their algorithm couldnt resist salt-n-pepper noise due to the many wrapped around pixel intensities. Vleeschouwer et al (2003) proposed an improvement over the Honsinger algorithm by circular interpretation of the bijective transformations of the image histograms that reduces salt-n-pepper visual artifacts. This algorithm is a Patchwork histogram rotation, where each bit of message is associated with a group of pixels. Each group of pixels is divided into two-pseudo random sets of pixel zones i.e. A and B. Since zones A and B are pseudo randomly generated, they have almost equal average values before embedding. After embedding, depending on the bit to embed, their luminance values are incremented or decremented. The extracted bit is inferred from the comparison between the mean values of zone A and B. Lossless compression technique Fridirch et al. (2002) proposed the joint bi-level image experts group (JBIG) lossless compression technique that compresses a set of selected features from a image to save space for data embedding. Lowest bitplane offering lossless compression can be used unless the image is not noisy. In his scheme, payload is highly dependent on the lossless compression technique. Celik et al (2002) proposed a reversible data hiding technique that uses prediction based conditional entropy coder utilizing static portions of the input signal as side information to improve the compression efficiency. This spatial domain method is a modification of Least Significant Bit embedding techniques, by using higher order bits. They also proposed a reversible data hiding method based on the idea

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of first compressing portion of the signal that are susceptible to embedding distortion and then transmitting it as part of embedded payload. Further in 2005, they improved Fridrichs technique and proposed the generalized-LSB scheme by compressing the quantization residuals of pixels to yield additional space to embed a message. Integer wavelet transform technique

Xuan et al (2002-2005) proposed a lossless data hiding method based on IWT, which embeds high capacity data into the least significant bit-planes of high frequency wavelet coefficients whose magnitudes are smaller than a certain predefined threshold. Histogram modification is applied as a pre-processing to prevent overflow/underflow. Luo and Yin (2011) have presented a new RDH scheme that utilizes the wavelet transform and better exploits the large wavelet coefficient variance to achieve high capacity and imperceptible embedding. Yang and Lin (2012) have proposed a RDH method that uses the coefficient shifting (CS) algorithm with a mean predictor. Further, they present a robust RDH method using a variant of the CS algorithm that is based on the IWT domain to resist common image processing operations. Yang, Lin and Hu (2012) have further presented a simple RDH scheme based on the IWT. By adjusting the coefficient values, data bits are effectively embedded into the low-high (LH) and high-low (HL) subbands of the IWT domain. Their experiments show that both the host media and secret message can be completely recovered, without distortion, if the stego-images remain intact. Moreover, the resulting perceived quality of the image is highly satisfactory, as is the hiding capacity. Difference expansion technique Tian (2003) proposed a high capacity RDH technique that expands the difference between two neighboring pixels to obtain redundant space for embedding a message. However, his scheme suffers from the location map problem that it is difficult to achieve capacity control. His algorithm was improved by Alattar (2004) who used the DE of vectors of adjacent pixels to obtain additional space for embedding. There have been many techniques developed thereafter to increase the payload and minimizing the distortion which can be referred to Chang and Lu, (2006), Weng et al.s (2007-2008),

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Thodi and Rodriguez (2007), Lin and Hsueh, (2008), Lou, Hu and Liu, (2009). Zhang (2013) has proposed a RDH with optimal value Transfer. In his scheme, the optimal rule of value modification under a payload-distortion criterion is found by using an iterative procedure and the secret data as well as the auxiliary information used for content recovery, are carried by the differences between the original pixel-values and the corresponding values estimated from the neighbors. The estimation errors are modified according to the optimal value transfer rule and the original host content can be perfectly restored after extraction of the hidden data on receiver side. Histogram shifting technique Ni et al. (2006) proposed a RDH scheme that uses the histogram of the pixel values in the cover image to embed secret data into the maximum frequency pixels. However, their payload is quite limited because few images contain a large number of pixels with maximum frequency. Further, their scheme may lead to significant overhead and insufficient visual quality. Chang et al. (2008) suggested the pixel difference instead of simple pixel value for obtaining the higher peak point to embed a large amount of message. Zeng and Li (2009) improved this algorithm using adjacent pixel difference based on scan path and multi-layer embedding to increase the embedding payload. Yu and Wang (2009) proposed an extended subsampling reversible data hiding method, which shifts the histogram of the differences between sub-images obtained through subsampling and embed data by modifying the pixel value according to embedding level. Yang, Hwang and Chou (2010) proposed a RDH based on the interleaving max-min difference histogram. Their experimental results reveal that their algorithm can offer higher embedding capacity. Zeng, L and Ping (2012) have proposed a lossless data hiding scheme based on the pixel difference histogram shifting to spare space for data hiding. Pixel differences are generated between a reference pixel and its neighbors on a pre-assigned block. They claim that the algorithm has very high embedding capacity and low image degradation.

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Dynamic reference pixel method Xian-ting Zeng et al. (2012) have proposed a lossless data hiding scheme by using dynamic reference pixel and multi-layer embedding. According to authors, their algorithm offers very high embedding capacity and low image degradation. Companding technique A reversible (lossless) steganographic algorithm based on thresholding technique proposed by Xuan G. et al. (2002, 2011). As discussed in Chapter 1, in the thresholding embedding, a threshold value T is predefined. To embed data into a high frequency coefficient x, the absolute value of the coefficient is compared with T. If |x| < T, the coefficient value is doubled and the new LSB is replaced with an information bit. Equivalently, the binary representation of the coefficient value is shifted towards left by one bit and the to-be-embedded bit is appended as the right-most bit. The resultant coefficient is denoted by x. Otherwise, if x T, the coefficient will be added by T, if x -T, the coefficient will be subtracted by (T-1) and no bit is embedded into this coefficient. In the data extraction stage, if the coefficient x is less than 2T and larger than (-2T+1), the LSB of this coefficient is the bit embedded into th

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