Wave atom transform based image hashing using distributed source coding

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Abstract

To reduce the size of hash code and enhance the security of wave atom transform (WAT) based image authentication system, a low-density parity-check code based distributed source coding (DSC) is employed to compress the hash code. With the help of a legitimately modified image, the compressed hash value could be correctly decoded while it will fail with the help of a maliciously attacked image. Therefore, the employed DSC provides a desired robustness to image authentication. Simulation results indicate that the proposed scheme provides a better performance with less hash code than existing WAT based image hash without using DSC. Moreover, the proposed scheme outperforms the random projection based approach in terms of authentication accuracy and data size.

Introduction

Along with the rapid development of information technologies, the broad popularity of image manipulation tools has led to an explosive growth of image illegal use, which makes image authentication more and more important. Three kinds of image authentication techniques, namely digital forensics (Zhao and Zhao, 2013), image watermarking (Chetan, Nirmala, 2015, Ghosal, Mandal, 2014) and perceptual hashing (Zhao et al., 2013), have been carried out on image authentication. Perceptual hashing is the transformation of an image into a usually shorter fixed-length value that represents the original image. It could verify the originality of an image by comparing the hash codes of the original image and the target image. Swaminathan et al. (2006) have developed a perceptual hashing scheme based on Fourier transform features and controlled randomization. By embedding the detected local features into shape-context-based descriptors, Lv and Wang (2012) used the most stable scale-invariant feature transform key points as the hash code. Zhao et al. (2013) employed Zernike moments to represent the luminance and chrominance of an image as global features, while they took position and texture information of salient regions as local features to produce the hash code.

Since target images are usually correlated to original image in the image authentication system, the hash codes of original image and target image are correlated, thus it is possible to compress hash code of the original image using distributed source coding (DSC). The redundancy of hash code can be further reduced and the compressed hash code will be statistically independent of the target image. Motivated by the potential benefits of using DSC such as reducing size of the hash code and improving the security of the authentication system, some researchers studied the compression processing for the follow-up procedures of hash construction (Lin et al, 2012, Sun et al, 2002, Tagliasacchi et al, 2009, Venkatesan et al, 2000). An error-correcting code is employed in Venkatesan et al. (2000) by projecting the hash into syndrome bits which are used to verify the authentication directly. The parity check bits of the binary feature vectors, which are produced by a systematic Hamming code, are taken as the hash code in Sun et al. (2002). In addition, DSC is combined with compressive sensing to identify sparse image tampering (Tagliasacchi et al., 2009). The hash code is produced by encoding the quantized random projections using a LDPC-based DSC encoder (Varodayan et al., 2012), while a DSC decoder is employed to decode the hash value with the help of target image. A training procedure is usually applied to find the minimum decodable rate (MDR) for all the legitimately modified images. Thus, if a legitimately modified image is taken as side information, the decoding will be successful, but it will fail with the help of illegitimately modified image due to the weak correlation between the original image and the illegitimately modified image.

On the other hand, wave atom transform (WAT) is a recent addition to the repertoire of mathematical transforms of computational harmonic analysis, which is introduced by Demanet and Ying (2007). WAT is constructed from tensor products of adequately chosen 1-D wave packets, and the 2-D orthonormal basis functions with four bumps can be formed by individually utilizing products of 1-D wave packets in the frequency plane. As a variant of 2-D wavelet packets, WAT could adapt to arbitrary local directions of a pattern, and sparsely represent anisotropic patterns aligned with the axes. Oscillatory functions and oriented textures in WAT have been proven to have a dramatically sparser expansion compared to some other fixed standard representations, such as Gabor filters, wavelets, and curvelets. A WAT based perceptual hashing was studied in Liu et al. (2012), which has reported that WAT based perceptual hash could outperform discrete cosine transform or discrete wavelet transform based schemes in terms of robustness and fragility. In order to reduce the size of hash code and improve the security of the WAT based perceptual hashing, this work employs a LDPC-based DSC (Varodayan et al., 2012) to compress the randomized wave atom features of the original image, which is also expected to show better performance than the scheme without DSC. The contributions of this work are listed as follows: (1) Since the compressed hash value could be correctly decoded but it will fail with the help of a maliciously attacked image, the employed DSC provides a desired robustness to image authentication. (2) The correlation between the hash value and images is removed by DSC, which certainly improves the security of the existing hash scheme. (3) The length of hash value is shortened.

The rest of this paper is structured as follows. The proposed authentication system is described in Section 2, and the experimental analyses are presented in Section 3. The conclusions are given in Section 4.

Section snippets

Proposed authentication system

The proposed authentication system is composed of two steps: In the first step, the randomized wave atoms are extracted from the original image (Liu et al., 2012). The randomized wave atoms will be further encoded by LDPC-based DSC in the second step. The encoded wave atoms are taken as the hash code. The target images are produced by two channels which include a legitimate channel and a tampered channel (Lin et al., 2012). In the legitimate channel, the target image is only processed with

Simulation analysis

In this work, 100 grayscale original images with size of 512 × 512 have been used for simulation. The legitimately modified images are produced by reconstruction of manipulations such as lossy compression, Gaussian noise, salt and pepper noise and low-pass filtering with different parameters. According to Lin et al. (2012), the reconstructed images of lossy compression manipulation with PSNR no less than 30 dB have been used. By overlaying a text banner with a size of 179 × 39 as shown in Fig. 1

Conclusion

A LDPC based DSC is employed in WAT based image authentication system in this work. The maliciously modified images are distinguished by assessing the Euclidean distance between wave atoms of the original and the target image. The employed DSC explores the correlation between wave atoms of the original and the target image to lower their statistical dependence. It not only reduces the size of the hash value but also improves the security of the image authentication system. The simulation

Acknowledgments

The work described in this paper was supported in part by the National Natural Science Foundation of China (Grant No. 61601337), by the Fundamental Research Funds for the Central Universities under Grant 2015III015-B04 and Grant 2015IVA034, by Key Project of Nature Science Foundation of Hubei Province (Grant No. ZRZ2015000393), by the National Key Technology Support Program of China (Grant No. 2012BAH45B01), by Science & Technology Pillar Program of Hubei Province (Grant No. 2014BAA146) and by

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