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Robustness is one of the most important requirements when digital watermarking is applied. Different from the StirMark test and various simulation tests, a mutual information function is defined as a criterion to measure the robustness of watermarking algorithm. Taking the additive spread spectrum watermarking scheme and quantization index modulation (QIM) watermarking scheme as two examples, the calculation formulas of mutual information function are derived to evaluate the robustness of the algorithms. Numerical computation of mutual information is performed with change of watermark noise rate (WNR). In the experiment, spread spectrum watermarking is implemented in discrete cosine transform (DCT) and QIM watermarking is implemented in discrete wavelet transform (DWT). The statistic bit error rate (BER) is derived against Gaussian distribution noise and JPEG compression. Experiment results show that the evaluation conclusion of mutual information method is in accordance with the empirical BER. Mutual information can be selected as a cost function to predict the BER.
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Keywords:
- digital watermarking /
- robustness /
- mutual information /
- bit error rate (BER)
[1] Cox I J, Miller M, Bloom J 2007 Digital Watermarking and Steganography (2nd ed) (Morgan Kaufmann) p7
[2] Petitcolas F A, Anderson R J, Kuhn M G 1998 Proceedings of 2nd International Workshop on Information Hiding Portland, Oregon, USA, April 14—17 p218
[3] Fan X H, Xiao J, Wang Y 2008 Journal of Image and Graphics 13 1979 (in Chinese) [樊晓华、肖 俊、王 颖 2008中国图形图象学报 13 1979]
[4] Xiao J, Wang Y 2009 Journal of Electronics and Information Technology 31 552 (in Chinese) [肖 俊、 王 颖 2009 电子与信息学报 31 552]
[5] Chen B, Wornell G 2001 IEEE Trans. on Information Theory 47 1423
[6] He H J, Zhang J S 2007 Acta Phys. Sin. 56 3092 (in Chinese) [和红杰、张家树 2007 物理学报 56 3092]
[7] Zou L J, Wang B, Feng J C 2008 Acta Phys. Sin. 57 2750 (in Chinese) [邹露娟、 汪 波、 冯久超 2008 物理学报 57 2750]
[8] Song W, Hou J J, Li Z H, Huang L 2009 Acta Phys. Sin. 58 4449 (in Chinese) [宋 伟、侯建军、李赵红、黄 亮 2009 物理学报 58 4449]
[9] Cox I J, Killian J, Leighton T 1997 IEEE Trans. on Image Processing 6 1673
[10] Feng J C, Yu Z B 2008 Acta Phys. Sin. 57 1409 (in Chinese) [冯久超、余振标 2008 物理学报 57 1409]
[11] Poor H V 1998 An Introduction to Signal Detection and Estimation (2nd ed) (New York: Springer)
[12] Cover T M, Thomas J A 2006 Elements of Information Theory (2nd ed) (New York: Wiley) p11 [阮吉寿、 张 华 2007 (译) 北京: 机械工业出版社 第11页]
[13] Gray R M, Neuhoff D L 1998 IEEE Trans. on Information Theory 44 2325
[14] Pérez-Freire L, Pérez-González F 2008 IEEE Trans. Information Forensics and Security 3 593
[15] Nie Z P, Xiao H L 2007 Acta Phys. Sin. 56 1948 (in Chinese) [聂在平、 肖海林 2007 物理学报 56 1948]
[16] Clarke R J 1985 Transform Coding of Images (New York: Academic)
[17] Sun Z W, Feng D G 2005 Journal of Software 16 1798 (in Chinese)[孙中伟、 冯登国 2005 软件学报 16 1798]
[18] Buccigrossi R W, Simoncelli P 1999 IEEE Trans. on Image Processing 8 1688
[19] Chen B 2000 Ph. D. Dissertation (Cambridge, USA: Massachusetts Institute of Technology)
[20] Fei C, Kundur D, Kwong R 2001 Proceedings of International Conference on Information Technology Los Alamitos Las Vegas, NV, USA, April 2—4 p79—84
[21] Xiao J, Wang Y, Li X L 2007 Acta Electronica Sin. 35 786(in Chinese) [肖 俊、 王 颖、 李象霖 2007 电子学报 35 786]
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[1] Cox I J, Miller M, Bloom J 2007 Digital Watermarking and Steganography (2nd ed) (Morgan Kaufmann) p7
[2] Petitcolas F A, Anderson R J, Kuhn M G 1998 Proceedings of 2nd International Workshop on Information Hiding Portland, Oregon, USA, April 14—17 p218
[3] Fan X H, Xiao J, Wang Y 2008 Journal of Image and Graphics 13 1979 (in Chinese) [樊晓华、肖 俊、王 颖 2008中国图形图象学报 13 1979]
[4] Xiao J, Wang Y 2009 Journal of Electronics and Information Technology 31 552 (in Chinese) [肖 俊、 王 颖 2009 电子与信息学报 31 552]
[5] Chen B, Wornell G 2001 IEEE Trans. on Information Theory 47 1423
[6] He H J, Zhang J S 2007 Acta Phys. Sin. 56 3092 (in Chinese) [和红杰、张家树 2007 物理学报 56 3092]
[7] Zou L J, Wang B, Feng J C 2008 Acta Phys. Sin. 57 2750 (in Chinese) [邹露娟、 汪 波、 冯久超 2008 物理学报 57 2750]
[8] Song W, Hou J J, Li Z H, Huang L 2009 Acta Phys. Sin. 58 4449 (in Chinese) [宋 伟、侯建军、李赵红、黄 亮 2009 物理学报 58 4449]
[9] Cox I J, Killian J, Leighton T 1997 IEEE Trans. on Image Processing 6 1673
[10] Feng J C, Yu Z B 2008 Acta Phys. Sin. 57 1409 (in Chinese) [冯久超、余振标 2008 物理学报 57 1409]
[11] Poor H V 1998 An Introduction to Signal Detection and Estimation (2nd ed) (New York: Springer)
[12] Cover T M, Thomas J A 2006 Elements of Information Theory (2nd ed) (New York: Wiley) p11 [阮吉寿、 张 华 2007 (译) 北京: 机械工业出版社 第11页]
[13] Gray R M, Neuhoff D L 1998 IEEE Trans. on Information Theory 44 2325
[14] Pérez-Freire L, Pérez-González F 2008 IEEE Trans. Information Forensics and Security 3 593
[15] Nie Z P, Xiao H L 2007 Acta Phys. Sin. 56 1948 (in Chinese) [聂在平、 肖海林 2007 物理学报 56 1948]
[16] Clarke R J 1985 Transform Coding of Images (New York: Academic)
[17] Sun Z W, Feng D G 2005 Journal of Software 16 1798 (in Chinese)[孙中伟、 冯登国 2005 软件学报 16 1798]
[18] Buccigrossi R W, Simoncelli P 1999 IEEE Trans. on Image Processing 8 1688
[19] Chen B 2000 Ph. D. Dissertation (Cambridge, USA: Massachusetts Institute of Technology)
[20] Fei C, Kundur D, Kwong R 2001 Proceedings of International Conference on Information Technology Los Alamitos Las Vegas, NV, USA, April 2—4 p79—84
[21] Xiao J, Wang Y, Li X L 2007 Acta Electronica Sin. 35 786(in Chinese) [肖 俊、 王 颖、 李象霖 2007 电子学报 35 786]
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