基于分数阶傅立叶变换的数字水印算法研究
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摘要
随着网络技术和多媒体技术的飞速发展,数字产品的应用越来越广泛,信息安全问题逐渐受到人们的关注,其中数字产品的版权保护成为一个迫在眉睫的问题。数字水印技术是实现版权保护的有效办法,已成为信息安全研究领域的一个热点。以分数阶傅立叶变换理论为基础,本文在以下几个方面进行了研究:(1)分析了分数阶傅立叶变换理论及其快速算法。(2)提出了一种基于分数阶傅立叶变换和纹理特征的数字水印算法。(3)结合多参量离散分数阶傅立叶变换理论,提出了基于MPDFRFT的数字水印算法。仿真实验结果表明两种算法很好地实现了水印的隐藏,并具有较好的鲁棒性和安全性。
With the development of the network and the multimedia technology, the application of the digital product is more and more wide. The information security becomes the concern in people’s life. Especially, the copyright protection of digital product has become an urgent problem. Digital watermarking technology is an effective way of copyright protection, and it becomes a focus in the information security domain. On the base of the fractional Fourier transform theory, what the author has studied and realized mainly are as follows: (1) The fractional Fourier transform and it’s fast algorithm have been analyzed. (2) A digital image watermarking algorithm has been proposed based on fractional Fourier transform and texture character. (3) Combining multiple-parameter discrete fractional Fourier transform theory, An image watermarking algorithm based on MPDFRFT has been proposed. The simulation experiment results have demonstrated that the two algorithms proposed not only realized watermark hidden well, and have better robustness and security.
With the development of the network and the multimedia technology, the application of the digital product is more and more wide. The information security becomes the concern in people’s life. Especially, the copyright protection of digital product has become an urgent problem. Digital watermarking technology is an effective way of copyright protection, and it becomes a focus in the information security domain. On the base of the fractional Fourier transform theory, what the author has studied and realized mainly are as follows: (1) The fractional Fourier transform and it’s fast algorithm have been analyzed. (2) A digital image watermarking algorithm has been proposed based on fractional Fourier transform and texture character. (3) Combining multiple-parameter discrete fractional Fourier transform theory, An image watermarking algorithm based on MPDFRFT has been proposed. The simulation experiment results have demonstrated that the two algorithms proposed not only realized watermark hidden well, and have better robustness and security.
引文
[1] 刘瑞祯,谭铁牛 数字图象水印研究综述[J]. 通信学报,2000,21(8):39-48.
[2] Liu. R. Z, Tan. T. N. Watermarking for digital images[A].Proc of ICSP’98 [C] . 1998.2:944-947
[3] Voyatzis. G, Nikolaidis. N, Pitas. I, Digital watermarking: An overview[J].Eur. Signal Processing Conf. EUSIPCO,Rhodes,Greece.1998,9:9-12.
[4] Barnett. R. Digital watermarking: Applications, techniques, and challenges[J]. Electronics and Communication Engineering Journal.1999,11(4) :173-183.
[5] Su. J. K, Hartung. F, Girod B. Digital watermarking of text, image, and video documents[J]. Computers & Graphics. 1998,22(6):687-695.
[6] R. G.van. Schyndel, A.Z. Tirkel, C.F.Osbrone. A Digital Watermark. IEEE International Conference on Image Processing, Vol.2,pp:86-90, Austin, Texas, USA, 1994
[7] A.Tirkel, G.A.Rankin, R.van.Schyndel. Electronic watermark, Digital Image Comp uting. Technology and Application-DICTA 93, Macquarie University, 1993:666-673.
[8] E.Wolfgang, R.Podilchuk, C.Delp. Perpetual watermarks for digital images and video. Proceedings of the IEEE,1999,87(7):1108-1126.
[9] T.Anox, Keith. “Reversible Digital Image” SPIE, 1999:397-401.
[10] W. Bender, D. Gruhl, N. Morimoto, A. Lu. “Techniques for data hiding”. IBM Syst.J.1996.35(3):313-336.
[11] 丁玮,闫伟齐,齐东旭. 基于置乱与融合的数字水印隐藏技术及其应用[J]. 中国图象图形学报,2000,5(8):644-649.
[12] I.J.K.O Ruanaith. Phase Watermarking of Digital Images. Proc. of ICIP, 1996,(1):239-242.
[13] M. H. Hayers. The Reconstruction of a Multi-dimensional Sequence from the Phase or Magnitude of the FFT.IEEE Trans. On ASSP, No.4,pp.140-154,1992.
[14] I. J. Cox, Joe Kilian, F. Thomson. Secure Spread Spectrum Watermarking for Multimedia. IEEE Transaction on Image Processing. Vol.8, NO.12,pp.1673-1687, December1997.
[15] E.Koch, J.Rindfery, J.Zhao. Copyright protection for multimedia data.[DB/OL]. http://citeseer.ist.psu.edu/context/43326/0
[16] A.G. Bors, I. Pitas. Image watermarking using DCT domain constraints, Proc. ofICIP’96,1996,3:231-234.
[17] A. Piva, M. Barni, F. Baolini, V. Capellini. DCT-based watermarking recovering without resorting to the uncorrupted original image, Proc. of ICIP’97,3:520-523.
[18] C.T.Hsu, J.L.Wu. Multiresolution Watermarking for digital image. IEEE Trans. on Circuits and Systems2:Analog and Digital Signal Processing.
[19] X.G.Xia, C.G.Boncelet, G.R.Arce. Wavelet Transform based Watermark for Digital Image. OPTICS EXPRESS, 1998,3(12):497-500.
[20] C. I. Podilchuk, Wenjun Zeng. Image-adaptive Watermarking using Visual Model. IEEE Journal on Selected Areas in Communications, 1998,16(4):525-539.
[21] H.M.Wang, P.C.Su, C.J.Kuo. Wavelet-based Digital Image Watermarking. OPTICS EXPRESS, 1998, 3(12): 491-496.
[22] 刘正君,赵海发,朱邦和等。分数傅立叶域数字水印算法[J] 光子学报,2003,32(3):332-335
[23] Yu. F. Q, Zhang. Z. K, Xu. M. H. A Digital Watermarking Algorithm for Image Based on Fractional Fourier Transform[C].Singapore:2006 1ST IEEE Conference On Industrial Electronics and Applications, Vols 1-3 2006:1441-1445
[24] 张峰,穆晓敏,杨守义等. 基于 FRFT 盲检测 Chirp 类数字水印算法[J]. 计算机工程与应用,2006,9(27):57-61
[25] W.Zeng, B.Liu. On resolving rightful ownerships of digital images by invisible watermarks. Proceedings of ICIP’97,Intern,Conf. on Image Processing, Vol.1,pp.552-555,S,Barbara, CA,USA, October 26-29,1997.
[26] I.J.Cox, M.L.Miller. The first 50 years of electronic watermarking. Journal of Applied Signal Processing, Vol.2,2002,pp.126-132.
[27] Fabien.A.P.Petitcolas, Ross.J.Anderson, Markus.G.Kuhn. Attacks on Copyright Marking Systems. David Aucsmith, Ed, Second workshop on information hiding, Vol1525 of Lecture Notes in Computer Science, Portland, Oregon, USA,14-17,April, 1998,pp.218-238.
[28] Chiou-Ting Hsu, Ja-Ling Wu. Hidden Digital Watermarks in Images. IEEE Transanctions on Image Processing, Vol.8,No.1,January 1999:58-68.
[29] 张 华 熊 , 仇 佩 亮 . 置 乱 技 术 在 数 字 水 印 中 的 应 用 [J]. 电 路 与 系 统 学报,2001,6(3):32-36.
[30] 谢荣生,刘承香等.基于模板匹配的抗集合攻击图象数字水印[J]. 哈尔滨工程大学学报,2002,23(3):54-58.
[31] 王秋生,孙圣和. 基于量化数字音频信号频域参数的水印嵌入算法[J]. 声学学报,2002,27(4):379-384.
[32] 张 华 熊 , 仇 佩 亮 . 数 字 水 印 信 道 模 型 的 快 速 估 算 [J]. 电 路 与 系 统 学报,2002,7(2):39-42.
[33] Keitli Hill. A Perspective: The role of identifiers in managing and Protecting intellectual property in the digital age. Proc IEEE.1999,87(7):1228-1238.
[34] Pettcolas.F, Anderson.R.J, Kun.M.G. Attacks on copyright marking system. Proc of Information Hidding98’,1998,213-238.
[35] Wang.Z, Bovik.A.C, Sheikh.H.R. Image quality assessment:from error visibility to structural similarity[J]. IEEE Transactions on Image Processing,2004,13(4): 600- 612.
[36] Stankovic.S, Djurovic.I, Pitas.I. Watermarking in the Space/Spatial-Frequency Domain Using Two-Dimensional Radon-Wigner Distribution[J]. IEEE Trans on Image Processing,2001,10(4):650-658.
[37] 曹荣, 王颖, 李象霖. 一种基于离散傅立叶变换域相位和幅度的数字水印算法[J]. 计算机应用,2005,25(11):2536-2543.
[38] Xin-Li Hong, Heather Yu. Transparent and robust audio data hiding in cepstrum domain[J].IEEE Int. Conf. Multimedia and Expo(1),2000:397-400.
[39] Sang-Kwang Lee, Yo-Sung Ho. Digital audio watermarking in cepstrum domain. IEEE Transactions on Consumer Electronics,2000,46(3):744-750.
[40] Joan Puate, Frederic Jordan. Using fractal compression scheme to embed a digital signature into an image. SPIE, Video Techniques and Software for Full-Service Networks.1996,2915:108-118.
[41] Namias V. The fractional order Fourier transform and its application to quantum mechanics[J].J Inst Math Appl, 1980,(25):241-265.
[42] H.M.Ozaktas, D.Mendlovic. Fractional Fourier optics [J], J. Opt. Soc. Amer. A, 1995,(12):743-751.
[43] A.W.Lohmann. Image rotation, Wigner rotation and the fractional Fourier transform[J], J.Opt.Soc. 1993,(10):2181-2186.
[44] 陶然,齐林,王越. 分数阶 Fourier 变换的原理与应用[M].北京:清华大学出版社,2004.
[45] 陶然,邓兵,王越. 分数阶 Fourier 变换在信号处理领域的研究进展[J]. 中国科学E 辑,信息科学 2006,36(2):113-136.
[46] 于凤芹, 曹家麟. 分数阶傅立叶变换的多种定义形式及其光学实现系统分析[J]. 光电子技术与信息,2004,17(4):25-29.
[47] Ozaktas. H. M, Kutay. M.A, Zalevsky.Z. The fractional Fourier transform with Application in Optics and Signal Processing. John Wiley & sons,2000.
[48] 汪玲. 分数阶傅立叶变换在线性调频信号侦察中的基本理论及应用:[硕士学位论文].成都:电子科技大学,2002.
[49] Santhanam .B and McClellan. J. H. The discrete rotational Fourier transform, IEEE Transaction on Signal Processing. 1996,(42):994-998.
[50] Dickinson.B.W, Steiglitz.K. Eigenvectors and functions of the discrete Fourier transform. IEEE Trans. Acoust. Speech. Signal Processing, Vol,ASSP-30,No.1, pp.25-31, Feb.1982.
[51] McClellan. J. H, Parks. T. W. Eigen-value and Eigenvector decomposition of the discrete Fourier transform, IEEE Trans. Audio Electroacoust, Vol.AU-20, pp.66-74, Mar.1972.
[52] Haldum M. Ozaktas, Orhan Arikan, Alper Kutay M. and Gozde Bozdagi. Digital Computation of the Fractional Fourier Transform. IEEE Transactions on Signal Processing, 1996,(44):2141-2150.
[53] Almeida.L.B. The fractional Fourier transform and time-frequency representations. IEEE Trans. on SP, 1994,42(11):3084-3091.
[54] Soo-Chang Pei, Min-Hung Yeh. A Novel Method for Discrete Fractional Fourier Transform Computation, IEEE,2001,585~588.
[55] S.C.Pei,M.H.Yeh. Two dimensional discrete fractional Fourier transform[J]. Signal Processing, 1998,67:99-108.
[56] Shen D, Horace.H.S.Ip. Discriminative Wavelet Shape Descriptors for Recognition of 2-D Patterns[J]. Pattern Recognition, 1999,32(2):151-165.
[57] Stefan Katzenbeisser Fabien, A.P.Petitcolas 著. 信息隐藏技术-隐写术与数字水印 [M]. 吴秋新,钮新忻,杨义先等译. 北京:人民邮电出版社.2001.
[58] J.Siuzdak. A single filter for edge detection. Pattern Recognition[J], 1998, 31:1681-1686.
[59] Wen-Liang Hsue, Soo-Chang Pei. The Multiple-Parameter Discrete Fractional Fourier Transform and Its Application[C], IEEE,ICASSP2006:416-419
[2] Liu. R. Z, Tan. T. N. Watermarking for digital images[A].Proc of ICSP’98 [C] . 1998.2:944-947
[3] Voyatzis. G, Nikolaidis. N, Pitas. I, Digital watermarking: An overview[J].Eur. Signal Processing Conf. EUSIPCO,Rhodes,Greece.1998,9:9-12.
[4] Barnett. R. Digital watermarking: Applications, techniques, and challenges[J]. Electronics and Communication Engineering Journal.1999,11(4) :173-183.
[5] Su. J. K, Hartung. F, Girod B. Digital watermarking of text, image, and video documents[J]. Computers & Graphics. 1998,22(6):687-695.
[6] R. G.van. Schyndel, A.Z. Tirkel, C.F.Osbrone. A Digital Watermark. IEEE International Conference on Image Processing, Vol.2,pp:86-90, Austin, Texas, USA, 1994
[7] A.Tirkel, G.A.Rankin, R.van.Schyndel. Electronic watermark, Digital Image Comp uting. Technology and Application-DICTA 93, Macquarie University, 1993:666-673.
[8] E.Wolfgang, R.Podilchuk, C.Delp. Perpetual watermarks for digital images and video. Proceedings of the IEEE,1999,87(7):1108-1126.
[9] T.Anox, Keith. “Reversible Digital Image” SPIE, 1999:397-401.
[10] W. Bender, D. Gruhl, N. Morimoto, A. Lu. “Techniques for data hiding”. IBM Syst.J.1996.35(3):313-336.
[11] 丁玮,闫伟齐,齐东旭. 基于置乱与融合的数字水印隐藏技术及其应用[J]. 中国图象图形学报,2000,5(8):644-649.
[12] I.J.K.O Ruanaith. Phase Watermarking of Digital Images. Proc. of ICIP, 1996,(1):239-242.
[13] M. H. Hayers. The Reconstruction of a Multi-dimensional Sequence from the Phase or Magnitude of the FFT.IEEE Trans. On ASSP, No.4,pp.140-154,1992.
[14] I. J. Cox, Joe Kilian, F. Thomson. Secure Spread Spectrum Watermarking for Multimedia. IEEE Transaction on Image Processing. Vol.8, NO.12,pp.1673-1687, December1997.
[15] E.Koch, J.Rindfery, J.Zhao. Copyright protection for multimedia data.[DB/OL]. http://citeseer.ist.psu.edu/context/43326/0
[16] A.G. Bors, I. Pitas. Image watermarking using DCT domain constraints, Proc. ofICIP’96,1996,3:231-234.
[17] A. Piva, M. Barni, F. Baolini, V. Capellini. DCT-based watermarking recovering without resorting to the uncorrupted original image, Proc. of ICIP’97,3:520-523.
[18] C.T.Hsu, J.L.Wu. Multiresolution Watermarking for digital image. IEEE Trans. on Circuits and Systems2:Analog and Digital Signal Processing.
[19] X.G.Xia, C.G.Boncelet, G.R.Arce. Wavelet Transform based Watermark for Digital Image. OPTICS EXPRESS, 1998,3(12):497-500.
[20] C. I. Podilchuk, Wenjun Zeng. Image-adaptive Watermarking using Visual Model. IEEE Journal on Selected Areas in Communications, 1998,16(4):525-539.
[21] H.M.Wang, P.C.Su, C.J.Kuo. Wavelet-based Digital Image Watermarking. OPTICS EXPRESS, 1998, 3(12): 491-496.
[22] 刘正君,赵海发,朱邦和等。分数傅立叶域数字水印算法[J] 光子学报,2003,32(3):332-335
[23] Yu. F. Q, Zhang. Z. K, Xu. M. H. A Digital Watermarking Algorithm for Image Based on Fractional Fourier Transform[C].Singapore:2006 1ST IEEE Conference On Industrial Electronics and Applications, Vols 1-3 2006:1441-1445
[24] 张峰,穆晓敏,杨守义等. 基于 FRFT 盲检测 Chirp 类数字水印算法[J]. 计算机工程与应用,2006,9(27):57-61
[25] W.Zeng, B.Liu. On resolving rightful ownerships of digital images by invisible watermarks. Proceedings of ICIP’97,Intern,Conf. on Image Processing, Vol.1,pp.552-555,S,Barbara, CA,USA, October 26-29,1997.
[26] I.J.Cox, M.L.Miller. The first 50 years of electronic watermarking. Journal of Applied Signal Processing, Vol.2,2002,pp.126-132.
[27] Fabien.A.P.Petitcolas, Ross.J.Anderson, Markus.G.Kuhn. Attacks on Copyright Marking Systems. David Aucsmith, Ed, Second workshop on information hiding, Vol1525 of Lecture Notes in Computer Science, Portland, Oregon, USA,14-17,April, 1998,pp.218-238.
[28] Chiou-Ting Hsu, Ja-Ling Wu. Hidden Digital Watermarks in Images. IEEE Transanctions on Image Processing, Vol.8,No.1,January 1999:58-68.
[29] 张 华 熊 , 仇 佩 亮 . 置 乱 技 术 在 数 字 水 印 中 的 应 用 [J]. 电 路 与 系 统 学报,2001,6(3):32-36.
[30] 谢荣生,刘承香等.基于模板匹配的抗集合攻击图象数字水印[J]. 哈尔滨工程大学学报,2002,23(3):54-58.
[31] 王秋生,孙圣和. 基于量化数字音频信号频域参数的水印嵌入算法[J]. 声学学报,2002,27(4):379-384.
[32] 张 华 熊 , 仇 佩 亮 . 数 字 水 印 信 道 模 型 的 快 速 估 算 [J]. 电 路 与 系 统 学报,2002,7(2):39-42.
[33] Keitli Hill. A Perspective: The role of identifiers in managing and Protecting intellectual property in the digital age. Proc IEEE.1999,87(7):1228-1238.
[34] Pettcolas.F, Anderson.R.J, Kun.M.G. Attacks on copyright marking system. Proc of Information Hidding98’,1998,213-238.
[35] Wang.Z, Bovik.A.C, Sheikh.H.R. Image quality assessment:from error visibility to structural similarity[J]. IEEE Transactions on Image Processing,2004,13(4): 600- 612.
[36] Stankovic.S, Djurovic.I, Pitas.I. Watermarking in the Space/Spatial-Frequency Domain Using Two-Dimensional Radon-Wigner Distribution[J]. IEEE Trans on Image Processing,2001,10(4):650-658.
[37] 曹荣, 王颖, 李象霖. 一种基于离散傅立叶变换域相位和幅度的数字水印算法[J]. 计算机应用,2005,25(11):2536-2543.
[38] Xin-Li Hong, Heather Yu. Transparent and robust audio data hiding in cepstrum domain[J].IEEE Int. Conf. Multimedia and Expo(1),2000:397-400.
[39] Sang-Kwang Lee, Yo-Sung Ho. Digital audio watermarking in cepstrum domain. IEEE Transactions on Consumer Electronics,2000,46(3):744-750.
[40] Joan Puate, Frederic Jordan. Using fractal compression scheme to embed a digital signature into an image. SPIE, Video Techniques and Software for Full-Service Networks.1996,2915:108-118.
[41] Namias V. The fractional order Fourier transform and its application to quantum mechanics[J].J Inst Math Appl, 1980,(25):241-265.
[42] H.M.Ozaktas, D.Mendlovic. Fractional Fourier optics [J], J. Opt. Soc. Amer. A, 1995,(12):743-751.
[43] A.W.Lohmann. Image rotation, Wigner rotation and the fractional Fourier transform[J], J.Opt.Soc. 1993,(10):2181-2186.
[44] 陶然,齐林,王越. 分数阶 Fourier 变换的原理与应用[M].北京:清华大学出版社,2004.
[45] 陶然,邓兵,王越. 分数阶 Fourier 变换在信号处理领域的研究进展[J]. 中国科学E 辑,信息科学 2006,36(2):113-136.
[46] 于凤芹, 曹家麟. 分数阶傅立叶变换的多种定义形式及其光学实现系统分析[J]. 光电子技术与信息,2004,17(4):25-29.
[47] Ozaktas. H. M, Kutay. M.A, Zalevsky.Z. The fractional Fourier transform with Application in Optics and Signal Processing. John Wiley & sons,2000.
[48] 汪玲. 分数阶傅立叶变换在线性调频信号侦察中的基本理论及应用:[硕士学位论文].成都:电子科技大学,2002.
[49] Santhanam .B and McClellan. J. H. The discrete rotational Fourier transform, IEEE Transaction on Signal Processing. 1996,(42):994-998.
[50] Dickinson.B.W, Steiglitz.K. Eigenvectors and functions of the discrete Fourier transform. IEEE Trans. Acoust. Speech. Signal Processing, Vol,ASSP-30,No.1, pp.25-31, Feb.1982.
[51] McClellan. J. H, Parks. T. W. Eigen-value and Eigenvector decomposition of the discrete Fourier transform, IEEE Trans. Audio Electroacoust, Vol.AU-20, pp.66-74, Mar.1972.
[52] Haldum M. Ozaktas, Orhan Arikan, Alper Kutay M. and Gozde Bozdagi. Digital Computation of the Fractional Fourier Transform. IEEE Transactions on Signal Processing, 1996,(44):2141-2150.
[53] Almeida.L.B. The fractional Fourier transform and time-frequency representations. IEEE Trans. on SP, 1994,42(11):3084-3091.
[54] Soo-Chang Pei, Min-Hung Yeh. A Novel Method for Discrete Fractional Fourier Transform Computation, IEEE,2001,585~588.
[55] S.C.Pei,M.H.Yeh. Two dimensional discrete fractional Fourier transform[J]. Signal Processing, 1998,67:99-108.
[56] Shen D, Horace.H.S.Ip. Discriminative Wavelet Shape Descriptors for Recognition of 2-D Patterns[J]. Pattern Recognition, 1999,32(2):151-165.
[57] Stefan Katzenbeisser Fabien, A.P.Petitcolas 著. 信息隐藏技术-隐写术与数字水印 [M]. 吴秋新,钮新忻,杨义先等译. 北京:人民邮电出版社.2001.
[58] J.Siuzdak. A single filter for edge detection. Pattern Recognition[J], 1998, 31:1681-1686.
[59] Wen-Liang Hsue, Soo-Chang Pei. The Multiple-Parameter Discrete Fractional Fourier Transform and Its Application[C], IEEE,ICASSP2006:416-419