基于量子Daubechies D(4)小波的图像水印算法
Quantum Image Watermarking Algorithm Based on Daubechies D(4) Wavelet Transform
摘要: 本文基于小波变换理论及其在图像水印算法中的应用,给出了利用量子Daubechies D(4)小波变换分解FRQI量子图像的量子线路设计以及基于量子Daubechies D(4)小波变换的分块量子水印算法。该算法首先将经典图像用量子图像形式表示,其次利用Daubechies D(4)小波变换对其进行一级分解,最后将量子水印信息插入到高频段的对角小波系数中。对载体图像影响较小,同时具有较强的嵌入容量以及嵌入质量。
Abstract: Based on wavelet transform theory and its applications in image watermarking algorithm, a watermarking algorithm based on the application of Quantum Daubechies D(4) Wavelet Transform (QDWT) to decompose quantum images represented by FRQI and the design of quantum circuit based on QDWT are proposed. Algorithm firstly shows classic image by using the quantum image representation, then the first decomposition is performed using DWT, and lastly watermarking information is embedded into ten carrier image’s diagonal wavelet coefficients of the high frequency subband. It has little influence on the carrier image, and has strong embedding capacity and embedding quality.
文章引用:孙师阳, 李万社. 基于量子Daubechies D(4)小波的图像水印算法[J]. 应用数学进展, 2020, 9(12): 2292-2300. https://doi.org/10.12677/AAM.2020.912268

参考文献

[1] 成礼智. 小波的理论与应用[M]. 北京: 科学出版社, 2004: 65-77.
[2] Cox, I. (2007) Digital Watermarking and Steganography. Morgan Kaufmann, San Mateo. [Google Scholar] [CrossRef
[3] Zhou, R.-G., Hu, W. and Fan, P. (2017) Quantum Watermarking Scheme through Arnold Scrambling and LSB Steganography. Quantum Information Processing, 16, 1-21. [Google Scholar] [CrossRef
[4] Heidari, S. and Farzadnia, E. (2017) A Novel Quantum LSB-Based Steganography Method Using the Gray Code for Colored Quantum Images. Quantum Information Processing, 16, 1-28. [Google Scholar] [CrossRef
[5] Zhang, W.-W., Gao, F., Liu, B., Wen, Q.-Y. and Chen, H. (2013) A Watermark Strategy for Quantum Images Based on Quantum Fourier Transform. Quantum Information Processing, 12, 793-803. [Google Scholar] [CrossRef
[6] Song, X.-H., Wang, S., Liu, S., El-Latif A.A.A. and Niu, X.-M. (2013) A Dynamic Watermarking Scheme for Quantum Images Using Quantum Wavelet Transform. Quantum Information Processing, 12, 3689-3706. [Google Scholar] [CrossRef
[7] Fijany, A. and Williams, C.P. (1999) Quantum Wavelet Transforms: Fast Algorithms and Complete Circuits. In: Quantum Computing and Quantum Communications QCQC, Springer, Berlin, 1509. [Google Scholar] [CrossRef
[8] Le, P.Q., Dong, F. and Hirota, K. (2011) A Flexible Representation of Quantum Images for Polynomial Preparation Image Compression and Processing Operations. Quantum Information Processing, 10, 63-84. [Google Scholar] [CrossRef
[9] Yan, F., Iliyasu, A.M. and Venegas-Andraca, S.E. (2016) A Survey of Quantum Image Representations. Quantum Information Processing, 15, 1-35. [Google Scholar] [CrossRef
[10] Venegas-Andraca, S.E. and Ball, J.L. (2010) Processing Images in Entangled Quantum Systems. Quantum Information Processing, 9, 1-11. [Google Scholar] [CrossRef
[11] Zhang, Y., Lu, K., Gao, Y. and Wang, M. (2013) NEQR: A Novel Enhanced Quantum Representation of Digital Images. Quantum Information Processing, 12, 2833-2860. [Google Scholar] [CrossRef
[12] 宋显华. 量子图像安全关键技术研究[D]: [博士学位论文]. 哈尔滨: 哈尔滨工业大学, 2015.
[13] Nielsen, M.A. and Chuang, I.L. (2000) Quantum Computation and Quantum Information. Cambridge Univ. Press, Cambridge.
[14] Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., et al. (1995) Elementary Gates for Quantum Computation. Physical Review A: General Physics, 52, 3457-3488. [Google Scholar] [CrossRef
[15] 毛安定, 管一弘, 段锐, 王艳华, 吕梁, 季云海. 基于Daubechies小波的图像边缘检测技术[J]. 图学学报, 2012, 33(1): 63-67.
[16] 杨亚男. 小波变换在彩色图像数字水印技术中的应用[D]: [硕士学位论文]. 西安: 电子科技大学, 2019.
[17] Hu, W.W., Zhou, R.G., El-Rafei, A., et al. (2019) Quantum Image Watermarking Algorithm Based on Haar Wavelet Transform. IEEE Access, 7, 121303-121320. [Google Scholar] [CrossRef
[18] Hoyer, P. (1997) Efficient Quantum Transforms. Quantum Physics.
[19] Van Loan, C.F. (2011) Computational Frameworks for the Fast Fourier Transform. Tsinghua University Press, Beijing.
[20] Porwik, P. and Lisowska, A. (2004) The Haar-Wavelet Transform in Digital Image Processing: Its Status and Achievements. Machine Graphics and Vision, 13, 79-98.
[21] Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (1993) Numerical Recipes in C: The Art of Scientific Computing, Second Edition. Cambridge University Press, Cambridge, 994.
[22] Yan, F., Le, P.Q., Iliyasu, A.M., Sun, B., Garcia, J.A., Dong, F., et al. (2012) Assessing the Similarity of Quantum Images Based on Probability Measurements. IEEE Congress on Evolutionary Computation, Brisbane, 10-15 June 2012, 1-6. [Google Scholar] [CrossRef