Abstract
The secure image coding scheme using compressed sensing (CS) is proposed and the secrecy of the scheme is explored. We verify that the CS-based coding scheme can provide a guarantee of secrecy by analysis and simulation. In our approach, random matrices are used as keys of decryption. Based on the feasibility of random symmetric signs matrices in compressed sensing, we obtain a theoretical result that the signal compressed sensing using sparse random binary matrices can be exactly recovered with high probability. Numerical results verify the theory and show matrices proposed in this paper perform equally to the prominent Gaussian matrices when measurement rate is higher than an equivalence threshold.
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References
Candès, E.J., Romberg, J., Tao, T.: Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information. IEEE Trans. Inform. Theory 52, 489–509 (2006)
Donoho, D.L.: Compressed Sensing. IEEE Trans. Inform. Theory 52, 1289–1306 (2006)
Duarte, M., Wakin, M., Baron, D., Baraniuk, R.: Universal Distributed Sensing via Random Projections. In: Proceedings of the 5th International Conference on Information Processing in Sensor Networks, pp. 177–185. ACM Press, New York (2006)
Lian, S., Liu, Z., Ren, Z., Wang, H.: Secure Advanced Video Coding Based on Selective Encryption Algorithms. IEEE Trans. on Consum. Electr. 52, 621–629 (2006)
Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear Total Variation Based Noise Removal Algorithms. Physical D 60, 259–268 (1992)
Tropp, J.A., Gilbert, A.C.: Signal Recovery from Partial Information via Orthogonal Matching Pursuit. IEEE Trans. Inform. Theory 53, 4655–4666 (2007)
Shannon, C.E.: Communication Theory of Secrecy Systems. Bell System Technical Journal 28, 654–715 (1949)
Candès, E.J.: The Restricted Isometry Property and Its Implications for Compressed Sensing. C. R. Acad. Sci. Paris Sr. I, Math. 346, 589–592 (2008)
Baraniuk, R.G., Davenport, M., DeVore, R.A., Wakin, M.: A Simple Proof of the Restricted Isometry Property for Random Matrices. Constructive Approximation 28, 253–263 (2008)
Candès, E.J., Tao, T.: Decoding by Linear Programming. IEEE Trans. Inform. Theory 51, 4203–4215 (2005)
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Zhang, G., Jiao, S., Xu, X. (2010). Application of Compressed Sensing for Secure Image Coding. In: Pandurangan, G., Anil Kumar, V.S., Ming, G., Liu, Y., Li, Y. (eds) Wireless Algorithms, Systems, and Applications. WASA 2010. Lecture Notes in Computer Science, vol 6221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14654-1_27
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DOI: https://doi.org/10.1007/978-3-642-14654-1_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14653-4
Online ISBN: 978-3-642-14654-1
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