离散混沌测量矩阵构造及其性能研究

doi:10.3969/j.issn.1001-506X.2020.04.03

系统工程与电子技术 ›› 2020, Vol. 42 ›› Issue (4): 749-755.doi: 10.3969/j.issn.1001-506X.2020.04.03

离散混沌测量矩阵构造及其性能研究

罗沅¹(), 党娇娇¹(), 宋祖勋^1,²(), 王保平^1,²()

1. 西北工业大学电子信息学院, 陕西西安 710072
2. 西北工业大学无人机特种技术重点实验室, 陕西西安 710065

收稿日期:2019-01-16 出版日期:2020-03-28 发布日期:2020-03-28
作者简介:罗沅(1988-),男,博士研究生,主要研究方向为认知无线电技术。E-mail:ztyjhly@163.com|党娇娇(1989-),女,博士研究生,主要研究方向为目标散射测量及外推算法研究。E-mail:15202442839@163.com|宋祖勋(1964-),男,研究员,博士,主要研究方向为无人机测控数据链、电磁兼容、微波通讯、电子系统仿真。E-mail:zxsong@nwpu.edu.cn|王保平(1964-),男,研究员,博士,主要研究方向为无人机遥感图像处理、雷达信号处理和雷达成像。E-mail:wbpluo@sina.com
基金资助:
国家自然科学基金(61472324)

Construction and performance research of discrete chaotic measurement matrix

Yuan LUO¹(), Jiaojiao DANG¹(), Zuxun SONG^1,²(), Baoping WANG^1,²()

1. School of Electronics and Information, Northwestern Polytechnical University, Xi'an, 710072, China
2. National Key Laboratory of Science and Technology on UAV, Northwestern Polytechnical University, Xi'an, 710065, China

Received:2019-01-16 Online:2020-03-28 Published:2020-03-28
Supported by:
国家自然科学基金(61472324)

摘要/Abstract

摘要：

若测量矩阵满足约束等距性(restricted isometric property, RIP),则样本能够完美恢复出原始信号。而对于给定矩阵很难验证其是否满足RIP需求,因此,本文采用李雅普诺夫指数作为一种针对离散混沌测量矩阵的验证指标。首先分析了RIP与李雅普诺夫指数之间的联系,然后给出了一种分段式混沌映射构造方法用以提高混沌性能,并从理论和仿真上证明了该方法的有效性。实验结果表明,这种方法不仅提高了混沌序列的随机性和自相关性,而且所生成的测量矩阵也具有更好的性能。因此,引进李雅普诺夫指数是一种有效的验证离散混沌测量矩阵性能的方法,提高李雅普诺夫指数能够提高混沌测量矩阵的性能。

关键词: 混沌映射, 测量矩阵, 李雅普诺夫指数, 约束等距性

Abstract:

If the sampling matrix has the restricted isometric property (RIP), the samples will contain enough information to recover the original signal extremely well. Actually, the RIP requirement is hard to verify for a given matrix. Therefore, the Lyapunov exponent as the metric is used to verify the performance of the discrete chaotic measurement matrix. Firstly, the relationship between the RIP and the Lyapunov exponent is analyzed, and a segmentation method is proposed for improving the performance of the chaotic map, then its validity is proved by theory and numerical results. The present results show that the method can both increase the Lyapunov exponent of chaotic map and improve the performance of the generated measurement matrix. Obviously, the Lyapunov exponent is a good metric to verify the performance of the discrete chaotic measurement matrix. By increasing the value of the Lyapunov exponent, the performance of the chaotic measurement matrix can be improved easily.

Key words: chaotic map, measurement matrix, Lyapunov exponent, restricted isometry property (RIP)

中图分类号:

TN95

罗沅, 党娇娇, 宋祖勋, 王保平. 离散混沌测量矩阵构造及其性能研究[J]. 系统工程与电子技术, 2020, 42(4): 749-755.

Yuan LUO, Jiaojiao DANG, Zuxun SONG, Baoping WANG. Construction and performance research of discrete chaotic measurement matrix[J]. Systems Engineering and Electronics, 2020, 42(4): 749-755.

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参考文献 29

1	DONOHO D L . Compressed sensing[J]. IEEE Trans.on Information Theory, 2006, 52 (4): 1289- 1306. doi: 10.1109/TIT.2006.871582
2	DUARTE M F , DAVENPORT M A , TAKHAR D , et al. Single-pixel imaging via compressive sampling[J]. IEEE Signal Processing Magazine, 2008, 25 (2): 83- 91. doi: 10.1109/MSP.2007.914730
3	XU M , FANG Y , LIU S , et al. Sparse channel estimation for MIMO-OFDM systems in high-mobility situations[J]. IEEE Trans.on Vehicular Technology, 2018, 67 (7): 6113- 6124. doi: 10.1109/TVT.2018.2811368
4	TANG V H , BOUZERDOUM A , PHUNG S L . Multi-polarization through-wall radar imaging using low-rank and jointly-sparse representations[J]. IEEE Trans.on Image Processing, 2018, 27 (4): 1763- 1776. doi: 10.1109/TIP.2017.2786462
5	WANG D , ZHANG N , LI Z , et al. Leveraging high order cumulants for spectrum sensing and power recognition in cognitive radio networks[J]. IEEE Trans.on Wireless Communications, 2018, 17 (2): 1298- 1310. doi: 10.1109/TWC.2017.2777488
6	MASSA A , ROCCA P , OLIVERI G . Compressive sensing in electromagnetics-a review[J]. IEEE Antennas & Propagation Magazine, 2015, 57 (1): 224- 238.
7	BARANIUK R , DAVENPORT M , DEVORE R , et al. A simple proof of the restricted isometry property for random matrices[J]. Constructive Approximation, 2008, 28 (3): 253- 263. doi: 10.1007/s00365-007-9003-x
8	LIU H , HAO Z , MA L . On the spark of binary LDPC measurement matrices from complete protographs[J]. IEEE Signal Processing Letters, 2017, 24 (11): 1616- 1620. doi: 10.1109/LSP.2017.2749043
9	周伟, 景博, 张航, 等. 一种基于复合混沌映射的压缩感知测量矩阵构造方法研究[J]. 电子学报, 2017, 45 (9): 2177- 2183. doi: 10.3969/j.issn.0372-2112.2017.09.018
	ZHOU W , JING B , ZHANG H , et al. Construction of measurement matrix in compressive sensing based on composite chaotic mapping[J]. Acta Electronica Sinica, 2017, 45 (9): 2177- 2183. doi: 10.3969/j.issn.0372-2112.2017.09.018
10	葛滨, 鲁华祥, 陈旭, 等. 基于超混沌的快速图像加密算法[J]. 系统工程与电子技术, 2016, 38 (3): 699- 705.
	GE B , LU H X , CHEN X , et al. Fast image encryption algorithm based on hyper-chaos[J]. Systems Engineering and Electronics, 2016, 38 (3): 699- 705.
11	CHANDRA S S , GARY R , JIN J , et al. Chaotic sensing[J]. IEEE Trans.on Image Processing, 2018, 27 (12): 6079- 6092. doi: 10.1109/TIP.2018.2864918
12	肖斌, 史文明, 李伟生, 等. 基于多阶分数离散切比雪夫变换和产生序列的图像加密方法[J]. 通信学报, 2018, 39 (5): 1- 10. doi: 10.3969/j.issn.1001-2400.2018.05.001
	XIAO B , SHI W M , LI W S , et al. Image encryption method based on multiple-order fractional discrete Tchebichef transform and generating sequence[J]. Journal on Communications, 2018, 39 (5): 1- 10. doi: 10.3969/j.issn.1001-2400.2018.05.001
13	QI J , HU X , MA Y , et al. A hybrid security and compressive sensing-based sensor data gathering scheme[J]. IEEE Access, 2015, 3, 718- 724. doi: 10.1109/ACCESS.2015.2439034
14	ZHANG Y , ZHANG L Y , ZHOU J , et al. A review of compressive sensing in information security field[J]. IEEE Access, 2016, 4, 2507- 2519. doi: 10.1109/ACCESS.2016.2569421
15	吴彦华, 马庆力. Duffing振子微弱信号盲检测方法[J]. 系统工程与电子技术, 2017, 39 (11): 2414- 2421. doi: 10.3969/j.issn.1001-506X.2017.11.04
	WU Y H , MA Q L . Blind detection method of weak signals with Duffing oscillator[J]. Systems Engineering and Electronics, 2017, 39 (11): 2414- 2421. doi: 10.3969/j.issn.1001-506X.2017.11.04
16	GU X , ZHOU X , YUAN B , et al. A Bayesian compressive data gathering scheme in wireless sensor networks with one mobile sink[J]. IEEE Access, 2018, 6, 47897- 47910. doi: 10.1109/ACCESS.2018.2867538
17	LIU J X , SUN Q S . Chaotic cellular automaton for generating measurement matrix used in CS coding[J]. IET Signal Processing, 2017, 11 (1): 115- 122.
18	MAHMOOD A A M K , GAZE A M . Combined speech compression and encryption using chaotic compressive sensing with large key size[J]. IET Signal Processing, 2018, 12 (2): 214- 218. doi: 10.1049/iet-spr.2016.0708
19	ZHU S , ZHU C , WANG W . A novel image compression-encryption scheme based on chaos and compression sensing[J]. IEEE Access, 2018, 6, 67095- 67107. doi: 10.1109/ACCESS.2018.2874336
20	GAN H , XIAO S , ZHAO Y . A novel secure data transmission scheme using chaotic compressed sensing[J]. IEEE Access, 2018, 6, 4587- 4598. doi: 10.1109/ACCESS.2017.2780323
21	CANDÈS E J . The restricted isometry property and its implications for compressed sensing[J]. Comptes Rendus-Mathématique, 2008, 346 (9-10): 589- 592. doi: 10.1016/j.crma.2008.03.014
22	WU G C . Discrete fractional logistic map and its chaos[J]. Nonlinear Dynamics, 2014, 75 (1-2): 283- 287. doi: 10.1007/s11071-013-1065-7
23	LI C , LUO G , KE Q , et al. An image encryption scheme based on chaotic tent map[J]. Nonlinear Dynamics, 2017, 87 (1): 127- 133.
24	PAK C , HUANG L . A new color image encryption using combination of the 1D chaotic map[J]. Signal Processing, 2017, 138 (3): 129- 137.
25	王光义, 袁方. 级联混沌及其动力学特性研究[J]. 物理学报, 2013, 62 (2): 103- 112.
	WANG G Y , YUAN F . Cascade chaos and its dynamic characteristics[J]. Acta Physica Sinica, 2013, 62 (2): 103- 112.
26	PENG H , TIAN Y , KURTHS J , et al. Secure and energy-efficient data transmission system based on chaotic compressive sensing in body-to-body networks[J]. IEEE Trans.on Biomedical Circuits and Systems, 2017, 11 (3): 558- 573. doi: 10.1109/TBCAS.2017.2665659
27	YAO S , WANG T , SHEN W , et al. Research of incoherence rotated chaotic measurement matrix in compressed sensing[J]. Multimedia Tools and Applications, 2017, 76 (17): 17699- 17717. doi: 10.1007/s11042-015-2953-2
28	FANG Y , WANG B , SUN C , et al. Near field 3-D imaging approach for joint high-resolution imaging and phase error correction[J]. Journal of Systems Engineering and Electronics, 2017, 28 (2): 199- 211. doi: 10.21629/JSEE.2017.02.01
29	ZHANG Y , ZHOU J , CHEN F , et al. A block compressive sensing based scalable encryption framework for protecting significant image regions[J]. International Journal of Bifurcation and Chaos, 2016, 26 (11): 1- 16.

Lyapunov指数	三分段	四分段	六分段
定义计算结果	1.036 3	1.218 5	1.698 0
式(12)计算结果	1.038 5	1.221 7	1.694 0

Lena图像	水平	垂直	对角
原始图像	0.914 0	0.963 3	0.887 0
非线性Logistic	0.245 5	0.245 9	-0.148 3
Chebyshev	0.050 1	0.284 6	0.070 0
L-T级联	-0.287 8	0.101 8	0.053 7
四分段Tent	0.119 7	0.035 3	0.104 3

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离散混沌测量矩阵构造及其性能研究

Construction and performance research of discrete chaotic measurement matrix

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