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

Abstract

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)

CLC Number:

TN95

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.

Figures/Tables 8

Fig.1

Table 1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Table 2

References 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

[1]	Ce JI, Jinzhi WANG, Boqun LI. OFDM sparse channel estimation based on RSAMP algorithm [J]. Systems Engineering and Electronics, 2021, 43(8): 2290-2296.
[2]	Weilin LUO, Hongbin JIN, Hao LI, Ronghua ZHOU. Blind source separation of radar signals based on chaotic adaptive firework algorithm [J]. Systems Engineering and Electronics, 2020, 42(11): 2497-2505.
[3]	HU Xing, MA Linhua, SUN Kangning, HUANG Tianyu, LIU Shiping. Theory performance limit and soft-decision based encoding and decoding algorithm of high order quantity error correction codes [J]. Systems Engineering and Electronics, 2017, 39(10): 2312-2319.
[4]	LIU Yi, DIAO Xing-chun, CAO Jian-jun, DING Kun, XU Yong-ping. Catfish bat algorithm-ant colony optimization for subset problems [J]. Systems Engineering and Electronics, 2016, 38(10): 2441-2448.
[5]	BI Hui, JIANG Cheng-long, WANG Wan-ying, ZHANG Bing-chen, HONG Wen. Track distribution optimization for tomographic synthetic aperture radar imaging [J]. Systems Engineering and Electronics, 2015, 37(8): 1787-1792.
[6]	CHEN Zhonghui, XIONG Yun. Research on the restricted isometry property for Toeplitz matrix [J]. Systems Engineering and Electronics, 2015, 37(5): 1023-1028.
[7]	WANG Cai-yun1, XU Jing2. Improved optimization algorithm for measurement matrix in compressed sensing [J]. Systems Engineering and Electronics, 2015, 37(4): 752-756.
[8]	PENG Zhen-ni, BEN De, ZHANG Gong. Measurement matrix optimization for CS-MIMO radar based on chaotic random filter [J]. Systems Engineering and Electronics, 2015, 37(3): 532-536.
[9]	CHEN Peng, WANG Cheng, MENG Chen. Block compressive sampling matching pursuit based on restricted isometry property [J]. Systems Engineering and Electronics, 2015, 37(2): 239-245.
[10]	WANG Shao-lei， CHEN Wei-yi， GU Xue-feng. Solving weapon-target assignment problems based on self-adaptive differential evolution algorithm [J]. Systems Engineering and Electronics, 2013, 35(10): 2115-2120.
[11]	WANG Guo-fu, ZHANG Hai-ru, ZHANG Fa-quan, XU Ting. Orthogonal matching pursuit signal reconstruction based on improved genetic algorithm [J]. Journal of Systems Engineering and Electronics, 2011, 33(5): 974-.
[12]	SUN Ming, ZHAO Lin, DING Ji-cheng, ZHAO Xin. Hysteretic chaotic neural network with wavelet scale annealing and its applications [J]. Journal of Systems Engineering and Electronics, 2010, 32(2): 396-400.
[13]	PENG Xiu-yan,MEN Zhi-guo,LIU Chang-de. Volterra-kernel estimation and its application based on Kalman filtering algorithm [J]. Journal of Systems Engineering and Electronics, 2010, 32(11): 2431-2435.
[14]	GUO Zhong-hai, CHEN Yong-guang, LI Qiong, YIN Can-bin, ZHANG Ting-hua. Improvement of frequency hopping sequences based on Logistic map [J]. Journal of Systems Engineering and Electronics, 2009, 31(4): 773-776.
[15]	FU Jing-chao, JING Yuan-wei, ZHANG Zhong-hua, ZHANG Si-ying. Chaos control on single-species models with harvesting coefficient [J]. Journal of Systems Engineering and Electronics, 2009, 31(2): 448-451.

Construction and performance research of discrete chaotic measurement matrix

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 8

References 29

Related Articles 15

Recommended Articles

Metrics

Comments