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http://dx.doi.org/10.3837/tiis.2019.09.018

Binary Sequence Family for Chaotic Compressed Sensing  

Lu, Cunbo (Institute of Applied Physics and Computational Mathematics)
Chen, Wengu (Institute of Applied Physics and Computational Mathematics)
Xu, Haibo (Institute of Applied Physics and Computational Mathematics)
Publication Information
KSII Transactions on Internet and Information Systems (TIIS) / v.13, no.9, 2019 , pp. 4645-4664 More about this Journal
Abstract
It is significant to construct deterministic measurement matrices with easy hardware implementation, good sensing performance and good cryptographic property for practical compressed sensing (CS) applications. In this paper, a deterministic construction method of bipolar chaotic measurement matrices is presented based on binary sequence family (BSF) and Chebyshev chaotic sequence. The column vectors of these matrices are the sequences of BSF, where 1 is substituted with -1 and 0 is with 1. The proposed matrices, which exploit the pseudo-randomness of Chebyshev sequence, are sensitive to the initial state. The performance of proposed matrices is analyzed from the perspective of coherence. Theoretical analysis and simulation experiments show that the proposed matrices have limited influence on the recovery accuracy in different initial states and they outperform their Gaussian and Bernoulli counterparts in recovery accuracy. The proposed matrices can make the hardware implement easy by means of linear feedback shift register (LFSR) structures and numeric converter, which is conducive to practical CS.
Keywords
Compressed sensing; measurement matrix; coherence; binary sequence family; chaotic sequence;
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1 Juan Castorena and Charles D. Creusere, "The restricted isometry property for banded random matrices," IEEE Transactions on Signal Processing, vol. 62, no. 19, pp. 5073-5084, October, 2014.   DOI
2 Hongping Gan, Song Xiao and Yimin Zhao, "A novel secure data transmission scheme using chaotic compressed sensing," IEEE Access, vol. 6, pp. 4587-4598, February, 2018.   DOI
3 Mahsa Lotfi and Mathukumalli Vidyasagar, "A fast noniterative algorithm for compressive sensing using binary measurement matrices," IEEE Transactions on Signal Processing, vol. 66, no. 15, pp. 4079-4089, May, 2018.   DOI
4 Li Zeng, Xiongwei Zhang, Liang Chen, Tieyong Cao and Jibin Yang, "Deterministic construction of toeplitzed structurally chaotic matrix for compressed sensing," Circuits, Systems, and Signal Processing, vol. 34, no. 3, pp. 797-813, March, 2015.   DOI
5 Hongping Gan, Song Xiao, Yimin Zhao and Xiao Xue, "Construction of efficient and structural chaotic sensing matrix for compressive sensing," Signal Processing: Image Communication, vol. 68, pp. 129-137, October, 2018.   DOI
6 Hongping Gan, Song Xiao and Yimin Zhao, "A large class of chaotic sensing matrices for compressed sensing," Signal Processing, vol. 149, pp. 193-203, August, 2018.   DOI
7 Guohua Zhang, Rudolf Mathar and Quan Zhou, "Deterministic bipolar measurement matrices with flexible sizes from Legendre sequence," Electronics Letters, vol. 52, no. 11, pp. 928-930, May, 2016.   DOI
8 Gang Wang, Min-Yao Niu and Fang-Wei Fu, "Deterministic constructions of compressed sensing matrices based on optimal codebooks and codes," Applied Mathematics and Computation, vol. 343, pp. 128-136, February, 2019.   DOI
9 Weizhi Lu, Tao Dai and Shu-Tao Xia, "Binary matrices for compressed sensing," IEEE Transactions on Signal Processing, vol. 66, no. 1, pp. 77-85, January, 2018.   DOI
10 Liu Haiqiang, Yin Jihang, Hua Gang, Yin Hongsheng and Zhu Aichun, "Deterministic construction of measurement matrices based on Bose balanced incomplete block designs," IEEE Access, vol. 6, pp. 21710-21718, April, 2018.   DOI
11 Tian Shujuan, Fan Xiaoping, Li Zhetao, Pan Tian, Choi Youngjune and Sekiya Hiroo, "Orthogonal-gradient measurement matrix construction algorithm," Chinese Journal of Electronics, vol. 25, no. 1, pp. 81-87, January, 2016.   DOI
12 Nam Yul Yu and Guang Gong, "A new binary sequence family with low correlation and large size," IEEE Transactions on Information Theory, vol. 52, no. 4, pp. 1624-1636, April, 2006.   DOI
13 Haiyang Liu, Hao Zhang and Lianrong Ma, "On the spark of binary LDPC measurement matrices from complete protographs," IEEE Signal Processing Letters, vol. 24, no. 11, pp. 1616-1620, November, 2017.   DOI
14 Jue Wang, Zhaoyang Zhang, Xianbin Wang, Hong Wang and Chunxu Jiao, "A low-complexity reconstruction algorithm for compressed sensing using Reed-Muller sequences," in Proc. of IEEE Int. Conf. on Communications, pp. 1-6, May 20-24, 2018.
15 Sung-Hsien Hsieh, Chun-Shien Lu and Soo-Chang Pei, "Compressive sensing matrix design for fast encoding and decoding via sparse FFT," IEEE Signal Processing Letters, vol. 25, no. 4, pp. 591-595, April, 2018.   DOI
16 Yan Tang, Guonian Lv and Kuixi Yin, "Deterministic sensing matrices based on multidimensional pseudo-random sequences," Circuits, Systems, and Signal Processing, vol. 33, no. 5, pp. 1597-1610, May, 2014.   DOI
17 Jarvis Haupt, Waheed U. Bajwa, Gil Raz and Robert Nowak, "Toeplitz compressed sensing matrices with applications to sparse channel estimation," IEEE Transactions on Information Theory, vol. 56, no. 11, pp. 5862-5875, November, 2010.   DOI
18 Shuai Liu, Weiling Bai, Gaocheng Liu, Wenhui Li and Hari M. Srivastava, "Parallel fractal compression method for big video data," Complexity, vol. 2018, pp. 1-16, October, 2018.
19 Emmanuel J. Candès, Justin Romberg and Terence Tao, "Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information," IEEE Transactions on Information Theory, vol. 52, no. 2, pp. 489-509, February, 2006.   DOI
20 David L. Donoho, "Compressed sensing," IEEE Transactions on Information Theory, vol. 52, no. 4, pp. 1289-1306, April, 2006.   DOI
21 Gaocheng Liu, Shuai Liu, Khan Muhammad, Arun Kumar Sangaiah and Faiyaz Doctor, "Object tracking in vary lighting conditions for fog based intelligent surveillance of public spaces," IEEE Access, vol. 6, pp. 29283-29296, May, 2018.   DOI
22 Zheng Pan, Shuai Liu, Arun Kumar Sangaiah and Khan Muhammad, "Visual attention feature (VAF): a novel strategy for visual tracking based on cloud platform in intelligent surveillance systems," Journal of Parallel and Distributed Computing, vol. 120, pp. 182-194, October, 2018.   DOI
23 Emmanuel J. Candès and Terence Tao, "Decoding by linear programming," IEEE Transactions on Information Theory, vol. 51, no. 12, pp. 4203-4215, December, 2005.   DOI
24 Scott Shaobing Chen, David L. Donoho and Michael A. Saunders, "Atomic decomposition by basis pursuit," SIAM Journal on Scientific Computing, vol. 20, no. 1, pp. 33-61, August, 1998.   DOI
25 Pradip Sasmal, R. Ramu Naidu, Challa S. Sastry and Phanindra Jampana, "Composition of binary compressed sensing matrices," IEEE Signal Processing Letters, vol. 23, no.8, pp. 1096-1100, August, 2016.   DOI
26 Joel A. Tropp, "Greed is good: Algorithmic results for sparse approximation," IEEE Transactions on Information Theory, vol. 50, no. 10, pp. 2231-2242, October, 2004.   DOI
27 R. Ramu Naidu, Phanindra Jampana and C. S. Sastry, "Deterministic compressed sensing matrices: construction via Euler Squares and applications," IEEE Transactions on Signal Processing, vol. 64, no. 14, pp. 3566-3575, July, 2016.   DOI
28 R. Ramu Naidu and Chandra R. Murthy, "Construction of binary sensing matrices using extremal set theory," IEEE Signal Processing Letters, vol. 24, no. 2, pp. 211-215, February, 2017.   DOI
29 Shuxing Li and Gennian Ge, "Deterministic sensing matrices arising from near orthogonal systems," IEEE Transactions on Information Theory, vol. 60, no. 4, pp. 2291-2302, April, 2014.   DOI
30 Jun Zhang, Guojun Han and Yi Fang, "Deterministic construction of compressed sensing matrices from protograph LDPC codes," IEEE Signal Processing Letters, vol. 22, no. 11, pp. 1960-1964, November, 2015.   DOI
31 Mohammad Fardad, Sayed Masoud Sayedi and Ehsan Yazdian, "A low-complexity hardware for deterministic compressive sensing reconstruction," IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 65, no. 10, pp. 3349-3361, October, 2018.   DOI
32 Hongping Gan, Zhi Li, Jian Li, Xi Wang and Zhengfu Cheng, "Compressive sensing using chaotic sequence based on chebyshev map," Nonlinear Dynamics, vol. 78, no. 4, pp. 2429-2438, December, 2014.   DOI
33 Jin-Wei Jhang and Yuan-hao Huang, "A high-SNR projection-based atom selection OMP processor for compressive sensing," IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 24, no. 12, pp. 3477-3488, December, 2016.   DOI