经验模态分解构造观测矩阵的方法

doi:10.3969/j.issn.1001-2400.2018.01.007

Abstract

Abstract:

In order to maintain the integrity information on the signal in high probability, the measuremental matrix is designed to be a random one. But this randomness results in the fact that both useful information and useless information are near the equiprobably measured, which leads to a low sensing efficiency. To improve the sensing efficiency, this paper proposes a new method of measurement matrix construction based on Empirical Mode Decomposition of the reference signal. It uses the Intrinsic Mode Function to construct a cyclic matrix, which is proved to satisfy the restricted isometry property condition by the Gersgorin disc theorem. It simulates the signal denoising process and uses signal noise reduction as the measure. Simulation results show: (1)it has a better effect on reducing noise by adding noise to the reference signal; (2)when the noisy signal and the reference signal are dislocated in the time domain, the effect of noise reduction is significantly decreased compared with the ideal condition. However, the reconstructed signal maintains its frequency information well, which is helpful in practical applications.

Key words: measurement matrix, compressive sensing, signal denosing, sparse reconstruction, circulant matrix

LIU Xuewen;XIAO Song;XUE Xiao. Measurement matrix construction based on empirical mode decomposition[J].Journal of Xidian University, 2018, 45(1): 35-41.

References

［1］ TIAN S, FAN X, LI Z, et al. Orthogonal-gradient Measurement Matrix Construction Algorithm［J］. Chinese Journal of Electronics, 2016, 25(1):81-87.
［2］ QIN S, ZHANG Y D, AMIN M G, et al. Generalized Coprime Sampling of Toeplitz Matrices for Spectrum Estimation［J］. IEEE Transactions on Signal Processing, 2017, 65(1): 81-94.
［3］ CANDES E, ROMBERG J. Sparsity and Incoherence in Compressive Sampling［J］. Inverse Problems, 2007, 23(3):969-985.
［4］ LIU W J. Some Quantum Estimates of Hermite-Hadamard Inequalities for Convex Functions［J］. Journal of Applied Analysis ＆ Computation, 2017, 7(2): 501-522.
［5］ MAHROUS H, WARD R. Block Sparse Compressed Sensing of Electroencephalogram (EEG) Signals by Exploiting Linear and Non-linear Dependencies［J］. Sensors, 2016, 16(2): 201.
［6］ LIN Y M, ZHANG J F, GENG J, et al. Structural Scrambling of Circulant Matrices for Cost-effective Compressive Sensing［J］. Journal of Signal Processing Systems, 2016: 1-13.
［7］ DUMER I. Recursive Decoding and Its Performance for Low-rate Reed-Muller Codes［J］. IEEE Transactions on Information Theory, 2004, 50(5): 811-823.
［8］郭海燕, 王天荆, 杨震. DCT域的语音信号自适应压缩感知［J］. 仪器仪表学报, 2010, 31(6):1262-1268.
GUO Haiyan, WANG Tianjin, YANG Zhen. Adaptive Speech Compressed Sensing in the DCT Domain［J］. Chinese Journal of Scientific Instrument, 2010, 31(6): 1262-1268.
［9］ ABTAHI A, MODARRES-HASHEMI M, MARVASTI F, et al. Power Allocation and Measurement Matrix Design for Block CS-based Distributed MIMO Radars［J］. Aerospace Science and Technology, 2016, 53(1): 128-135.
［10］ TONG S, LIU B, GUO Q, et al. Multiple-rate Codes from Block Markov Superposition Transmission of First-order Reed-Muller and Extended Hamming Codes［J］. Electronics Letters, 2016, 52(18): 1531-1533.
［11］ MASOUMIAN S H S, TAZEHKAND B M. On Joint Compressed Sensing Based Channel Estimation and Nonuniform PTS PAPR Reduction without Side Information［J］. National Academy Science Letters, 2016, 39(6): 445-449.
［12］ JI S, XUE Y, CARIN L. Bayesian Compressive Sensing［J］. IEEE Transactions on Signal Processing, 2008, 56(6): 2346-2356.
［13］ HUANG B C, WAN J W, NIAN Y J. Measurement Matrix Design for Hyperspectral Image Compressive Sensing［C］//Proceedings of the 2015 International Conference on Signal Processing. Piscataway: IEEE, 2015: 1111-1115.
［14］ BOUCHHIMA B, AMARA R, ALOUANE M T H. Design of Optimal Matrices for Compressive Sensing: Application to Environmental Sounds［C］//Proceedings of the 2015 23rd European Signal Processing Conference. Piscataway: IEEE, 2015: 130-134.
［15］ SINTUNAVARAT W. The Upper Bound Estimation for the Spectral Norm of r-circulant and Symmetric r-circulant Matrices with the Padovan Sequence［J］. Journal of Nonlinear Science ＆ Applications, 2016, 9(1): 92-101.
［16］张君昌, 刘海鹏, 樊养余. 一种自适应时移与阈值的DCT语音增强算法［J］. 西安电子科技大学学报, 2014, 41(6): 155-159.
ZHANG Junchang, LIU Haipeng, FAN Yangyu. Speech Enhancement Method Using Self-adaptive Time-shift and Threshold Discrete Cosine Transform［J］. Journal of Xidian University, 2014, 41(6): 155-159.
［17］王峰, 向新, 易克初, 等. 支撑驱动的非凸压缩感知恢复算法［J］. 西安电子科技大学学报, 2016, 43(2): 1-5.
WANG Feng, XIANG Xin, YI Kechu, et al. Support Driven Recovery Algorithm for Non-convex Compressed Sensing［J］. Journal of Xidian University, 2016, 43(2): 1-5.
［18］ HAUPT J, BAJWA W U, RAZ G, et al. Toeplitz Compressed Sensing Matrices with Applications to Sparse Channel Estimation［J］. IEEE Transactions on Information Theory, 2010, 56(11): 5862-5875.
［19］ SUN J M, WANG S, DONG Y. Sparse Block Circulant Matrices for Compressed Sensing［J］. IET Communications, 2013, 7(13): 1412-1418.
［20］孙晶明. 压缩感知中观测矩阵的研究［D］. 武汉: 华中科技大学, 2013.

[1]	HUANG Chen,LIU Hongqing,LUO Zhen,ZHOU Yi. Method for suppressing clutters with the joint low-rank and sparse model [J]. Journal of Xidian University, 2019, 46(6): 60-66.
[2]	SUN Chen, CHENG Liye. Spatial sensing matrix learning for PolSAR image classification [J]. Journal of Xidian University, 2018, 45(6): 92-98.
[3]	WEI Juan;JI Yongxiang;NIU Junru. Novel algorithm for DOA estimation based on the sparse reconstruction [J]. Journal of Xidian University, 2018, 45(5): 13-18.
[4]	LV Zhiguo;LI Ying. Compressed sensing-based Bayesian channel estimation algorithm [J]. Journal of Xidian University, 2018, 45(2): 13-18+25.
[5]	LI Wei;DENG Weibo;YANG Qiang;YSUO Ying;MIGLIORE Marco Donald. Diagnosis method for defective array elements based on compressive sensing [J]. Journal of Xidian University, 2018, 45(2): 160-165.
[6]	LI Yanlong;CHEN Xiao;ZHAN Deman;WANG Junyi. Method of sparse multi-user detection in non-orthogonal multiple access [J]. Journal of Xidian University, 2017, 44(3): 151-156.
[7]	QUAN Lei;XIAO Song;XUE Xiao;LI Ying. Fast sensing method in compressive sensing with low complexity [J]. Journal of Xidian University, 2017, 44(1): 106-111.
[8]	WANG Yong;QIAO Qianqian;YANG Xiaoyu;XU Wenjuan;JIA Zheng;CHEN Chuchu;GAO Quanxue. Sparse Bayesian reconstruction combined with self-adaptive dictionary learning [J]. Journal of Xidian University, 2016, 43(4): 1-4+122.
[9]	KUANG Tao;HUANG Liyu;ZHONG Yufang;LI Chao. Improved compressive sensing algorithm for CT image reconstruction with incomplete projection data [J]. J4, 2015, 42(4): 95-99+113.
[10]	DANG Kui;MA Linhua;TIAN Yu;ZHANG Haiwei;RU Le;LI Xiaobei. Construction of the compressive sensing measurement matrix based on m sequences [J]. J4, 2015, 42(2): 186-192.
[11]	FANG Biao;HUANG Gaoming;GAO Jun;ZUO Wei. Compressive sensing of linear frequency modulated echo signals in fractional Fourier domains [J]. J4, 2015, 42(1): 200-206.
[12]	FANG Biao;HUANG Gaoming;GAO Jun;ZUO Wei. Design of a segmented and blocked compressive sampling model [J]. J4, 2014, 41(4): 151-157.
[13]	TIAN Yumin;SONG Jun2. Compressive sensing with sparse domain division using probability [J]. J4, 2013, 40(6): 52-57.
[14]	HE Yibao;BI Duyan. Signal reconstruction algorithm based on the probabilistic structured sparse model [J]. J4, 2013, 40(2): 194-200.
[15]	WANG Shuzhen;LI Li;ZOU Zijian;ZHANG Xiaoping. Research on the solar image reconstruction method based on compressive sensing [J]. J4, 2013, 40(1): 76-80.

Measurement matrix construction based on empirical mode decomposition

PDF (PC)

Like

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10