Construction of Convolution Compressed Sensing Measurement Matrices Based on Cyclotomic Classes

Yubo LI; Jingjing ZHANG; Chenghuan HAN; Xiuping PENG

doi:10.11999/JEIT190878

Volume 43 Issue 2

Feb. 2021

Turn off MathJax

Article Contents

Article Navigation > Journal of Electronics & Information Technology > 2021 > 43(2): 419-425

Xu Shao-Kun, Liu Ji-Hong, Yuan Xiang-Yu, Lu Jing. Two Dimensional Geometric Feature Inversion Method for Midcourse Target Based on ISAR Image[J]. Journal of Electronics & Information Technology, 2015, 37(2): 339-345. doi: 10.11999/JEIT140338

Citation:

Yubo LI, Jingjing ZHANG, Chenghuan HAN, Xiuping PENG. Construction of Convolution Compressed Sensing Measurement Matrices Based on Cyclotomic Classes[J]. Journal of Electronics & Information Technology, 2021, 43(2): 419-425. doi: 10.11999/JEIT190878

Citation:

PDF( 2098 KB)

Construction of Convolution Compressed Sensing Measurement Matrices Based on Cyclotomic Classes

doi: 10.11999/JEIT190878

School of Information Science & Engineering, Yanshan University, Qinhuangdao 066004, China

Funds: The National Natural Science Foundation of China (61671402, 61501395), The Natural Science Foundation of Hebei Province (F2020203043), The Fundation of Top Young Talents Program in Colleges and Universities of Hebei Province (BJ2018018)

Received Date: 2019-11-04
Rev Recd Date: 2020-07-15

Available Online: 2020-12-09

Publish Date: 2021-02-23

Abstract

Abstract

Convolutional compressed sensing emerging in recent years is a new type of compressed sensing technology. By using cyclic matrix as measurement matrices, the sampling in convolutional compressed sensing can be simplified into convolution process, thus the complexity of the algorithm is greatly reduced. In this paper, a construction of measurement matrices for convolutional compressed sensing based on cyclotomic classes is proposed. The measurements are obtained by using the circulate convolution signal of the deterministic sequence and then by random subsampling. The correlation of the measurement matrix constructed in this paper is smaller than that of the existing constructions in the literature. The simulation results show that the measurement matrix constructed in this paper can recover the sparse signal better than the random Gaussian matrix under the same conditions. The proposed matrix can also be applied to channel estimation and reconstruction of two-dimensional images.
- Signal processing,
- Compressed sensing,
- Convolution,
- Cyclotomic class,
- Random sampling

FullText(HTML)

References(20)

References

DONOHO D L. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289–1306. doi: 10.1109/TIT.2006.871582

DONOHO D L and ELAD M. Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ¹ minimization[J]. Proceedings of the National Academy of Sciences of the United States of America, 2003, 100(5): 2197–2202. doi: 10.1073/pnas.0437847100

范剑英, 马明阳, 赵首博. 基于压缩感知高反光成像技术研究[J]. 电子与信息学报, 2020, 42(4): 1013–1020. doi: 10.11999/JEIT190512

FAN Jianying, MA Mingyang, and ZHAO Shoubo. Research on high reflective imaging technology based on compressed sensing[J]. Journal of Electronics &Information Technology, 2020, 42(4): 1013–1020. doi: 10.11999/JEIT190512

李玮, 邓维波, 杨强, 等. 基于确定性压缩感知采样策略的阵列失效单元远场诊断方法[J]. 电子与信息学报, 2018, 40(11): 2541–2546. doi: 10.11999/JEIT180175

LI Wei, DENG Weibo, YANG Qiang, et al. Far-field diagnosis method of array failure cells based on deterministic compressed sensing sampling strategy[J]. Journal of Electronics &Information Technology, 2018, 40(11): 2541–2546. doi: 10.11999/JEIT180175

LI Yubo, XUAN Hongqian, JIA Dongyan, et al. A construction of sparse deterministic measurement matrices[J]. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2019, E102. A(11): 1575–1579. doi: 10.1587/transfun.e102.a.1575

NOUASRIA H and ET-TOLBA M. Sensing matrix based on Kasami codes for compressive sensing[J]. IET Signal Processing, 2018, 12(8): 1064–1072. doi: 10.1049/iet-spr.2017.0537

GU Zhi, ZHOU Zhengchun, YANG Yang, et al. Deterministic compressed sensing matrices from sequences with optimal correlation[J]. IEEE Access, 2019, 7: 16704–16710. doi: 10.1109/ACCESS.2019.2896006

LIU Haiqiang, YIN Jihang, HUA Gang, et al. Deterministic construction of measurement matrices based on Bose balanced incomplete block designs[J]. IEEE Access, 2018, 6: 21710–21718. doi: 10.1109/ACCESS.2018.2824329

CUI Xiang. Construction of deterministic measurements matrix using decimated Legendre sequences[J]. MATEC Web of Conferences, 2015, 22: 01047. doi: 10.1051/matecconf/20152201047

YU N Y and GAN Lu. Convolutional compressed sensing using decimated sidelnikov sequences[J]. IEEE Signal Processing Letters, 2014, 21(5): 591–594. doi: 10.1109/LSP.2014.2311659

LI Kezhi, GAN Lu, and LING Cong. Convolutional compressed sensing using deterministic sequences[J]. IEEE Transactions on Signal Processing, 2013, 61(3): 740–752. doi: 10.1109/TSP.2012.2229994

TROPP J A. Random filters for compressive sampling[C]. The 2006 40th Annual Conference on Information Sciences and Systems, Princeton, USA, 2006: 216–217. doi: 10.1109/CISS.2006.286465.

BAJWA W U, HAUPT J D, RAZ G M, et al. Toeplitz-structured compressed sensing matrices[C]. 2007 IEEE/SP 14th Workshop on Statistical Signal Processing, Madison, USA, 2007: 294–298. doi: 10.1109/SSP.2007.4301266.

ROMBERG J. Compressive sensing by random convolution[J]. SIAM Journal on Imaging Sciences, 2009, 2(4): 1098–1128. doi: 10.1137/08072975X

CANDÈS E J, ROMBERG J K, and TAO T. Stable signal recovery from incomplete and inaccurate measurements[J]. Communications on Pure and Applied Mathematics, 2006, 59(8): 1207–1223. doi: 10.1002/cpa.20124

BOURGAIN J, DILWORTH S J, FORD K, et al. Explicit constructions of RIP matrices and related problems[J]. Duke Mathematical Journal, 2011, 159(1): 145–185. doi: 10.1215/00127094-1384809

申颖. 基于分圆类和广义分圆类的几乎差集偶构造方法研究[D]. [硕士论文], 燕山大学, 2016: 1–62.

SHEN Ying. The constructions of almost difference set pairs based on cyclotomy and generalized cyclotomy[D]. [Master dissertation], Yanshan University, 2016: 1–62.

TROPP J A and GILBERT A C. Signal recovery from random measurements via orthogonal matching pursuit[J]. IEEE Transactions on Information Theory, 2007, 53(12): 4655–4666. doi: 10.1109/TIT.2007.909108

YANG Junfeng, ZHANG Yin, and YIN Wotao. A fast alternating direction method for TVL1-L2 signal reconstruction from partial Fourier data[J]. IEEE Journal of Selected Topics in Signal Processing, 2010, 4(2): 288–297. doi: 10.1109/JSTSP.2010.2042333

HALE E T, YIN W, and ZHANG Yin. Fixed-point continuation for ℓ₁-minimization: Methodology and convergence[J]. SIAM Journal on Optimization, 2008, 19(3): 1107–1130. doi: 10.1137/070698920

Relative Articles

Supplements(0)

Cited By

Cited by

Periodical cited type(12)

1.	于卫刚，徐少坤，吴昌松，袁翔宇. 基于特征提取的ISAR成像欺骗干扰评估方法研究. 航天电子对抗. 2024(03): 16-20 .
2.	韩立珣，田波，冯存前. 基于MIMO-ISAR的弹道目标结构参数估计方法. 系统工程与电子技术. 2020(03): 603-612 .
3.	霍超颖，殷红成，邢笑宇，满良. 基于雷达图像特征的空间目标载荷指向估计方法. 电波科学学报. 2019(01): 45-51 .
4.	鲁逸杰，宫志华，张群，王剑钦，李开明. 基于变分模态分解的进动目标微多普勒特征提取方法. 探测与控制学报. 2019(04): 30-35 .
5.	任枫轩，王忠勇. 基于ISAR像序列的多旋翼无人机参数估算. 电光与控制. 2018(04): 55-60 .
6.	王超，叶春茂，文树梁. 低重频宽带雷达中小幅微动目标的周期估计. 系统工程与电子技术. 2018(09): 1945-1952 .
7.	徐少坤，刘记红，袁翔宇. 基于HRRP序列的中段目标二维几何特征反演方法. 电子与信息学报. 2017(10): 2366-2373 . 本站查看
8.	刘浩，杨清亮，陈佳东. 近程弹道导弹防御目标识别技术研究. 飞航导弹. 2017(06): 73-77 .
9.	束长勇，张生俊，黄沛霖，姬金祖. 基于微多普勒估计进动锥体目标特征参数. 系统工程与电子技术. 2017(01): 15-20 .
10.	王英，束长勇，张生俊，黄沛霖，姬金祖. 快慢时间域间歇采样转发干扰生成进动锥体ISAR群阵列. 电子与信息学报. 2016(02): 450-454 . 本站查看
11.	周叶剑，张磊，王虹现，邢孟道，牛威. 多站ISAR空间目标姿态估计方法. 电子与信息学报. 2016(12): 3182-3188 . 本站查看
12.	黄小红，文贡坚. L波段雷达电离层高速运动目标ISAR成像补偿方法. 电子与信息学报. 2015(12): 2971-2976 . 本站查看