[1]李霞丽,吴立成,樊艳明.易于硬件实现的压缩感知观测矩阵的研究与构造[J].智能系统学报,2017,12(3):279-285.[doi:10.11992/tis.201606037]
LI Xiali,WU Licheng,FAN Yanming.Study and construction of a compressed sensing measurement matrix that is easy to implement in hardware[J].CAAI Transactions on Intelligent Systems,2017,12(3):279-285.[doi:10.11992/tis.201606037]
点击复制
LI Xiali,WU Licheng,FAN Yanming.Study and construction of a compressed sensing measurement matrix that is easy to implement in hardware[J].CAAI Transactions on Intelligent Systems,2017,12(3):279-285.[doi:10.11992/tis.201606037]
易于硬件实现的压缩感知观测矩阵的研究与构造
《智能系统学报》[ISSN 1673-4785/CN 23-1538/TP] 卷:
12
期数:
2017年第3期
页码:
279-285
栏目:
学术论文—机器感知与模式识别
出版日期:
2017-06-25
- Title:
- Study and construction of a compressed sensing measurement matrix that is easy to implement in hardware
- Keywords:
- image processing; machine vision; compressed sensing; sampling and reconstruction; measurement matrix; sequence partial Hadamard; sequence pseudo-random; restricted isometry property
- 分类号:
- TP391
- 摘要:
- 在压缩感知过程中，观测矩阵在信号采样及重构中具有重要作用，构造易于硬件实现、结构简单且占内存较小的观测矩阵是压缩感知理论能否实际应用的关键问题之一。提出两种易于硬件实现的观测矩阵，即顺序部分哈达玛观测矩阵和循环伪随机观测矩阵，其中循环伪随机观测矩阵可分为循环m序列和循环gold序列，并证明了伪随机序列所构造的观测矩阵满足有限等距准则。为验证上述两种观测矩阵性能，对二维图像信号进行仿真，结果表明，在较低的采样率下顺序部分哈达玛观测矩阵的重构效果最优，但是采样信号长度必须是2的k次幂；循环伪随机观测矩阵的重构效果虽然弱于顺序部分哈达玛观测矩阵，但是明显优于高斯随机观测矩阵，克服了顺序部分哈达玛矩阵观测信号必须是2的k次幂的限制。提出的两种观测矩阵易于硬件实现，避免了随机矩阵的不确定性且克服了随机矩阵浪费存储资源的缺陷，具有良好的实际应用价值。
- Abstract:
- In the compressed sensing process, the measurement matrix plays a significant role in signal sampling and reconstruction. Therefore, a measurement matrix that is simple in structure, has a small memory, and is easy to implement in hardware is the key to applying compressed sensing theory. Based on the partial Hadamard measurement matrix and a circulating pseudo-random sequence, this paper presents two measurement matrixes that are easy to implement in hardware, namely the sequence partial Hadamard measurement matrix and the recycled pseudo-random sequence measurement matrix. The latter consists of a recycled m sequence and a recycled gold sequence measurement matrix. This further proves that a measurement matrix constructed by a pseudo-random sequence complies with the RIP principle. To test the performance of the two measurement matrixes, a two-dimensional image signal was simulated. It was found that under a low sampling rate, the reconstruction of the sequence partial Hadamard measurement matrix is optimal provided that the length of the sampling signal is 2k. Although reconstruction of the recycled pseudo-random sequence measurement matrix is inferior to the sequence partial Hadamard measurement matrix, it exceeds the Gaussian random measurement matrix, and also overcomes the sequence partial Hadamard measurement matrix’s limitation of a 2k signal length. These two types of measurement matrix are easy to implement in hardware, and avoid the uncertainty and storage waste of a random matrix. Therefore, they are suitable for practical application.
- 参考文献/References:
-
[1] CANDES E, ROMBERG J. Robust signal recovery from incomplete observations[C]//Proceedings of International Conference on Image Processing. Atlanta, GA: IEEE, 2006: 1281-1284.
[2] CANDES E J, TAO T. Decoding by linear programming[J]. IEEE transactions on information theory, 2005, 51(12): 4203-4215.
[3] DONOHO D L. Compressed sensing[J]. IEEE transactions on information theory, 2006, 52(4): 1289-1306.
[4] 戴琼海, 付长军, 季向阳. 压缩感知研究[J]. 计算机学报, 2011, 34(3): 425-434. DAI Qionghai, FU Changjun, JI Xiangyang. Research on compressed sensing[J]. Chinese journal of computers, 2011, 34(3): 425-434.
[5] CANDES E J, TAO T. Near-optimal signal recovery from random projections: universal encoding strategies?[J]. IEEE transactions on information theory, 2007, 52(12): 5406-5425.
[6] 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.
[7] DEVORE R A. Deterministic constructions of compressed sensing matrices[J]. Journal of complexity, 2007, 23(4/5/6): 918-925.
[8] 蒋留兵, 黄韬, 沈翰宁, 等. 基于局部随机化哈达玛矩阵的正交多匹配追踪算法[J]. 系统工程与电子技术, 2013, 35(5): 914-919. JIANG Liubing, HUANG Tao, SHEN Hanning, et al. Orthogonal multi matching pursuit algorithm based on local randomized Hadamard matrix[J]. Systems engineering and electronics, 2013, 35(5): 914-919.
[9] 刘记红, 徐少坤, 高勋章, 等. 基于随机卷积的压缩感知雷达成像[J]. 系统工程与电子技术, 2011, 33(7): 1485-1490. LIU Jihong, XU Shaokun, GAO Xunzhang, et al. Compressed sensing radar imaging based on random convolution[J]. Systems engineering and electronics, 2011, 33(7): 1485-1490.
[10] 徐皓波, 于凤芹. 基于稀疏预处理和循环观测的语音压缩感知[J]. 计算机工程与应用, 2014, 50(23): 220-224. XU Haobo, YU Fengqin. Speech compressed sensing based on sparse pre-treatment and circulant measurement[J]. Computer engineering and applications, 2014, 50(23): 220-224.
[11] 党骙, 马林华, 田雨, 等. M序列压缩感知测量矩阵构造[J]. 西安电子科技大学学报: 自然科学版, 2015(2): 186-192. DANG Kui, MA Linhua, TIAN Yu, et al. Construction of the compressive sensing measurement matrix based on m sequences[J]. Journal of Xidian University: Natural Science, 2015(2): 186-192.
[12] 王学伟, 崔广伟, 王琳, 等. 基于平衡GOLD序列的压缩感知测量矩阵的构造[J]. 仪器仪表学报, 2014, 35(1): 97-102. WANG Xuewei, CUI Guangwei, WANG Lin, et al. Construction of measurement matrix in compressed sensing based on balanced Gold sequence[J]. Chinese journal of scientific instrument, 2014, 35(1): 97-102.
[13] 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.
[14] ZHANG G S, JIAO S H, XU X L, et al. Compressed sensing and reconstruction with bernoulli matrices[C]//Proceedings of 2010 IEEE International Conference on Information and Automation (ICIA). Harbin: IEEE, 2010: 455-460.
[15] ZHANG G S, JIAO S H, XU X L. Compressed sensing and reconstruction with Semi-Hadamard matrices[C]//Proceedings of 2010 2nd International Conference on Signal Processing Systems (ICSPS). Dalian: IEEE, 2010: V1-194-V1-197.
[16] SONG, YUN CAO Wei, SHEN Yanfei, et al. Compressed sensing image reconstruction using intra prediction[J]. Neurocomputing, 151(3):1171-1179.
[17] WU X, HUANG G, WANG J, et al. Image reconstruction method of electrical capacitance tomography based on compressed sensing principle[J]. Measurement science and technology,2013,24 (7):075-085.
[18] LANGET H,RIDDELL C, TROUSSET Y,et al. Compressed sensing dynamic reconstruction in rotational angiography[J]. Med image comput comput assist interv,2012, 7510 (1):223-230.
[19] SHCHUCKINA A,KASPRZAK P,DASS R,et al. Pitfalls in compressed sensing reconstruction and how to avoid them[J]. Journal of biomolecular Nmr,2016:1-20.
[20] PARK JY, YAP HL,ROZELL CJ,et al. Concentration of measure for block diagonal matrices with applications to compressive signal processing[J]. IEEE transactions on signal processing, 2011, 59(12) : 5859-5875.
- 相似文献/References:
-
[1]田国会,吉艳青,李晓磊.家庭智能空间下基于场景的人的行为理解[J].智能系统学报,2010,5(1):57.
TIAN Guo-hui,JI Yan-qing,LI Xiao-lei.Human behaviors understanding based on scene knowledge in home intelligent space[J].CAAI Transactions on Intelligent Systems,2010,5():57.
[2]李庆武,蔡艳梅,徐立中.基于分块分类的智能视频监控背景更新算法[J].智能系统学报,2010,5(3):272.
LI Qing-wu,CAI Yan-mei,XU Li-zhong.Background update algorithm based on blocks classification forintelligent video surveillance[J].CAAI Transactions on Intelligent Systems,2010,5():272.
[3]邵真天,袁杰.一种基于曲波变换的图像去块算法[J].智能系统学报,2012,7(2):102.
SHAO Zhentian,YUAN Jie.An image deblocking algorithm based on curvelet transformation[J].CAAI Transactions on Intelligent Systems,2012,7():102.
[4]王锦榕,袁学海,刘增良.基于图像处理技术的瞳孔和角膜反射中心提取算法[J].智能系统学报,2012,7(5):423.
WANG Jinrong,YUAN Xuehai,LIU Zengliang.An extraction method of pupil and corneal reflection centers based on image processing technology[J].CAAI Transactions on Intelligent Systems,2012,7():423.
[5]傅博,姜勇,王洪光,等.输电线路巡检图像智能诊断系统[J].智能系统学报,2016,11(1):70.[doi:10.11992/tis.201503043]
FU Bo,JIANG Yong,WANG Hongguang,et al.Intelligent diagnosis system for patrol check images of power transmission lines[J].CAAI Transactions on Intelligent Systems,2016,11():70.[doi:10.11992/tis.201503043]
[6]任晓霞,孙秀明,耿鹏,等.多小波和NSDFB组合域递归滤波多聚焦图像融合[J].智能系统学报,2016,11(2):241.[doi:10.11992/tis.201509017]
REN Xiaoxia,SUN Xiuming,GENG Peng,et al.Multifocus image fusion using a recursive filter in the combined domain of multiwavelets and NSDFB[J].CAAI Transactions on Intelligent Systems,2016,11():241.[doi:10.11992/tis.201509017]
[7]姜婷,袭肖明,岳厚光.基于分布先验的半监督FCM的肺结节分类[J].智能系统学报,2017,12(5):729.[doi:10.11992/tis.201706018]
JIANG Ting,XI Xiaoming,YUE Houguang.Classification of pulmonary nodules by semi-supervised FCM based on prior distribution[J].CAAI Transactions on Intelligent Systems,2017,12():729.[doi:10.11992/tis.201706018]
[8]王科俊,赵彦东,邢向磊.深度学习在无人驾驶汽车领域应用的研究进展[J].智能系统学报,2018,13(1):55.[doi:10.11992/tis.201609029]
WANG Kejun,ZHAO Yandong,XING Xianglei.Deep learning in driverless vehicles[J].CAAI Transactions on Intelligent Systems,2018,13():55.[doi:10.11992/tis.201609029]
[9]郭晓峰,王耀南,周显恩,等.中国象棋机器人棋子定位与识别方法[J].智能系统学报,2018,13(4):517.[doi:10.11992/tis.201709020]
GUO Xiaofeng,WANG Yaonan,ZHOU Xianen,et al.Chess-piece localization and recognition method for Chinese chess robot[J].CAAI Transactions on Intelligent Systems,2018,13():517.[doi:10.11992/tis.201709020]
[10]安果维,王耀南,周显恩,等.基于显著性检测的双目测距系统[J].智能系统学报,2018,13(6):913.[doi:10.11992/tis.201712005]
AN Guowei,WANG Yaonan,ZHOU Xianen,et al.Binocular distance measurement system based on saliency detection[J].CAAI Transactions on Intelligent Systems,2018,13():913.[doi:10.11992/tis.201712005]
[11]梁义辉,战强.一种面向无线图像传输的视觉平台[J].智能系统学报,2016,11(5):608.[doi:10.11992/tis.201512014]
LIANG Yihui,ZHAN Qiang.A visual platform for wireless image transmission[J].CAAI Transactions on Intelligent Systems,2016,11():608.[doi:10.11992/tis.201512014]
[12]赵立明,龙大周,徐晓东,等.工业机器人加工轨迹双目3D激光扫描成像修正方法[J].智能系统学报,2021,16(4):690.[doi:10.11992/tis.202008008]
ZHAO Liming,LONG Dazhou,XU Xiaodong,et al.Binocular 3D laser scanning imaging-based industrial robot machining trajectory correction method[J].CAAI Transactions on Intelligent Systems,2021,16():690.[doi:10.11992/tis.202008008]
备注/Memo
收稿日期:2016-06-21。
基金项目:国家自然科学基金项目（51375504，61602539）.
作者简介:李霞丽,女,1979年生,副教授,研究方向为计算机博弈、智能系统及其应用。主持国家自然科学基金项目1项,发表学术论文20余篇,出版专著1部;吴立成,男,1972年生,教授,主要研究方向为智能系统及其应用、机器人。主持国家级项目5项,发表学术论文50余篇,出版专著2部;樊艳明,男,1991年生,硕士研究生,主要研究方向为机器视觉。发表学术论文3篇。
通讯作者:吴立成.E-mail:wulicheng@tsinghua.edu.cn.
更新日期/Last Update:
2017-06-25