[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(03):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(03):279-285.[doi:10.11992/tis.201606037]
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易于硬件实现的压缩感知观测矩阵的研究与构造(/HTML)
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《智能系统学报》[ISSN:1673-4785/CN:23-1538/TP]

卷:
第12卷
期数:
2017年03期
页码:
279-285
栏目:
出版日期:
2017-06-25

文章信息/Info

Title:
Study and construction of a compressed sensing measurement matrix that is easy to implement in hardware
作者:
李霞丽 吴立成 樊艳明
中央民族大学 信息工程学院, 北京 100081
Author(s):
LI Xiali WU Licheng FAN Yanming
School of Information Engineering, Minzu University of China, Beijing 100081, China
关键词:
图像处理机器视觉压缩感知采样及重构观测矩阵顺序部分哈达玛循环伪随机矩阵有限等距
Keywords:
image processingmachine visioncompressed sensingsampling and reconstructionmeasurement matrixsequence partial Hadamardsequence pseudo-randomrestricted isometry property
分类号:
TP391
DOI:
10.11992/tis.201606037
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.

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备注/Memo

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