一种适用于图像信号的压缩感知测量矩阵

李文宗; 华钢

doi:10.13272/j.issn.1671-251x.2021070048

一种适用于图像信号的压缩感知测量矩阵

doi: 10.13272/j.issn.1671-251x.2021070048

李文宗,
华钢^,

中国矿业大学信息与控制工程学院, 江苏徐州　221116

基金项目: 国家自然科学基金面上资助项目(51574232)。

详细信息

作者简介:
李文宗(1997−), 男, 内蒙古赤峰人, 硕士研究生, 研究方向为压缩感知, E-mail: 563795537@qq.com

通讯作者:
华钢(1963−), 男, 江苏徐州人, 教授, 博士, 研究方向为图像处理与模式识别、压缩感知, E-mail: ghua3323@163.com

中图分类号: TD67
计量
- 文章访问数: 120
- HTML全文浏览量: 37
- PDF下载量: 21
- 被引次数: 0
出版历程
- 收稿日期: 2021-07-18
- 修回日期: 2021-12-10
- 刊出日期: 2022-01-20

A compressive sensing measurement matrix for image signal

LI Wenzong,
HUA Gang^,

School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China

摘要

摘要: 矿井无人工作区监控图像信息量较大，在图像的传输、存储阶段对硬件性能要求较高，造成传感器节点耗能增大、寿命骤减等问题，目前Gause、Bernoulli等压缩感知测量矩阵在重建矿井监控图像信号时精度较低。针对上述问题，设计了一种新的基于帕斯卡矩阵的块状压缩感知测量(BPCSM)矩阵。BPCSM矩阵利用时域非均匀采样与分块思想，将多个相同的小尺寸帕斯卡矩阵以对角线方式排列，同时结合联合正交匹配追踪算法实现井下监控图像信号的压缩采样与重建，利用帕斯卡矩阵行元素有序排列的特点加强对图像信号低频段的采样，提高重建精度。实验结果表明：BPCSM矩阵对矿井监控图像信号的重建精度远高于Gause、Bernoulli等常用测量矩阵，当采样率为0.3时，基于BPCSM矩阵重建的矿工图像的峰值信噪比(PSNR)约为26 dB，矿工面部轮廓较为清晰；当采样率为0.5时，基于BPCSM矩阵重建的矿工图像的PSNR已达30 dB，几乎可以恢复矿工图像的全部细节，表明BPCSM矩阵具有较好的重建性能；通过选择合适的帕斯卡矩阵尺寸能够进一步提高图像信号的重建性能，满足矿井环境应用要求。
- 矿井监控图像 /
- 无线传感器网络 /
- 块状压缩感知 /
- 测量矩阵 /
- 图像重建 /
- 图像压缩 /
- 帕斯卡矩阵 /
- WSN
Abstract: The amount of monitoring image information in unmanned working area of mine is large, and the hardware performance requirements are high in the image transmission and storage stage, which causes the problems of increased energy consumption and sudden decrease of the service life of sensor nodes. At present, when reconstructing mine monitoring image signal, the precision of compressive sensing measurement matrices such as Gause and Bernoulli is low. In order to solve the above problems, a new block Pascal compressive sensing measurement matrix (BPCSM) is designed. The BPCSM matrix uses the idea of non-uniform sampling and blocking in time domain, arranges multiple identical small-size Pascal matrices in a diagonal manner, and combines with the joint orthogonal matching tracking algorithm so as to realize the compression sampling and reconstruction of underground monitoring image signals. And the characteristics of orderly arrangement of row elements of Pascal matrices are used to strengthen the sampling of low frequency band of image signals so as to improve the reconstruction precision. The experimental results show that the reconstruction precision of BPCSM matrix for mine monitoring image signals is much higher than that of the commonly used measurement matrices such as Gause and Bernoulli. When the sampling rate is 0.3, the peak signal-to-noise ratio (PSNR) of the miner image reconstructed based on BPCSM matrix is about 26 dB, and the miner's facial contour is clear. When the sampling rate is 0.5, the PSNR of the miner image reconstructed based on BPCSM matrix has reached 30 dB, which can recover almost all the details of the miner image, indicating the better reconstruction performance of the BPCSM matrix. By selecting the appropriate Pascal matrix size, the reconstruction performance of the image signal can be further improved to meet the application requirements of the mine environment.
- mine monitoring image /
- wireless sensor network /
- blockcompressive sensing /
- measurement matrix /
- image reconstruction /
- imagecompression /
- Pascal matrix /
- WSN

HTML全文

图 1 图像能量

Figure 1. Image energy

下载: 全尺寸图片幻灯片

图 2 基于BPCSM矩阵的矿井监控图像信号的压缩采样、重建

Figure 2. Compression sampling and reconstruction steps for mine monitoring images signals based on BPCSM matrix

下载: 全尺寸图片幻灯片

图 3 测试图像

Figure 3. Test images

下载: 全尺寸图片幻灯片

图 4 矿工图像重建效果

Figure 4. Reconstruction effect of miner images

下载: 全尺寸图片幻灯片

图 5 Lena图像重建效果

Figure 5. Reconstruction effect of Lena images

下载: 全尺寸图片幻灯片

图 6 不同测量矩阵在不同采样率下的图像重建性能对比

Figure 6. Comparison of images reconstruction performance with different measurement matrices at different sampling rates

下载: 全尺寸图片幻灯片

表 1 不同基矩阵尺寸下BPCSM矩阵重建图像效果客观对比

Table 1. Objective comparison of images reconstruction effects of BPM matrix under different base matrix sizes

基矩阵尺寸	PSNR/dB
基矩阵尺寸	Lena	煤块	矿工	顶板支撑
$ {\text{2}} \times {\text{4}} $	25.9343	23.5096	30.3761	27.7568
$ {\text{3}} \times {\text{6}} $	26.8431	24.2209	31.2294	28.5349
$ {\text{4}} \times {\text{8}} $	25.6847	23.3564	30.1094	27.5590
$ {\text{5}} \times {\text{10}} $	20.6204	23.1191	26.2840	22.0924
$ {\text{6}} \times {\text{12}} $	19.1721	21.6420	24.5401	19.1721

下载: 导出CSV

参考文献(20)

[1]	尹珠, 黄友锐, 陈珍萍. 煤矿井下压缩感知图像处理算法[J]. 工矿自动化,2016,42(11):38-40. YIN Zhu, HUANG Yourui, CHEN Zhenping. Compressed sensing image processing algorithm of underground coal mine[J]. Industry and Mine Automation,2016,42(11):38-40.
[2]	DONOHO D L. Compressed sensing[J]. IEEE Transactions on Information Theory,2006,52(4):1289-1306.
[3]	GILBERT A, INDYK P. Sparse recovery using sparse matrices[J]. Proceedings of the IEEE,2010,98( 6):937-947. doi: 10.1109/JPROC.2010.2045092
[4]	RONALD A D. Deterministic constructions of compressed sensing matrices[J]. Journal of Complexity,2007,23(4/6):918-925. doi: 10.1016/j.jco.2007.04.002
[5]	CANDES E, TAO T. Decoding by linear programming[J]. IEEE Transactions on Information Theory,2005,51(12):4203-4251. doi: 10.1109/TIT.2005.858979
[6]	刘海强. 分布式压缩感知及其在煤矿监控信源编码中的研究与应用[D]. 徐州: 中国矿业大学, 2018. LIU Haiqiang. Distributed compressed sensing and its application in coalmine monitoring source coding[D]. Xuzhou: China University of Mining and Technology, 2018.
[7]	吴凤和, 张宁, 李元祥, 等. 基于改进高斯随机测量矩阵的切削力信号压缩感知方法[J]. 中国机械工程,2021,32(18):2231-2238. doi: 10.3969/j.issn.1004-132X.2021.18.012 WU Fenghe, ZHANG Ning, LI Yuanxiang, et al. Compressed sensing method for cutting force signals based on improved Gause random measurement matrix[J]. China Mechanical Engineering,2021,32(18):2231-2238. doi: 10.3969/j.issn.1004-132X.2021.18.012
[8]	SANJEEV S, ANUBHA G, VIMAL B. Compressed sensing based UWB receiver using signal-matched sparse measurement matrix[J]. IEEE Transactions on Vehicular Technology,2019,68(1):993-998. doi: 10.1109/TVT.2018.2881509
[9]	干红平, 张涛, 花燚, 等. 基于双极性混沌序列的托普利兹块状感知矩阵[J]. 物理学报,2021,70(3):285-296. GAN Hongping, ZHANG Tao, HUA Yi, et al. Toplitz blocky perception matrix based on bipolar chaotic sequence[J]. Acta Physica Sinica,2021,70(3):285-296.
[10]	李玉博, 张景景, 韩承桓, 等. 基于分类圆构造卷积压缩感知测量矩阵[J]. 电子与信息学报,2021,43(2):419-425. LI Yubo, ZHANG Jingjing, HAN Chenghuan, et al. Construction of convolution compressed sensing measurement matrices based on cyclotomic classes[J]. Journal of Electronics & Information Technology,2021,43(2):419-425.
[11]	LIU Haiqiang, HUA Gang, YIN Hongsheng, et al. A simple deterministic measurement matrix based on GMW pseudo-random sequence[J]. IEICE Transactions on Information and Systems,2019,E102.D(7):1296-1301. doi: 10.1587/transinf.2018EDP7324
[12]	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
[13]	NOUASRIA H, 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
[14]	CHEN S S, DONOHO D L, SAUNDERS M A. Atomic decomposition by basis pursuit[J]. SIAM Journal on Scientific Computing,1998,20(1):33-61. doi: 10.1137/S1064827596304010
[15]	EMMANUEL J C. The restricted isometry property and its implications for compressed sensing[J]. Comptes Rendus Mathematique,2008,346(8/9):589-592.
[16]	JEAN B, STEPHEN D, KEVIN F et al. Explicit constructions of RIP matrices and related problems[J]. Duke Mathematical Journal,2011,159(1):145-185.
[17]	EDELMAN A, STRANG G. Pascal matrices[J]. American Mathematical Monthly,2004,111(3):189-197. doi: 10.1080/00029890.2004.11920065
[18]	赵瑞珍, 王若乾, 张凤珍, 等. 分块的有序范德蒙矩阵作为压缩感知测量矩阵的研究[J]. 电子与信息学报,2015,37(6):1317-1322. ZHAO Ruizhen, WANG Ruoqian, ZHANG Fengzhen, et al. Research on the blocked ordered Vandermonde matrix used as measurement matrix for compressed sensing[J]. Journal of Electronics & Information Technology,2015,37(6):1317-1322.
[19]	ZHAO Ruizhen , LI Hao, QIN Zhou, et al. A new construction method for generalized Hadamard matrix in compressive sensing[C]//Proceedings of the 2011 Cross-Strait Conference on Information Science and Technology, Danshui, 2011: 309-313.
[20]	MARCO F D, SHRIRAM S, DROR B, et al. Distributed compressed sensing of jointly sparse signals[C]// Proceedings of Asilomar Conference on Signals, Systems and Computers, CA, 2005: 1537-1541.