探地雷达线性逆散射成像算法研究
摘要
探地雷达成像是最直接和最有效的探地雷达目标检测与识别技术,探地雷达成像方法一直是探地雷达信号处理方法的研究热点。目前,偏移成像及合成孔径成像等方法较成熟,但均不能重建地下目标物体的电性参数,从而不能对目标物体进行分类识别。逆散射成像能重建地下目标物体的电性参数,但逆散射成像是个非线性问题,而非线性逆散射成像算法计算量巨大,难以适应实际应用。因此研究计算量小的线性逆散射成像算法具有非常重要的实用价值。本论文针对近似无损和有损介质,并考虑到探地雷达应用中一些实际因素,研究并实现了线性逆散射成像算法,使之达到能够在现场进行处理的程度。
首先,研究了基于探地雷达数值模拟软件GprMax的正演模拟相关技术,包括激励源、离散步长及吸收边界条件等的选取原则;通过对多个模型的散射数据进行模拟,分析了影响散射数据质量的因素,也为后面逆散射成像算法提供了所需要的散射数据。
其次,根据衍射层析成像理论,并考虑到空气和土壤分界面的情况,提出了一种无损或近似无损介质的三维探地雷达线性逆散射成像算法。在此基础上,从目标函数的空间谱域角度分析了探地雷达工作频率及水平测线对算法的影响,并对算法频率步长的选取进行了优化,使得在保证算法成像效果的同时,最大限度地避免对冗余数据的采集和处理,从而提高了算法计算效率,节约了大量数据采集时间。对仿真数据和实测数据的成像例子表明该算法能对目标物体进行快速且准确的重建,且取优化频率步长时计算效率更高。
最后,基于一阶born近似、并矢格林函数及奇异值分解技术,提出了一种有损介质的线性逆散射成像算法。该算法考虑到了天线辐射类型和空气土壤界面的情况,使得算法更符合实际应用环境;采用渐进近似方法对描述目标函数与频域散射数据关系的线性算子进行近似,避免了离散线性算子时对多个积分进行计算,使得离散步骤更简单,且大大减少了计算量,进一步提高了算法的计算效率。对仿真数据和实测数据的成像结果表明该算法能对目标物体进行快速且较好的重建。
Ground penetrating radar (GPR) is a nondestructive testing technique of buried targets developed in these decades. It has been widely used in many fields such as demining, archaeology and civil engineering. The imaging technique of ground penetrating radar is the most promising data processing technique for GPR application. So far, the migration imaging algorithms are more mature and they can reconstruct the location and shape of buried object accurately, but they can not reconstruct the dielectric and conductive properties of the buried objects. Both non-linear and linear inverse scattering algorithms can reconstruct the dielectric and conductive properties of the buried objects. But non-linear methods have heavy computational burden, so they are not suitable for engineering application. Thus, it is highly desirable and valuable to do research on linear inverse scattering imaging algorithms. The research work in this thesis aims to improve the performance of GPR linear inverse scattering algorithms for lossless and lossy soil respectively.
Firstly, the forward modelling is investigated based on GprMax which is a numerical modelling tool of GPR. The main work of this part includes the following three aspects: The research on excitation source, discretization steps and absorbing boundary conditions, which are techniques relating to the forward modelling based on GprMax; The research on the input and output file of GprMax; The analysis of the factors that influence the quality of scattered field data according to the basic theory and the numerical modelling results of serveral models, the purpose of which is to get high-quality scattered field data by selecting the right parameters and methods when collecting or modelling the data.
Secondly, a three-dimensional linear GPR inverse scattering imaging algorithm which takes the planar air-soil interface into account is derived for lossless soil. The first Born Approximation and the dyadic Green function for a two-layer medium are used to get a linear forward model, the forward model is then inverted using Fourier transform. Basing on the above work, the influences of the frequecy diversity and observation line are analyzed with reference to the spatial spectral of the unknown object function, and then an optimal frequency step for the algorithm is determined, which can ensure nonredundancy in the data, thereby enhancing the computational effectiveness of the algorithm and economizing a large amount of time for collecting data. Numercial examples show that the algorithm can reconstruct the buried object rapidly and accurately.
Finally, a three-dimensional linear GPR inverse scattering imaging algorithm based on the first Born Approximation, the dyadic Green function for a two-layer medium and singular value decomposition (SVD) is derived for lossy soil. The algorithm takes the radiation patterns and the planar air-soil interface into account, which makes it accord with the practical application of GPR better. Meanwhile, the asymptotic approximation is used to achieve the linear relationship between the unknown object function and the spectrum of the scattered field, which makes it avoid evaluating several integrals when discretizing the linear operator, thereby making it much easier to implement the discretizing step and reducing the computational burden, thus enhancing the computational effectiveness of the algorithm. Numerical examples show that the algorithm can reconstruct the buried object well.
首先,研究了基于探地雷达数值模拟软件GprMax的正演模拟相关技术,包括激励源、离散步长及吸收边界条件等的选取原则;通过对多个模型的散射数据进行模拟,分析了影响散射数据质量的因素,也为后面逆散射成像算法提供了所需要的散射数据。
其次,根据衍射层析成像理论,并考虑到空气和土壤分界面的情况,提出了一种无损或近似无损介质的三维探地雷达线性逆散射成像算法。在此基础上,从目标函数的空间谱域角度分析了探地雷达工作频率及水平测线对算法的影响,并对算法频率步长的选取进行了优化,使得在保证算法成像效果的同时,最大限度地避免对冗余数据的采集和处理,从而提高了算法计算效率,节约了大量数据采集时间。对仿真数据和实测数据的成像例子表明该算法能对目标物体进行快速且准确的重建,且取优化频率步长时计算效率更高。
最后,基于一阶born近似、并矢格林函数及奇异值分解技术,提出了一种有损介质的线性逆散射成像算法。该算法考虑到了天线辐射类型和空气土壤界面的情况,使得算法更符合实际应用环境;采用渐进近似方法对描述目标函数与频域散射数据关系的线性算子进行近似,避免了离散线性算子时对多个积分进行计算,使得离散步骤更简单,且大大减少了计算量,进一步提高了算法的计算效率。对仿真数据和实测数据的成像结果表明该算法能对目标物体进行快速且较好的重建。
Ground penetrating radar (GPR) is a nondestructive testing technique of buried targets developed in these decades. It has been widely used in many fields such as demining, archaeology and civil engineering. The imaging technique of ground penetrating radar is the most promising data processing technique for GPR application. So far, the migration imaging algorithms are more mature and they can reconstruct the location and shape of buried object accurately, but they can not reconstruct the dielectric and conductive properties of the buried objects. Both non-linear and linear inverse scattering algorithms can reconstruct the dielectric and conductive properties of the buried objects. But non-linear methods have heavy computational burden, so they are not suitable for engineering application. Thus, it is highly desirable and valuable to do research on linear inverse scattering imaging algorithms. The research work in this thesis aims to improve the performance of GPR linear inverse scattering algorithms for lossless and lossy soil respectively.
Firstly, the forward modelling is investigated based on GprMax which is a numerical modelling tool of GPR. The main work of this part includes the following three aspects: The research on excitation source, discretization steps and absorbing boundary conditions, which are techniques relating to the forward modelling based on GprMax; The research on the input and output file of GprMax; The analysis of the factors that influence the quality of scattered field data according to the basic theory and the numerical modelling results of serveral models, the purpose of which is to get high-quality scattered field data by selecting the right parameters and methods when collecting or modelling the data.
Secondly, a three-dimensional linear GPR inverse scattering imaging algorithm which takes the planar air-soil interface into account is derived for lossless soil. The first Born Approximation and the dyadic Green function for a two-layer medium are used to get a linear forward model, the forward model is then inverted using Fourier transform. Basing on the above work, the influences of the frequecy diversity and observation line are analyzed with reference to the spatial spectral of the unknown object function, and then an optimal frequency step for the algorithm is determined, which can ensure nonredundancy in the data, thereby enhancing the computational effectiveness of the algorithm and economizing a large amount of time for collecting data. Numercial examples show that the algorithm can reconstruct the buried object rapidly and accurately.
Finally, a three-dimensional linear GPR inverse scattering imaging algorithm based on the first Born Approximation, the dyadic Green function for a two-layer medium and singular value decomposition (SVD) is derived for lossy soil. The algorithm takes the radiation patterns and the planar air-soil interface into account, which makes it accord with the practical application of GPR better. Meanwhile, the asymptotic approximation is used to achieve the linear relationship between the unknown object function and the spectrum of the scattered field, which makes it avoid evaluating several integrals when discretizing the linear operator, thereby making it much easier to implement the discretizing step and reducing the computational burden, thus enhancing the computational effectiveness of the algorithm. Numerical examples show that the algorithm can reconstruct the buried object well.
引文
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[3]吴宝杰.探地雷达二维正演模拟及其工程实例[D].浙江:浙江大学,2007.
[4]李大心.探地雷达方法与应用[M].北京:地质出版社,1994.
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[6]李想堂,王端宜,张肖宁.探地雷达技术的回顾与展望[J].无损检测,2006,28(9):479-484.
[7]黄玲.基于VNA的探地雷达系统开发[D].吉林:吉林大学,2007.
[8]http://www.pt-cn.com/application.
[9]Brian Karlsen,Jan Larsen,Kai B.Jakobsen,et al.Comparison of PCA and ICA based clutter reduction in GPR systems for anti-personal landmine detection[J].Proceedings of the 11th IEEE Signal Processing Workshop on Statistical Signal Processing,2001,146-149.
[10]Mark P.Kolba,Ismail I.Jouny.Clutter suppression and feature extraction for landmine detection using ground penetrating radar[J].IEEE International Symposium on Antennas and Propagation Society,2003,2:203-206.
[11]Andria van der Merwe,Inder J.Gupta.A Novel Signal Processing Technique for Clutter Reduction in GPR Measurements of Small,Shallow Land Mines[J].IEEE Transactions On Geoscience And Remote Sensing,2000,38(6):2627-2637.
[12]Hakan Brunzell.Detection of Shallowly Buried Objects Using lmpulse Radar[J].IEEE Transactions On Geoscience And Remote Sensing,1999,37(2):875-886.
[13]Guifu Zhang,Leung Tsang,Yasuo Kuga.Studies of the Angular Correlation Function of Scattering by Random Rough Surfaces with and without a Buried Object[J].IEEE Transactions On Geoscience And Remote Sensing,1997,35(2):444-453.
[14]Traian Dogaru,Lawrence Carin.Time-Domain Sensing of Targets Buried Under a Rough Air-Ground Interface[J].IEEE Transactions On antennas and propagation,1998,46(3):360-372.
[15]粟毅,黄春琳,需文太.探地雷达理论与应用[M].北京:科学出版社,2006.
[16]Plumb R G,Leuschen C.A class of migration algorithms for ground-penetrating radar data [C].Geoscience And Remote Sensing Symposium,1999.IGARSS' 99 Proceeding.NewYork:IEEE,1999,2519-2521.
[17]Song Jiayu,Liu Qinghuo,Torrione Pete,et al.Two-dimensional and three-dimensional NUFFT migration method for landmine detection using ground-penetrating radar[J].IEEE Transaction On Geoscience And Remote Sensing,2006,44(6):1462-1469.
[18]Wu Renbiao,Gu Kunlong,Li Jian,et al.Propagation velocity uncertainty on GPR SAR processing[J].IEEE Transaction On Aerospace And Electronic Systems,2003,39(3):849-861.
[19]张明新.探地需达三维成像算法研究[D].天津:中国民用航空学院,2003.
[20]张立国,孔令讲,周正欧.浅地层探地雷达合成孔径处理的一种快速算法[J].电子与信息学报,2004,26(10):1645-1649.
[21] 张春城,周正欧.浅地层探地雷达自动目标检测与定位研究[J].电子与信息学报, 2005,27(7):1065-1068.
[22] A.J.Patterson , J.M.Tealby, N.M.Allinsonl. Ground Penetrating Radar Migration with Uncertain Parameters [J]. Geoscience and Remote Sensing Symposiun, 1995, IGARSS'95, 'Quantitative Remote Sensing for Science and Applications', International, 1995, 1:27-29.
[23] Aya Sayedelahl, R.Phillip Bording, Mohamed Chouikha, et al. A study of seismic Inverse Methods for Radar Signal Processing [J]. Proceedings of the 34th Applied Imagery and Pattern Recongnition Workshop , 2005, 146-149.
[24] Nadine Joachimowicz, Christian Pichot, Jean-Paul Hugonin. Inverse Scattering: An Iterative Numerical Method for Electromagnetic Imaging [J]. IEEE Transactions On antennas and propagation, 1991,39(12): 1742-1752.
[25] Pawan Chaturvedi, Richard G. Plumb. Electromagnetic Imaging of Underground Targets Using Constrained Optimization [J]. IEEE Transactions On Geoscience And Remote Sensing, 1995, 33(3): 551-561.
[26] Tommaso Isernia, Vito Pascazio, Rocco Pierri. A Nonlinear Estimation Method in Tomographic Imaging [J]. IEEE Transactions On Geoscience And Remote Sensing, 1997, 35(4): 910-923.
[27] Aria Abubaker, Peter M. van den Berg. Three-Dimensional Inverse Scattering Applied to Cross-Well Induction Sensors [J]. IEEE Transactions On Geoscience And Remote Sensing, 2000,38(4): 1669-1681.
[28] Tie Jun Cui, Weng Cho Chew, Alaeddin A. Aydiner, et al. Inverse Scattering of Two-Dimensional Dielectric Objects Buried in a Lossy Earth Using the Distorted Born Iterative Method [J]. IEEE Transactions On Geoscience And Remote Sensing, 2001, 39(2): 339-346.
[29] Zhong Qing Zhang, Qing Huo Liu. Two Nonlinear Inverse Methods for Electromagnetic Induction Measurements [J]. IEEE Transactions On Geoscience And Remote Sensing, 2001, 39(6): 1331-1339.
[30] Ilaria Catapano, Lorenzo Crocco, Raffaele Persico, et al. Linear and Nonlinear Microwave Tomography Approaches for Subsurface Prospecting: Validation on real Data [J]. IEEE Antennas and wireless propagation, 2006, 5: 49-53.
[31] John E. Molyneux, Alan J.Witten. Diffraction tomographic imaging in a monostatic measurement geometry [J]. IEEE Transactions On Geoscience And Remote Sensing, 1993. 31:507-511.
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