探地雷达成像技术研究
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摘要
探地雷达(GPR)是一种利用电磁波对地下区域进行无损探测的装置，它根据电磁波在地下介质不连续处产生的反射和散射等现象来反演地下场景和目标的信息，实现对地下目标的检测和识别。通过GPR成像技术，可以对地下目标的信息进行直观显示，便于人们对地下目标的解译。由于GPR成像技术具有非破坏性、高分辨率、探测速度快、操作方便、安全性高等优点，其在军事和民用领域中得到广泛的应用，具有很好的发展前景。与传统雷达成像不同，GPR成像场景较为特殊，具体表现为GPR工作于近场条件，且工作场景和目标特性均比较复杂。为了克服上述问题，本文分别从时域和频域成像技术、超分辨成像技术和压缩感知成像技术等方面对GPR成像进行了深入研究。
首先研究了时域的反向投影(BP)成像算法。GPR成像场景中分层介质的存在使得电磁波发生折射现象，在成像时必须对介质分界面上折射点的位置进行求解，然而该求解过程计算量大、复杂性高。本文从改进近似求解方法和降低算法冗余性两个角度出发提出了优化的折射点求解方法，极大地提高了算法的精度和计算效率。研究发现标准BP算法具有成像速度慢和成像结果干扰严重的缺点，针对前者本文提出了FBP算法，通过子孔径划分和极坐标处理降低了算法复杂度，提高了计算速度，且便于并行实时计算；针对后者本文提出了CBP算法，通过在数据叠加前引入互相关操作，对成像结果中的旁瓣和杂波具有良好的抑制效果。
其次研究了频域的距离偏移(RM)成像算法。当使用经典RM算法进行GPR成像时，成像结果中目标不能正确聚焦，该问题的原因是在GPR成像的分层介质模型下波场传播的连续性被破坏。本文在建立分层介质场景中的爆炸源模型基础上，提出了适合于分层介质成像的LRM算法。LRM算法通过将波场的非连续传播过程分解为多个局部连续传播过程，不仅克服了经典RM算法无法有效聚焦的问题，还保持了RM算法计算速度快的特点。
在对传统的时域和频域算法研究之后，本文研究了基于谱估计理论的超分辨成像算法。传统算法受信号有限带宽的限制，成像结果中存在大量的旁瓣和杂波等干扰。而现代谱估计领域中的鲁棒Capon波束形成(RCB)理论和正弦幅度相位估计(APES)理论具有分辨率高、干扰抑制效果好、鲁棒性强的优点，本文分别根据这两种理论提出了RCB成像算法和APES成像算法，得到了高分辨率低干扰的成像结果。但是这两种算法受高维矩阵运算的限制，其计算效率不高。本文通过在子图像域进行预波束形成处理进而构造低维波束矢量，实现了协方差矩阵维度的降低，从而提出了DR-RCB算法和DR-APES算法。这两种算法在保持前两种算法成像质量的同时，显著地提高了计算速度。
最后研究了基于压缩感知(CS)理论的成像算法。由于CS理论突破了传统数据采集中Nyquist采样率的限制，可以从少量的数据中精确恢复出原始的稀疏信号，极大地简化了数据采集、编码解码和数据传输的工作。结合GPR成像的实际场景中目标空间满足稀疏性要求，本文提出了CS成像算法，并以聚焦度、成像误差等为指标系统分析了测量矩阵维度、信噪比、数据损失率和目标密集度等因素对成像结果的影响，证实了CS算法具有优良的成像性能和干扰抑制能力，以及较强的鲁棒性。
GPR (Ground Penetrating Radar) uses electromagnetic waves to probe theunderground region nondestructively. GPR can be used to reconstruct the information ofunderground scenes and targets by the reflection and scattering phenomena stimulatedby the discontinuity of the underground medium, as well as underground targetdetection and recognition. The information of underground targets can be displayeddirectly by GPR imaging technique, which is also convenient for the interpretation ofunderground targets. Because of the advantages such as nondestructive, high resolution,fast probing and high safety, GPR has been widely used both in military and civilianapplications, and it possesses great developing potential. Unlike traditional radarimaging, the observing scene of GPR is relatively special because GPR works in nearfield conditions and the characteristics of both the imaging scene and targets are rathercomplicated. In order to solve these problems, an in-depth and detailed research hasbeen carried out in this thesis in the aspects of time domain imaging technique,frequency domain imaging technique, super resolution imaging technique andcompressive sensing imaging technique.
First of all, the BP (Back Projection) algorithm in time domain is investigated. Thelayered mediums in the scene of GPR imaging cause the refraction phenomenon ofelectromagnetic waves on the interface between different mediums. In the procedure ofimaging the calculation of the coordinates of the refraction point must be performed,which has a huge workload and high complexity. An optimized method for solving theposition of refraction point is proposed by improving the approximation method anddecresing the redundancy. The accuracy and effectiveness of the imaging algorithm areboth improved. It turns out that standard BP algorithm suffers from low calcualtionspeed and severe interference in imaging results. In order to accelerate the speed of BPalgorithm, a novel FBP (Fast Back Projection) algorithm is proposed by subaperturedivision and processing in polar coordinate. The FBP algorithm is fast than the originalalgorithm, and it is convenient to perform parallel or real time calculation. In order tosuppress the interference in imaging results, a novel CBP (Cross-correlation BackProjection) algorithm is proposed by using the cross-correlation information of thereceiving data. The CBP algorithm can receive better performance of artifactssuppression.
Then the RM (Range Migration) algorithm in frequency domain is investigated.The imaging results of classic RM algorithm will not focus correctly because in layeredmediums the the discontinuity in space results in the discontinuity of the wavefield.Base on the exploding source model for layered mediums, a novel LRM (LayeredRange Migration) algorithm is proposed. The LRM algorithm divides the discontinuous propagation of the wavefield into several local continuous propagation. Not only can theLRM algorithm focus effectively, but also it maintains the computational efficiency ofclassic RM algorithm.
After the studies on traditional imaging algorithms in time and frequency domain,the super resolution imaging algorithms based on the theory of spectral estimation areinvestigated. Subjected to the constraint on limit bandwidth, there are lots of artifactslike sidelobes and clutters in the imaging results. Considering that in the field of modernspectral estimation the theory of both RCB (Robust Capon Beamforming) and APES(Amplitude and Phase Estimation of a Sinusoid) have the advantage of high resolution,good artifacts suppression and high robustness, the RCB and APES algorithms areproposed and better imaging results with high resolution and artifacts suppression areachieved. However, the proposed algorithms are computationally ineffective because ofthe calculation of high dimensional matrixes. More efficient algorithms called DR-RCB(Dimensionality Reduced RCB) and DR-APES (Dimensionality Reduced APES) areproposed by pre-beamforming in the sub-image domain and constructing lowdimensional beamforming vectors, that is equivalent to reducing the dimensionality ofcovariance matrix. The DR-RCB and DR-APES algorithms accelerate the RCB andAPES algorithms dramatically, meanwhile, they preserve the high imaging quality.
In the end, the CS (Compressive Sensing) algorithm is investigated. The CS theory,which can reconstruct the original sparse signal with very few measurements, breakthrough the traditional framework of Nyquist sampling theory. The relational work suchas data acquisition, coding, decoding and data transmission could be simplified.Combining with the fact that in practical GPR imaging scene the targets are sparsecomparing to the background, the CS imaging algorithm is proposed. The effects ofparameters like the dimension of measurement matrix, SNR (Signal to Noise Ratio),data lacking ratio, compactness of targets on imaging results are systematic analysed. Ithas been proved that the CS algorithm has remarkable ability on imaging performance,artifacts suppression and robustness.
首先研究了时域的反向投影(BP)成像算法。GPR成像场景中分层介质的存在使得电磁波发生折射现象，在成像时必须对介质分界面上折射点的位置进行求解，然而该求解过程计算量大、复杂性高。本文从改进近似求解方法和降低算法冗余性两个角度出发提出了优化的折射点求解方法，极大地提高了算法的精度和计算效率。研究发现标准BP算法具有成像速度慢和成像结果干扰严重的缺点，针对前者本文提出了FBP算法，通过子孔径划分和极坐标处理降低了算法复杂度，提高了计算速度，且便于并行实时计算；针对后者本文提出了CBP算法，通过在数据叠加前引入互相关操作，对成像结果中的旁瓣和杂波具有良好的抑制效果。
其次研究了频域的距离偏移(RM)成像算法。当使用经典RM算法进行GPR成像时，成像结果中目标不能正确聚焦，该问题的原因是在GPR成像的分层介质模型下波场传播的连续性被破坏。本文在建立分层介质场景中的爆炸源模型基础上，提出了适合于分层介质成像的LRM算法。LRM算法通过将波场的非连续传播过程分解为多个局部连续传播过程，不仅克服了经典RM算法无法有效聚焦的问题，还保持了RM算法计算速度快的特点。
在对传统的时域和频域算法研究之后，本文研究了基于谱估计理论的超分辨成像算法。传统算法受信号有限带宽的限制，成像结果中存在大量的旁瓣和杂波等干扰。而现代谱估计领域中的鲁棒Capon波束形成(RCB)理论和正弦幅度相位估计(APES)理论具有分辨率高、干扰抑制效果好、鲁棒性强的优点，本文分别根据这两种理论提出了RCB成像算法和APES成像算法，得到了高分辨率低干扰的成像结果。但是这两种算法受高维矩阵运算的限制，其计算效率不高。本文通过在子图像域进行预波束形成处理进而构造低维波束矢量，实现了协方差矩阵维度的降低，从而提出了DR-RCB算法和DR-APES算法。这两种算法在保持前两种算法成像质量的同时，显著地提高了计算速度。
最后研究了基于压缩感知(CS)理论的成像算法。由于CS理论突破了传统数据采集中Nyquist采样率的限制，可以从少量的数据中精确恢复出原始的稀疏信号，极大地简化了数据采集、编码解码和数据传输的工作。结合GPR成像的实际场景中目标空间满足稀疏性要求，本文提出了CS成像算法，并以聚焦度、成像误差等为指标系统分析了测量矩阵维度、信噪比、数据损失率和目标密集度等因素对成像结果的影响，证实了CS算法具有优良的成像性能和干扰抑制能力，以及较强的鲁棒性。
GPR (Ground Penetrating Radar) uses electromagnetic waves to probe theunderground region nondestructively. GPR can be used to reconstruct the information ofunderground scenes and targets by the reflection and scattering phenomena stimulatedby the discontinuity of the underground medium, as well as underground targetdetection and recognition. The information of underground targets can be displayeddirectly by GPR imaging technique, which is also convenient for the interpretation ofunderground targets. Because of the advantages such as nondestructive, high resolution,fast probing and high safety, GPR has been widely used both in military and civilianapplications, and it possesses great developing potential. Unlike traditional radarimaging, the observing scene of GPR is relatively special because GPR works in nearfield conditions and the characteristics of both the imaging scene and targets are rathercomplicated. In order to solve these problems, an in-depth and detailed research hasbeen carried out in this thesis in the aspects of time domain imaging technique,frequency domain imaging technique, super resolution imaging technique andcompressive sensing imaging technique.
First of all, the BP (Back Projection) algorithm in time domain is investigated. Thelayered mediums in the scene of GPR imaging cause the refraction phenomenon ofelectromagnetic waves on the interface between different mediums. In the procedure ofimaging the calculation of the coordinates of the refraction point must be performed,which has a huge workload and high complexity. An optimized method for solving theposition of refraction point is proposed by improving the approximation method anddecresing the redundancy. The accuracy and effectiveness of the imaging algorithm areboth improved. It turns out that standard BP algorithm suffers from low calcualtionspeed and severe interference in imaging results. In order to accelerate the speed of BPalgorithm, a novel FBP (Fast Back Projection) algorithm is proposed by subaperturedivision and processing in polar coordinate. The FBP algorithm is fast than the originalalgorithm, and it is convenient to perform parallel or real time calculation. In order tosuppress the interference in imaging results, a novel CBP (Cross-correlation BackProjection) algorithm is proposed by using the cross-correlation information of thereceiving data. The CBP algorithm can receive better performance of artifactssuppression.
Then the RM (Range Migration) algorithm in frequency domain is investigated.The imaging results of classic RM algorithm will not focus correctly because in layeredmediums the the discontinuity in space results in the discontinuity of the wavefield.Base on the exploding source model for layered mediums, a novel LRM (LayeredRange Migration) algorithm is proposed. The LRM algorithm divides the discontinuous propagation of the wavefield into several local continuous propagation. Not only can theLRM algorithm focus effectively, but also it maintains the computational efficiency ofclassic RM algorithm.
After the studies on traditional imaging algorithms in time and frequency domain,the super resolution imaging algorithms based on the theory of spectral estimation areinvestigated. Subjected to the constraint on limit bandwidth, there are lots of artifactslike sidelobes and clutters in the imaging results. Considering that in the field of modernspectral estimation the theory of both RCB (Robust Capon Beamforming) and APES(Amplitude and Phase Estimation of a Sinusoid) have the advantage of high resolution,good artifacts suppression and high robustness, the RCB and APES algorithms areproposed and better imaging results with high resolution and artifacts suppression areachieved. However, the proposed algorithms are computationally ineffective because ofthe calculation of high dimensional matrixes. More efficient algorithms called DR-RCB(Dimensionality Reduced RCB) and DR-APES (Dimensionality Reduced APES) areproposed by pre-beamforming in the sub-image domain and constructing lowdimensional beamforming vectors, that is equivalent to reducing the dimensionality ofcovariance matrix. The DR-RCB and DR-APES algorithms accelerate the RCB andAPES algorithms dramatically, meanwhile, they preserve the high imaging quality.
In the end, the CS (Compressive Sensing) algorithm is investigated. The CS theory,which can reconstruct the original sparse signal with very few measurements, breakthrough the traditional framework of Nyquist sampling theory. The relational work suchas data acquisition, coding, decoding and data transmission could be simplified.Combining with the fact that in practical GPR imaging scene the targets are sparsecomparing to the background, the CS imaging algorithm is proposed. The effects ofparameters like the dimension of measurement matrix, SNR (Signal to Noise Ratio),data lacking ratio, compactness of targets on imaging results are systematic analysed. Ithas been proved that the CS algorithm has remarkable ability on imaging performance,artifacts suppression and robustness.
引文
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