基于TSOM算法的电磁波逆散射成像研究
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摘要
逆问题研究,顾名思义,是一种由果索因的研究。电磁波逆散射成像是一种重要的无损无接触式检测方法。近年来,电磁检测方法已经广泛应用在定位、微波遥感、地球物理探测、无损检测、生物医学成像等多种领域。电磁逆散射问题是应用被测物体对入射波的散射,通过测量物体外部的散射场或其远场模式,反演或重构物体的物理、几何特性,包括其位置、尺寸、数量、边界和电磁参数分布等。
本文研究的主要内容为电磁场的逆散射成像。通过分析逆散射成像的基本模型,我们介绍了一种基于子空间的优化算法(Subspace-based Optimization Method, SOM)。SOM算法从电流在空间映射的频谱分析的角度上着手,将感应电流区分为确定性电流与模糊性电流。确定性电流可通过计算获得,而易受噪声干扰的模糊性电流则通过迭代优化获得。这样不仅提高了算法的抗噪声性能,又降低了优化的求解空间,提高了算法的稳定性。并且,通过在矩阵运算中引入FFT的计算方法,可大大提高算法的运行效率。而对感应电流在目标区域自身内部的映射函数的分析,TSOM (Two-fold SOM)算法可进一步压缩求解的空间。通过对散射体的实例分析,与其它的梯度优化算法相比,SOM算法具有快速收敛和抗噪声两个显著的优点。
然后,我们探讨了与金属有关的逆散射成像问题。金属散射体在TE波入射下的逆散射成像问题一直是计算电磁学领域的难题。应用TSOM算法,我们实现了对任意位置,任意数量,任意形状的金属物体的逆散射成像。而且,不需要借助任何散射体的先验信息。并且应用实验数据,验证了TSOM算法的准确性和实用性。进一步,通过在探测区域外部引入一已知的金属圆柱体,探讨了多重散射效应对逆散射成像的影响。我们发现反演结果的质量,包括目标函数和介电常数反演的误差,与金属的尺寸或其与散射体间距之间并不存在线性变化的关系;值得注意的是,多重散射效应并不能保证反演结果一定得到改善。
最后我们设计了散射场测量系统,并基于实验数据实现了逆散射成像。TSOM算法可在高噪声的背景下得到良好的反演结果,非常适用于实验数据的逆散射成像。通过分析无散射体时入射场理论值与实测值的区别,对测量的散射场进行校准,可在一定程度上缓解外部散射体对散射场的干扰,包括天线间的互耦作用。通过分析一已知的二维散射体的理论散射场与实测场的区别,对其它的测量散射场进行校准,可降低由于散射体,入射天线的非理想性造成的固有误差。
Solving of the inverse problems, as the words suggest, is a study method to find the reasons with results. The inverse scattering problems of electromagnetic is an important non-touch and non-destructive detection technique. Recently, it has been widely used in many fields, including the location, the microwave remote sensing, the geographical detection, the non-destruction detec-tion, the biological imaging. In common, the inverse scattering problems of electromagnetic is to retrieve or reconstruct the unknown objects's physical and geometric information, including the location, size, quantity, boundary and distribution of permittivity, with the measured scattered field or far field outside of the unknown objects, due to the incidence to the unknown objects.
The main topic of this thesis is the inverse scattering imaging with electromagnetic wave, we analyzed the model of the inverse scattering problems, and introduced a Sub-space based Opti-mization Method (SOM). The characteristics of the SOM algorithm is the analysis of the induced current in its space spectrum. The induced current is decomposed into deterministic current and ambiguous current. The deterministic current applies to the space spectrum with high singular val-ue and is obtained by directly calculation. But the ambiguous current is very sensitive to the noise or other interference and has to be obtained by the optimization method. Thus, this method not only improved the robust against noise, but reduced the space of solution and favours the stabili-ty. Based on the FFT method in matrix calculation, we introduced a FFT-SOM algorithm, which could heavily increase the calculation efficiency. Based on the spectrum analysis of the mapping function of the induced current into the region under detection, a two-fold SOM algorithm could further reduced the space of solution. In the numerical simulations, the SOM algorithm showed fast convergence and high noise robust advantages.
Then, the inverse scattering problem of PEC scatterers were investigated. The inverse scatter-ing problems of PEC scatterers under transverse electric (TE) wave has been a difficult problem in computational electromagnetics. Applied the TSOM algorithm, we realized the reconstruction of PEC scatterers with any location, any quantities and any boundary. Moreover, the algorithm did not need any prior information of the scatterers. Then, the TSOM algorithm was further verified with the measured scattered field and obtained good reconstruction results. The influence of mul-tiple scattering effect to the SOM algorithm was discussed by introducing a known PEC circular cylinder beside the region under detection. It is seen that the reconstruction results (both the objec- tive function and relative error of permittivity) were not a monotonic function of either the radius of cylinder or the separation distance; the auxiliary cylinder is not always helpful in the inverse scattering problems.
At last,we designed a measurement system of scattered field and realized the reconstruction with experimental data. The measured data suffered from the noise and other disturbance, the TSOM algorithm was especially excellent in dealing with experimental data, due to its high robust against noise. The influence from the outside objects, including the coupling effect between the antennas, could be decreased by analyzing the difference between the theoretical incident field and the analytical incident field. And the introduce of correction method,based on the comparison between a theoretical scattered field and analytical scattered field from a known scatterer, could improve the inherent error due to the non ideality of the scatterers and incident fields in two-dimensional measurement.
本文研究的主要内容为电磁场的逆散射成像。通过分析逆散射成像的基本模型,我们介绍了一种基于子空间的优化算法(Subspace-based Optimization Method, SOM)。SOM算法从电流在空间映射的频谱分析的角度上着手,将感应电流区分为确定性电流与模糊性电流。确定性电流可通过计算获得,而易受噪声干扰的模糊性电流则通过迭代优化获得。这样不仅提高了算法的抗噪声性能,又降低了优化的求解空间,提高了算法的稳定性。并且,通过在矩阵运算中引入FFT的计算方法,可大大提高算法的运行效率。而对感应电流在目标区域自身内部的映射函数的分析,TSOM (Two-fold SOM)算法可进一步压缩求解的空间。通过对散射体的实例分析,与其它的梯度优化算法相比,SOM算法具有快速收敛和抗噪声两个显著的优点。
然后,我们探讨了与金属有关的逆散射成像问题。金属散射体在TE波入射下的逆散射成像问题一直是计算电磁学领域的难题。应用TSOM算法,我们实现了对任意位置,任意数量,任意形状的金属物体的逆散射成像。而且,不需要借助任何散射体的先验信息。并且应用实验数据,验证了TSOM算法的准确性和实用性。进一步,通过在探测区域外部引入一已知的金属圆柱体,探讨了多重散射效应对逆散射成像的影响。我们发现反演结果的质量,包括目标函数和介电常数反演的误差,与金属的尺寸或其与散射体间距之间并不存在线性变化的关系;值得注意的是,多重散射效应并不能保证反演结果一定得到改善。
最后我们设计了散射场测量系统,并基于实验数据实现了逆散射成像。TSOM算法可在高噪声的背景下得到良好的反演结果,非常适用于实验数据的逆散射成像。通过分析无散射体时入射场理论值与实测值的区别,对测量的散射场进行校准,可在一定程度上缓解外部散射体对散射场的干扰,包括天线间的互耦作用。通过分析一已知的二维散射体的理论散射场与实测场的区别,对其它的测量散射场进行校准,可降低由于散射体,入射天线的非理想性造成的固有误差。
Solving of the inverse problems, as the words suggest, is a study method to find the reasons with results. The inverse scattering problems of electromagnetic is an important non-touch and non-destructive detection technique. Recently, it has been widely used in many fields, including the location, the microwave remote sensing, the geographical detection, the non-destruction detec-tion, the biological imaging. In common, the inverse scattering problems of electromagnetic is to retrieve or reconstruct the unknown objects's physical and geometric information, including the location, size, quantity, boundary and distribution of permittivity, with the measured scattered field or far field outside of the unknown objects, due to the incidence to the unknown objects.
The main topic of this thesis is the inverse scattering imaging with electromagnetic wave, we analyzed the model of the inverse scattering problems, and introduced a Sub-space based Opti-mization Method (SOM). The characteristics of the SOM algorithm is the analysis of the induced current in its space spectrum. The induced current is decomposed into deterministic current and ambiguous current. The deterministic current applies to the space spectrum with high singular val-ue and is obtained by directly calculation. But the ambiguous current is very sensitive to the noise or other interference and has to be obtained by the optimization method. Thus, this method not only improved the robust against noise, but reduced the space of solution and favours the stabili-ty. Based on the FFT method in matrix calculation, we introduced a FFT-SOM algorithm, which could heavily increase the calculation efficiency. Based on the spectrum analysis of the mapping function of the induced current into the region under detection, a two-fold SOM algorithm could further reduced the space of solution. In the numerical simulations, the SOM algorithm showed fast convergence and high noise robust advantages.
Then, the inverse scattering problem of PEC scatterers were investigated. The inverse scatter-ing problems of PEC scatterers under transverse electric (TE) wave has been a difficult problem in computational electromagnetics. Applied the TSOM algorithm, we realized the reconstruction of PEC scatterers with any location, any quantities and any boundary. Moreover, the algorithm did not need any prior information of the scatterers. Then, the TSOM algorithm was further verified with the measured scattered field and obtained good reconstruction results. The influence of mul-tiple scattering effect to the SOM algorithm was discussed by introducing a known PEC circular cylinder beside the region under detection. It is seen that the reconstruction results (both the objec- tive function and relative error of permittivity) were not a monotonic function of either the radius of cylinder or the separation distance; the auxiliary cylinder is not always helpful in the inverse scattering problems.
At last,we designed a measurement system of scattered field and realized the reconstruction with experimental data. The measured data suffered from the noise and other disturbance, the TSOM algorithm was especially excellent in dealing with experimental data, due to its high robust against noise. The influence from the outside objects, including the coupling effect between the antennas, could be decreased by analyzing the difference between the theoretical incident field and the analytical incident field. And the introduce of correction method,based on the comparison between a theoretical scattered field and analytical scattered field from a known scatterer, could improve the inherent error due to the non ideality of the scatterers and incident fields in two-dimensional measurement.
引文
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