DEVELOPMENT OF AN EFFICIENT DIFFRACTION TOMOGRAPHY TECHNIQUE WITH FAST-CONVERGENCE AND HIGH-RESOLUTION PROPERTIES APPLIED TO IMAGING OF UNDERGROUND OBJECTS

1.利用改进的Marquardt方法，研究了井间均匀矩形物体的成像问题。数值结果证明，无论接收电场的极化如何，迭代方案都能提供高质量的快速收敛性重构。进一步研究了自由空间中非均匀立方物体的逆散射。从数值结果可以看出，即使在散射场数据存在测量误差的情况下，也可以成功地重建物体的介电常数。在圆柱体电磁散射中，将物体的介电常数曲线进行小波级数展开，得到散射场。结果表明，与传统的矩量法相比，该方法可大大减少存储空间和计算时间。其次，我们用时域有限差分法处理脉冲波在两层圆柱体中的散射。数值计算结果证实，通过散射响应可以估计出物体的内部结构和介质参数。本文研究了用时域有限差分法重建两层和四层介质的介电常数。采用修正的拟牛顿法和小波展开，推导出一种迭代算法。数值计算结果表明，该方法可以获得快速收敛的高分辨率介电常数图像。该算法也适用于介质圆柱的成像。数值算例表明，我们可以成功地估计出目标的位置和介电常数。澄清物体的性质与散射场波形之间的关系是必要的。此外，利用真实数据进行图像重建是非常重要的。这些都是今后工作的主题。

1.The problem of imaging a homogeneous rectangular object in cross-well geometry is considered using the revised Marquardt method. Numerical results prove that the iterative scheme provides high-quality reconstructions with fast cnvergence property regardless of the polarization of the received electric field. Furthermore we investigate the inverse scattering of an inhomogeneous cubic object, which is located in free space. It is seen from the numerical results that the object's permittivity can be successfully reconstructed even in the presence of measurement error in the scattered field data.2.In the electromagnetic scattering by a circular cylinder, we expand the permittivity profile of the object in a wavelet series to obtain the scattered field. It is shown that the memory storage and the computation time can be cosiderably reduced in comparison with the conventional moment method. Next, we deal with the scattering of a pulsed wave by a two-layred cylinder using the FDTD method. Numerical results confirm the we can esimate the inner structure and the medium parameter of the object from the scattering response.3.We study the reconstructinon of the permittivity of two-and four-layred media using the FDTD method. An iterative algorithm is derived employing the revised quasi-Newton method and wavelet expansion. It is concluded from the numerical results that we can obtain the fast-convergence and high-resolution image of the permittivity. This algorithm is also applied to imaging of a dielectric circular cylinder. Numerical examples demonstrate that we can successfully estimate the position and the permittivity of the object.It is neccessary to clarify the relationship between the object's properties and the waveform of the scattered field. Furthermore image reconstruction using real data is very important. These are the topics for future work.