The Inversion Algorithms For Large Sized 3D Buried Objects

The electromagnetic inverse scattering methods have been developed rapidly since the 1980s, which have been widely used in sensing and remote sensing applications. However, it is a rather difficult task for the inversion of buried objects. Generally, the inverse scattering theory can roughly be categorized into linear inverse scattering theory and nonlinear inverse scattering theory. The purpose of this thesis is to find a fast algorithm for the inversion of large-scale structures buried under the ground. The main contributions of the thesis are listed as follows.1. The lower and upper decomposition (LUD) method with conventional Tikhonov regularization and modified Tikhonov regularization has been used to solve small-sized inversion problems. Numerical experiments have shown that the modified Tikhonov regularization provides a better image resolution than the conventional regularization. Theoretically, the Born approximation is valid for weak scatterers. This has been demonstrated by changing the contrast between the object and the background.2. A fast algorithm for the inversion of large-size problems has been proposed, where the conjugate- gradient (CG) method is used to solve the large matrix equation. Considering the fact that the transmitter location and receiver location have a simple relation in a VETEM system, we can get a 2D convolution from the relationship of the object function and the scattered field, which can be performed efficiently through FFT. The numerical examples involving 16,384 unknowns are given to demonstrate the efficiency of new algorithm.3. The resolution and super resolution of 3D imaging for half-space problems have been discussed. The analytical study shows that the image resolution for inversion has been limited to 0.1768 wavelength using the diffraction tomography (DT) algorithm when the measurement domain is located in the near-field. The numerical study shows that the resolution of image is less than 0.033 wavelength in the VETEM system using the Born approximation method.