Linear Inverse Scattering Imaging Algorithms For Ground Penetrating Radar

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.