Research On Polarimetric Inverse Scattering Through Enforcing Sparsity

It is an important inverse scattering problem to retrieve geometrical structure parameters of targets from the measurements of the eletromagnetic scattered responses, based on the dependence of target scattered responses on target geometrical structures, radar frequency, aspect angle and polarization. This problem is non-linear and ill-posed. Generally, the low-dimensional approximation of the problem model as well as the discretization of the parameters can transform ill-posed problems to the well-posed ones, and both increasing the dimensionalities and reducing the discrete intervals will improve the modeling accuracy and increase the solving difficulty. The primary purpose of the studies in this thesis is to improve the modeling accuracy and overcome the ill-posedness.The ideal point scattering model has only two degrees of freedom so that it has been the most intensively used parametric model. Image reconstruction is essentially to solve the inverse scattering problem through discretizing the parameters of this model. Particularly, both super-resolution- and sparse representation-based imaging methods create redundant dictionary matrices with discrete values of the parameters, and improve the imaging qualities by introducing prior information; whereas, the super-linear computation and the inherent grid error make them inapplicable to the problems with relatively large scales. Thus, this thesis develops the updated dictionary matrix-based p-norm sparse representation method to eliminate the grid error, and proposes the extrapolationbased filtering strategy for sub-band decomposition to decrease the computation complexity.The ideal point scattering model neglects the frequency and aspect dependences that are both the important information closely related to target local structures. The attributed scattering model, proposed from the geometrical theory of diffraction, introduces the frequency and aspect dependences to improve the modeling accuracy. However, its drawbacks consists of, the inconsistency of the aspect dependence function with canonical scattering models, the deficiency in representing the scattering response for arc-like scatterers, and the disregard of the existence of shadowing and mitigating effects etc. To improve the modeling accuracy, this thesis proposes the improved attributed scattering model by modifying the aspect dependence function, adding the dependence on the orientation angle, introducing the migrating displacement factor and the window function.The improved model mathematically unifies the scattered model of all six canonical scatterers, including sphere, top-hat, cylinder, dihedral, trihedral and rectangular plate. The representation ability of the proposed model has been verified by the experimental results.Comparatively, the improved attributed scattering model has relatively many degrees of freedom, and it means that the dictionary matrix-based inverse scattering methods will encounter unacceptable computational burden. Thus, this thesis utilizes the extended complex version of the real-valued incremental sparse Bayesian learning method to solve the inverse scattering problem. This method directly optimizes continous parameters with derivatives, which can not only avoid the excessive computation and the grid error introduced by the dictionary matrices, but also efficiently promote the sparsity and the accuracy of the solution. The inverse scattering experiment of the target with complicated shapes has demonstrated the effectiveness of the proposed method.Based on the abovementioned works, this thesis proposes an extended method from the basic multi-task sparse Bayesian learning method for the polarimetric inverse scattering problem. The original prior assumption is redesigned to avoid information-sharing across unrelated tasks. In addition, this thesis also proposes the generalized iterative adaptive algorithm and the matrix filtering-introduced incremental sparse Bayesian learning algorithm for the compressed sensing inverse scattering problem. The inverse scattering experiments have verified the performance of these methods. Further researches will focus on bi-static polarimetric inverse scattering and three-dimensional inverse scattering problems, etc.