On the Solution of Linearized Inverse Scattering Problems in Near-Field Microwave Imaging by Operator Inversion and Matched Filtering

Microwave imaging is commonly based on the solution of linearized inverse scattering problems by matched-filtering algorithms, i.e., by applying the adjoint of the forward scattering operator to the observation data. A more rigorous approach is the explicit inversion of the forward scattering operator, which is performed in this work for quasi-monostatic imaging scenarios based on a planar plane-wave representation according to the Weyl-identity and hierarchical acceleration algorithms. The inversion is achieved by a regularized iterative linear system of equations solver, where irregular observations as well as full probe correction are supported. In the spatial image generation, low-pass filtering can be considered in order to reduce imaging artifacts. A corresponding spectral back-projection algorithm (BPA) and a spatial BPA together with improved focusing operators are also introduced, and the resulting image generation algorithms are analyzed and compared for a variety of examples, comprising both simulated and measured observation data. It is found that the inverse source solution generally performs better in terms of robustness, focusing capabilities, and image accuracy compared with the adjoint imaging algorithms either operating in the spatial or spectral domain. This is especially demonstrated in the context of irregular sampling grids with nonideal or truncated observation data and by evaluating all reconstruction results based on a rigorous quantitative analysis.