Near-Field Focusing Operators for Planar Multi-Static Microwave Imaging Using Back-Projection in the Spatial Domain

Based on a plane-wave expansion of the observation data in quasi-planar multi-static scattering scenarios, an improved formalism for image creation utilizing back-projection in the spatial domain is derived. The underlying integral expressions for different focusing operators are derived analytically leading to magnitude correction factors, which are mostly relevant for reconstructing microwave images when the distance from the scattering object to the aperture plane is small. It is shown that the derived imaging procedure is superior to the traditional back-projection only compensating the phase delay of the measurement signals and validate our findings based on simulated as well as measured data. Since the derived focusing operators correspond to a low-pass filtering of the spatial images, the resulting modified multi-static back-projection algorithms effectively suppress imaging artifacts as well.

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 and a spatial back-projection algorithm 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.