Three-dimensional quantitative microwave imaging from measured data with multiplicative smoothing and value picking regularization

This paper presents reconstructions of four targets from the 3D Fresnel database. The electromagnetic inverse scattering problem is treated as a nonlinear optimization problem for the complex permittivity in an investigation domain. The goal of this paper is to explore the achievable reconstruction quality when such a quantitative inverse scattering approach is employed on real world measurements, using only single-frequency data. Two regularization techniques to reduce the ill-possedness of the inverse scattering problem are compared. The first one is a multiplicative smoothing regularization, applied directly to the cost function, which yields smoothed reconstructions of the homogeneous Fresnel targets without much experimentation to determine the regularization parameter. The second technique is the recently proposed value picking (VP) regularization which is particularly suited for the class of piecewise (quasi-) homogeneous targets, such as those of the Fresnel database. In contrast to edge-preserving regularization methods, VP regularization does not operate on the spatial distribution of permittivity values, but it clusters them around some reference values, the VP values, in the complex plane. These VP values are included in the cost function as auxiliary optimization variables and their number can be gradually increased using a stepwise relaxed VP regularization scheme. Both regularization strategies are incorporated in a Gauss-Newton minimization framework with line search. It is shown that the reconstruction quality using single-frequency Fresnel data is good when using multiplicative smoothing and even better when using the VP regularization. In particular, the completely blind reconstruction of the mystery target in the database provides us with a detailed quantitative image of a plausible object