Enhanced nonlinear inverse scattering through linear super-resolution techniques

In microwave inverse scattering, the dielectric properties of an object are retrieved starting from the knowledge of samples of the electromagnetic field it scatters. The mathematical model of the problem gives rise to a couple of nonlinear and ill-posed integral equations which can be successfully solved using Newton methods. Unfortunately, the discretization of the equations involves the computation of very large-scale and ill-posed linear systems. Due to the high numerical complexity, generally low resolution output images are provided. In this paper we adopt linear super-resolution techniques in order to obtain high quality output images. In practice, a fixed number of low resolution approximations of the output object are combined together to reconstruct a single output image with higher resolution, and only a linear increase in the numerical costs.