A Novel Microwave Imaging Approach Based on Regularization in $L^{p}$ Banach Spaces

Inverse problems arising in microwave imaging suffer from high ill-posedness. As it is well known, it is necessary to employ regularized inversion methods, in order to mitigate such behavior. Usually, such approaches are formulated in standard Hilbert spaces. Recently, a more generic regularization theory, working in Banach spaces, has been investigated, in order to overcome some limitations of the Hilbert-space regularization. In this paper, a novel imaging algorithm, performing a L
^p
Banach-space regularization, is proposed for 2-D electromagnetic inverse scattering problems. The reconstruction capabilities of the methods are evaluated by using numerical and experimental data.