The development of regularization algorithms in the framework of Banach spaces is an emerging scientific topic. This approach provides several advantages with respect to standard methods, which are all developed in Hilbert spaces. In particular, it allows reducing the over-smoothing effects and the oscillations that are often present in standard Hilbert-space solutions. In this paper, the Banach-space regularization theory is used to solve an electromagnetic inverse-scattering problem related to microwave imaging. In particular, an ad-hoc developed two-step algorithm is introduced and some numerical results are reported.
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