Inverse scattering in the framework of unconventional Lebesgue spaces: A case study

An inverse scattering procedure working in the unconventional Lebesgue spaces with variable exponent is considered in this paper. In this method, instead of adopting a single and constant value of the exponent, a variable function is adaptively defined based on the evolution of the inverse scattering problem solution during inexact-Newton iterations. In particular, the effects of the choice of the range of admissible values for the exponent function used in the definition of the involved Luxemburg norm are analyzed. To this end, an experimental case study involving a dielectric cylindrical target is considered as reference scenario.