Novel Inversion Techniques for Electromagnetic Diagnostics

This thesis deals with the development and validation of innovative inversion techniques for electromagnetic diagnostics. Specifically, regularization strategies in the framework of Lebesgue spaces are proposed to address inverse problems in microwave imaging and antenna diagnostics. As to microwave imaging, the thesis presents a technique which is formulated in variable-exponent Lebesgue spaces and relies on the finite element method to model the electromagnetic problem accurately. The aim is to reconstruct the distribution of the dielectric properties of the region of interest starting from measurements of scattering parameters at antenna ports. Concerning antenna diagnostics, a Lebesgue-space inversion technique is proposed to reconstruct excitation coefficients of antenna arrays from radiated far-field measurements. In both contexts, the developed methods have been found effective in dealing with the ill-posed nature of the underlying inverse problems. These approaches have been validated through numerical and experimental studies, showing their applicability across various scenarios.