A regularisation scheme for electromagnetic inverse problems: application to crack detection in civil structures

A new regularisation scheme is proposed for the solution of the inverse scattering problem arising in electromagnetic imaging. The aim is to efficiently reconstruct defects and cracks with sharp boundaries when inspecting civil structures. The approach is developed in Banach spaces and tends to alleviate the over-smoothing effects of the usually adopted regularisation schemes in Hilbert spaces. Preliminary numerical results concerning the tomographic reconstruction of defects in cylindrical models made of cement paste are reported and discussed. The improved reconstruction quality (in terms of the reduction in the smoothing effect) is proven in those cases.