Subsurface inspection of 2D domains via a rectangular BTHB-Landweber method in Banach spaces

This paper introduces an iterative regularization strategy formulated in Banach spaces for addressing the inverse problem linked to a two-dimensional linear integral model, which characterizes the interaction between the subsurface and a frequency-domain electromagnetic (FDEM) sensor. The discretization of the forward model is achieved by expressing the solution as a linear combination of basis functions, followed by a collocation approach. For the inversion, we adopt the dual Landweber method and incorporate efficient computational techniques for managing (rectangular) block Toeplitz with (rectangular) Hankel blocks (BTHB) coefficient matrices, enabling improved efficiency. Numerical simulations highlight the method’s capability to accurately recover the electrical conductivity distribution of the subsurface, even in the presence of sharp contrasts.