ETNA - Electronic Transactions on Numerical Analysis, pp. 173-195, 2025/02/03
The applicative motivation of this paper is the reconstruction of some electromagnetic features of the earth superficial layer by measurements taken above the ground. We resort to frequency domain electromagnetic data inversion through a well-known linear integral model by considering three different collocation methods to approximate the solution of the continuous problem as a linear combination of linearly independent functions. The discretization leads to a strongly ill-conditioned linear system. To overcome this difficulty, an iterative regularization method based on Landweber iterations in Banach spaces is applied to reconstruct solutions which present discontinuities or have a low degree of smoothness. This kind of solutions are common in many imaging applications. Several numerical experiments show the good performance of the algorithm in comparison to other regularization techniques.
Keywords: first-kind Fredholm integral equations, electromagnetic induction, inverse problems in geophysics, collocation methods, iterative regularization, Landweber method, Banach spaces
