The use of nonlinear operator equation techniques, and the Newton-Kantorovich method in particular, to solve inverse problems is outlined. The application of the method to two problems - inverse refractive index scattering and an inverse problem of steady-state diffusion - is then considered.
T. J. Connolly,
D. J.N. Wall,
R. H.T. Bates,
"Inverse Problems And The Newton-Kantorovich Method", Proc. SPIE 0558, Inverse Optics II, (25 October 1985); doi: 10.1117/12.949569; https://doi.org/10.1117/12.949569