A BEM based methodology to solve inverse problems considering fictitious background media

This paper proposes a new BEM based inversion methodology named Fictitious Background Media Inverse Formulation (FBMIF) to solve inverse problems described in terms of the Helmholtz equation for inhomogeneous media. The BEM based approach considers a Green’s function related to a homogeneous background medium, a fictitious medium, which works as a transfer function. Thereafter, considering a nonrestrictive linearization scheme, the FBMIF is completely defined. Three examples are used to test the efficacy of the proposed model of inversion, which can be extended to other mathematical models different from those governed by the Helmholtz equation.