On the recovery of two function-valued coefficients in the Helmholtz equation for inverse scattering problems via inverse Born series^*

Abstract In this work, we construct the Born and inverse Born approximation and series to recover two function-valued coefficients in the Helmholtz equation for inverse scattering problems from the scattering data at two different wave-numbers. An analysis of the convergence and approximation error of the proposed regularized inverse Born series is provided. The results show that the proposed series converges when the inverse Born approximations of the perturbations are sufficiently small. The preliminary numerical results show the capability of the proposed regularized inverse Born approximation and series for recovering the isotropic inhomogeneous media.