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 frequencies. 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.

翻译：本文工作中，我们构建了玻恩近似、逆玻恩近似及其级数展开，旨在利用两个不同频率下的散射数据，反演亥姆霍兹方程中两个函数值系数以求解逆散射问题。我们对所提出的正则化逆玻恩级数的收敛性与近似误差进行了分析。结果表明，当微扰的逆玻恩近似足够小时，所提出的级数收敛。初步数值结果表明，所提出的正则化逆玻恩近似及其级数能够有效反演各向同性非均匀介质。