Abstract
Regularized recursive linearization methods are presented for solving a two-dimensional inverse medium scattering problem, which reconstructs the scatterer of an inhomogeneous medium from the measurements of near field current densities. Energy estimates of the scattered field are obtained on which the Born approximation is based. The methods start from the Born approximation corresponding to the weak scattering, each update is obtained via recursive linearization with respect to the wavenumber or the spatial frequency by solving one forward problem and one adjoint problem of the Helmholtz equation. In the case that the weak scattering criterion is not satisfied, a technique based on a direct imaging algorithm may be developed to generate an initial guess. Numerical examples are presented to illustrate the efficiency and robustness of the underlying computational method.
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