Three-Dimensional Reconstruction of Objects Embedded in Spherically Layered Media Using Variational Born Iterative Method

The variational Born iterative method (VBIM) is employed here to reconstruct 3-D objects with permittivity contrast buried in spherically multilayered media. The nonlinear inverse problem is solved iteratively via the conjugate-gradient method, and in each iteration, the scattered field is linearized by using the Born approaximation. The forward solver is provided by the method of moments combined with a Krylov subspace method. The dyadic Green’s function for spherically layered media is constructed in terms of the spherical vector wave functions by using the scattering superposition in the spherical coordinate system and then transformed into the Cartesian coordinate system. Thus, the inversion region is discretized into $N$ uniform cubic cells and the reconstructed result can be obtained in the Cartesian coordinate system by employing VBIM. Numerical results with high resolution are presented to validate the capability of our method in reconstructing 3-D multiple objects of arbitrary shapes buried in spherically multilayered media.

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