An Adaptive Basis Function Solution to the 1D and 2D Inverse Scattering Problems using the DBIM and the BIM
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An Adaptive Basis Function Solution to the 1D and 2D Inverse Scattering Problems using the DBIM and the BIMAbstract
We present the use of an adaptive set of basis functions used in conjunction with the MoM to solve the linearized scalar inverse electromagnetic scattering problem. The basis functions, which are whole-domain and harmonic, are selected to provide a perfectly conditioned solution under the first-order Born approximation when multiple frequency experiments are considered. In order to iteratively solve the full nonlinear problem by the Distorted Born Iterative Method (DBIM) and/or the Born Iterative Method (BIM), we introduce a single parameter into the basis function expansion to demonstrate that it is possible to maintain a well-conditioned linearized inverse problem by selecting the parameter value that minimizes the condition number of the discrete matrix operator. The proposed technique eliminates the need for Tikhonov regularization or equivalent regularization schemes commonly applied to the single-frequency, pulse-basis formulation of the linearized inverse scattering problem.
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