Singular value decomposition of the current-to-field operator in solving inverse scattering problems

This paper investigates the relationship between the singular vector of G̅_D and the Fourier basis for solving inverse scattering problems. By operating SVD of the operator G̅_D, G̅_D behaves as a low-pass filter, which guarantees the drop-off of high frequency components. Importantly, such a relationship is determined by the domain of interest and the grid mesh, independent of scatterers, which can be utilized in the inverse problem to reduce the number of unknowns and to boost the converge rate. Numerical simulations validate the efficacy of the operator.