Fast three-dimensional GPR forward and inverse scattering based on wideband diagonal tensor approximation

A fast three-dimensional (3D) ground penetrating radar (GPR) forward and inverse scattering method is presented based on the diagonal tensor approximation (DTA). For the forward scattering problem, the first iteration about the frequency-dependent scattering coefficients in the DTA is used. By further evaluating the scattering tensor at the GPR center frequency to remove its frequency dependence, the DTA is simplified while maintaining higher accuracy than the classical Born approximation method. For the inverse scattering problem, the DTA-based algorithm is derived for the plane-wave GPR, and can be implemented efficiently by the NUFFT combined with the stabilized bi-conjugate gradient FFT (BiCGS-FFT) method. The proposed inversion algorithm is much cheaper than the existing DTA-based methods, and has a higher accuracy and a wider range of applicability than the fast method based on the Born approximation.