A comparison of the Colton–Kirsch inverse scattering methods with linearizedtomographic inverse scattering

Abstract

We present a numerical comparison of the so-called ‘linear sampling’ inversescattering methods developed by Colton and Kirsch, published in this journal, andlinearized tomographic inverse scattering algorithms based on either holographicfiltered backpropagation principles or a plain matrix inversion scheme. Althoughwe restrict ourselves to two-dimensional obstacle scattering, we investigate boththe transverse magnetic (TM) and the transverse electric (TE) polarizationmodes. The comparison of the TM-polarization mode is performed with a specificfiltered backpropagation algorithm derived here whereas the comparison of theTE-polarization mode is performed with a matrix inversion scheme. Bothsuggested schemes, with which we compare the linear sampling method, make useof linearizing approximations whereas the linear sampling method does notintroduce any such approximations.Numerical examples are given for a monofrequent plane wave excitation inangular diversity mode with either full or limited aperture data. In theseparticular experiments, the linearized tomographic methods appear to provideclearer visual results than the linear sampling methods.