A comparison of the Colton–Kirsch inverse scattering methods with linearized tomographic inverse scattering

We present a numerical comparison of the so-called ‘linear sampling’ inverse scattering methods developed by Colton and Kirsch, published in this journal, and linearized tomographic inverse scattering algorithms based on either holographic filtered backpropagation principles or a plain matrix inversion scheme. Although we restrict ourselves to two-dimensional obstacle scattering, we investigate both the transverse magnetic (TM) and the transverse electric (TE) polarization modes. The comparison of the TM-polarization mode is performed with a specific filtered backpropagation algorithm derived here whereas the comparison of the TE-polarization mode is performed with a matrix inversion scheme. Both suggested schemes, with which we compare the linear sampling method, make use of linearizing approximations whereas the linear sampling method does not introduce any such approximations. Numerical examples are given for a monofrequent plane wave excitation in angular diversity mode with either full or limited aperture data. In these particular experiments, the linearized tomographic methods appear to provide clearer visual results than the linear sampling methods.