Two direct factorization methods for inverse scattering problems

Abstract

In this paper, we propose and analyze two new direct factorization methods for solving inverse scattering problems. Both direct factorization methods are built upon the mathematically justified factorization method developed by Kirsch. The first one is naturally derived from a recent direct sampling method by replacing the corresponding far-field operator F in the indicator function by the factorized far-field operator . The second one is based on a truncated Neumann series approximation of the inverse of an appropriately scaled factorized far-field operator. Both direct factorization methods are shown to be stable with respect to noise and mathematically equivalent. Numerical results with both synthetic and real experimental data are presented to illustrate the promising accuracy of our proposed direct factorization methods in comparison to Kirsch’s factorization method and the direct sampling method.