STRENGTHENED LINEAR SAMPLING METHOD WITH A REFERENCE BALL

By adding a reference ball as an extra artificial obstacle component to the underlying scattering system, we propose a simple but robust and effective technique to choose the crucial cut-off value required in the linear sampling method (LSM) for inverse scattering problems. The reference ball technique causes few extra computational costs to the LSM, but brings in a practically important byproduct, i.e., it eliminates the interior eigenvalue problem automatically, a well-known barrier when applying the LSM. Some mathematical justifications of the new technique are provided, and numerical experiments are also presented to demonstrate its feasibility and effectiveness. © 2009 Society for Industrial and Applied Mathematics.