Theoretical Study on Non-Improvement of the Multi-Frequency Direct Sampling Method in Inverse Scattering Problems

Abstract

Generally, it has been confirmed that applying multiple frequencies guarantees a successful imaging result for various non-iterative imaging algorithms in inverse scattering problems. However, the application of multiple frequencies does not yield good results for direct sampling methods (DSMs), which has been confirmed through simulation but not theoretically. This study proves this premise theoretically by showing that the indicator function with multi-frequency can be expressed by the Bessel and Struve functions and the propagation direction of the incident field. This is based on the fact that the indicator function with single frequency can be expressed by the exponential and Bessel function of order zero of the first kind. Various simulation outcomes are shown to support the theoretical result.