Detection of small inhomogeneities via direct sampling method in transverse electric polarization
This work provides a theoretical explanation for a known limitation of the direct sampling method in electromagnetic imaging, which is relevant for researchers in inverse scattering problems.
The paper explains why the direct sampling method fails to identify the location of small inhomogeneities when their permeability differs from the background, and provides a theoretical explanation using Bessel functions, supported by numerical results with noisy data.
Various studies have confirmed the possibility of identifying the location of a set of small inhomogeneities via a direct sampling method; however, when their permeability differs from that of the background, their location cannot be satisfactorily identified. However, no theoretical explanation for this phenomenon has been verified. In this study, we demonstrate that the indicator function of the direct sampling method can be expressed by the Bessel function of order one of the first kind and explain why the exact locations of inhomogeneities cannot be identified. Numerical results with noisy data are exhibited to support our examination.