A Novel Study on Direct Sampling Method for Imaging Multiple Targets

Abstract

Abstract. The Direct Sampling Method (DSM) is well known to be a fast, stable, and effective detection technique in inverse scattering problems, but its analysis is restricted to imaging of a single target. Motivated by this, we investigate the mathematical structure of DSM for imaging small multiple dielectric targets by establishing a relationship with the radii and permittivities of targets, and Bessel function of order zero. This structure explains why DSM can be applied to the imaging of multiple targets. Numerical results support our findings.

Optimal Mesh Size for Inverse Medium Scattering Problems

“…In this subsection, we illustrate the efficiency of the optimal meshing procedure using the DSM, which is introduced in subsection 2.2. For further details on the DSM, we refer to [30,31,32,13,31,33,34,14,15,26,27,28].…”

“…For instance, some effective methods are developed for the homogeneous background model: the linear sampling or probing methods (LSM) [16], the time-reversal multiple signal classification method (MUSIC) [7,8,12], the direct sampling method (DSM) [25], the multilevel sampling method (MSM) [32], the contrast source inversion method (CSIM) [11], etc. Moreover, several efficient algorithms are applied in various practical situations, e.g., in the stratified ocean waveguide model: the simple method (SM) [30], extended direct sampling methods (EDSMs) [13,14,15,26,27,28,31,33,34], the extended MUSIC method (EMUSIC) [6,24], the topological based imaging functional [3], etc. Furthermore, several efficient approaches are introduced in the two-layered medium model: the extended multilevel sampling method (EMSM) [36], the extended linear sampling method (ELSM) [18], etc.…”