Interpretation of linear sampling method in terms of induced multipoles

Linear sampling method is a qualitative inversion technique employed for imaging scatterers. Although it is well understood from the perspective of mathematics, despite few good efforts, its physical interpretation still eludes the research community. This article presents a physical interpretation of the linear sampling method. We demonstrate that linear sampling method can effectively be understood as finding the locations in the domain, where the monopole current is the most significant part of the induced current. To this end, we have provided a new mathematical formulation in terms of the induced multipoles which is equivalent to LSM. We further show that this mathematical model can be used to enhance the imaging results.