Characterizing nonlinear information in the linear sampling method for inverse medium scattering

Abstract

This work is concerned with the nonlinear information in the linear sampling method for the inverse medium scattering problem. In addition to the well-known capability in shape characterization, we demonstrate that the imaging indicator represents nonlinear information about the unknown contrast. We further demonstrate additional representations for this nonlinear information using the generalized linear sampling method. We shed light on this new result using the Born model and analytical examples.