A quantitative direct sampling method for inhomogeneities from multi-frequency backscattering measurements

The inverse scattering problem from the multi-frequency backscattering data is a long-standing open problem. We advance the theory by proving a local uniqueness result. Moreover, we introduce a direct sampling method for quantitatively reconstructing unknown inhomogeneities. Comprehensive numerical experiments validate the robustness, accuracy, and computational effectiveness of the proposed quantitative direct sampling method.