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The direct sampling method (DSM) has been introduced for non-iterativeimaging of small inhomogeneities and is known to be fast, robust, and effectivefor inverse scattering problems. However, to the best of our knowledge, a fullanalysis of the behavior of the DSM has not been provided yet. Such an analysisis proposed here within the framework of the asymptotic hypothesis in the 2Dcase leading to the expression of the DSM indicator function in terms of theBessel function of order zero and the sizes, shapes and permittivities of theinhomogeneities. Thanks to this analytical expression the limitations of theDSM method when one of the inhomogeneities is smaller and/or has lowerpermittivity than the others is exhibited and illustrated. An improved DSM isproposed to overcome this intrinsic limitation in the case of multiple incidentwaves. Then we show that both the traditional and improved DSM are closelyrelated to a normalized version of the Kirchhoff migration. The theoreticalelements of our proposal are supported by various results from numericalsimulations with synthetic and experimental data.

Direct sampling method for imaging small dielectric inhomogeneities: analysis and improvement