Various studies have confirmed the possibility of identifying the location ofa set of small inhomogeneities via a direct sampling method; however, whentheir permeability differs from that of the background, their location cannotbe satisfactorily identified. However, no theoretical explanation for thisphenomenon has been verified. In this study, we demonstrate that the indicatorfunction of the direct sampling method can be expressed by the Bessel functionof order one of the first kind and explain why the exact locations ofinhomogeneities cannot be identified. Numerical results with noisy data areexhibited to support our examination.
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