Abstract
This paper is concerned with the three-dimensional inverse scattering problem ofimaging the support of a penetrable object from far-field data of time-harmonicacoustic scattered waves. An indicator function, which has much largervalues inside the obstacle than outside the scatterer, is derived. Based onthe property of the indicator function, an indicator sampling method ispresented and analysed for solving the inverse transmission problem, whichis achieved by using the set of points for which the indicator functionarrives at its local extrema in a sampling domain containing the unknownpenetrable object as a reliable visualization of the penetrable obstacle. Themethod has the interesting feature of being independent of any priorknowledge about the geometrical and material properties of the penetrableobstacle. Another attractive feature of the approach is that it needs only theknowledge of far-field data of the acoustic scattered waves at a finite number ofincidence and observation directions distributed over some limited apertures.Numerical examples for several three-dimensional penetrable obstacles having avariety of shapes are given, showing the performance of the algorithm.
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