Abstract
The results of inverse scattering of plane acoustic waves from penetrable, homogeneous acoustic obstacles in two space dimensions are reported. The shape and the material parameters of the obstacles are recovered from both and limited-aperture, far-field patterns in the presence of random noise. The forward problem is solved via a combination of shape differentiation of the scattered field and the Padé approximation. Not being an integral equation based approach, the method is free of the non-uniqueness problem associated with the interior eigenvalues of the scatterer. Moreover, it is shown that all necessary scattering and Jacobian calculations need to be performed only with respect to a circle of a fixed radius. In addition, by the construction of the forward solution, the objective function to be minimized for inversion does not contain terms arising from the boundary conditions. This, along with the fact that the domain of calculations remains invariant to the stage of iteration, results in a substantial simplification in the implementation of a Gauss-Newton type of inversion procedure which is used here. Finally, the method is illustrated with several transmission obstacles of various shapes and with different initial conditions.
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