Results are reported for the inverse scattering problem of the plane acoustic wave by a two-dimensional penetrable obstacle. A nonlinear optimization scheme for solving the ill posed and nonlinear inverse problem is proposed. A particularly attractive feature of the scheme is that it can reproduce a good reconstruction of the unknown penetrable obstacle from the knowledge of only one Fourier coefficient of the far-field pattern. Furthermore, an adaptive iteration algorithm with two steps for numerically implementing the optimization scheme is presented. Numerical results for noiseless and noisy synthetic data have demonstrated the effectiveness and practicality of the inversion algorithm.
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You et al. (2001) studied this question.
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