Abstract
Results are reported for the inverse scattering problem of theplane acoustic wave by a two-dimensional penetrable obstacle. Anonlinear optimization scheme for solving the ill posed andnonlinear inverse problem is proposed. A particularlyattractive feature of the scheme is that it can reproduce agood reconstruction of the unknown penetrable obstacle from theknowledge of only one Fourier coefficient of the far-fieldpattern. Furthermore, an adaptive iteration algorithm with two steps for numerically implementing the optimization schemeis presented. Numerical results for noiseless and noisysynthetic data have demonstrated the effectiveness andpracticality of the inversion algorithm.
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