Inverse acoustic impedance obstacle problem

An inverse problem of recovering the shape of a sound-impedance obstacle from a knowledge of the far-field pattern of the acoustic scattering wave is investigated in this paper. A nonlinear optimization scheme is developed for solving the inverse problem, and a two-step adaptive iteration algorithm is proposed for numerically implementing the nonlinear optimization scheme. The use of the two-step procedure results in a large reduction in the number of unknowns in the nonlinear optimization step for determining the shape of the scatterer. The use of the adaptive iteration technique yields a considerable improvement in the quality of the reconstruction by utilizing the knowledge of the reconstruction obtained from the previous iteration step. Numerical experiments for several two-dimensional obstacles having a variety of shapes have been presented showing the practicality and effciency of the inversion approach.