We present a hybrid method to numerically solve the inverse scattering problem for shape and impedance, given the far-field pattern for one incident direction. This method combines ideas of both iterative and decomposition methods, inheriting advantages of each of them, such as getting good reconstructions and not needing a forward solver at each step. An optimization problem is presented as the theoretic background of the method and numerical results show its feasibility. AMS classification scheme numbers: 81Uxx 1.
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Pedro Serranho (2006) studied this question.
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