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A Numerical Method for the Inverse Impedance Obstacle Problem

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Numerical experiments are reported for the inverse scattering problem of time-harmonic acoustic waves by a sound-impedance obstacle. A nonlinear optimization scheme is proposed to solve the inverse impedance obstacle problem. The scheme has the particularly attractive feature of being able to produce the satisfactory reconstruction of the shape of the sound-impedance target from the knowledge of only one Fourier coefficient of the far-field pattern of the scattered wave. A two-step adaptive iteration algorithm is presented to numerically implement the nonlinear optimization scheme. Some numerical examples for several two-dimensional obstacles having a variety of shapes are given, showing the effects of the quality of the inversion of different orders of Fourier coefficients, various impedance values and random noise in the data.
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Document Type: Research Article

Publication date: January 1, 2002

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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