Inverse obstacle problem for the scalar Helmholtz equation

Giovanni F. Crosta

doi:10.1117/12.179727

8 July 1994 Inverse obstacle problem for the scalar Helmholtz equation

Giovanni F. Crosta

Proceedings Volume 2241, Inverse Optics III; (1994) https://doi.org/10.1117/12.179727
Event: SPIE's International Symposium on Optical Engineering and Photonics in Aerospace Sensing, 1994, Orlando, FL, United States

Abstract

The method presented is aimed at identifying the shape of an axially symmetric, sound soft acoustic scatterer from knowledge of the incident plane wave and of the scattering amplitude. The method relies on the approximate back propagation (ABP) of the estimated far field coefficients to the obstacle boundary and iteratively minimizes a boundary defect, without the addition of any penalty term. The ABP operator owes its structure to the properties of complete families of linearly independent solutions of Helmholtz equation. If the obstacle is known, as it happens in simulations, the theory also provides some independent means of predicting the performance of the ABP method. The ABP algorithm and the related computer code are outlined. Several reconstruction examples are considered, where noise is added to the estimated far field coefficients and other errors are deliberately introduced in the data. Many numerical and graphical results are provided.

Citation Download Citation

Giovanni F. Crosta "Inverse obstacle problem for the scalar Helmholtz equation", Proc. SPIE 2241, Inverse Optics III, (8 July 1994); https://doi.org/10.1117/12.179727

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