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Uniqueness and stability of the solution to an inverse acoustic scattering problem

Uniqueness and stability of the solution to an inverse acoustic scattering problem Abstract The uniqueness and stability of a discrete inverse scattering problem (functional description) is considered. The number of degrees of freedom, which determines the way of sampling for the functions of the scatterer and the secondary sources induced in it, may considerably vary from one problem to another, thus providing the adequacy of the discrete formulation of a specific problem. This number depends on the size of the scattering region in space and on the widths of the spatial spectra of both the scatterer and the secondary sources. Nonuniqueness of the solution occurs because of the configurations of secondary sources that exist in the scattering region and are not observable in any of the experiments. It is shown that precisely the number of degrees of freedom of the secondary sources determines the amount of discrete scattering data that is necessary to provide a unique solution. If this amount is collected in the experiments without exceeding a certain classical limiting resolution, the solution to the inverse problem is unique and stable. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acoustical Physics Springer Journals

Uniqueness and stability of the solution to an inverse acoustic scattering problem

Acoustical Physics , Volume 49 (5): 12 – Sep 1, 2003

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References (16)

Publisher
Springer Journals
Copyright
2003 MAIK "Nauka/Interperiodica"
ISSN
1063-7710
eISSN
1562-6865
DOI
10.1134/1.1608973
Publisher site
See Article on Publisher Site

Abstract

Abstract The uniqueness and stability of a discrete inverse scattering problem (functional description) is considered. The number of degrees of freedom, which determines the way of sampling for the functions of the scatterer and the secondary sources induced in it, may considerably vary from one problem to another, thus providing the adequacy of the discrete formulation of a specific problem. This number depends on the size of the scattering region in space and on the widths of the spatial spectra of both the scatterer and the secondary sources. Nonuniqueness of the solution occurs because of the configurations of secondary sources that exist in the scattering region and are not observable in any of the experiments. It is shown that precisely the number of degrees of freedom of the secondary sources determines the amount of discrete scattering data that is necessary to provide a unique solution. If this amount is collected in the experiments without exceeding a certain classical limiting resolution, the solution to the inverse problem is unique and stable.

Journal

Acoustical PhysicsSpringer Journals

Published: Sep 1, 2003

Keywords: Acoustics

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