Access the full text.
Sign up today, get DeepDyve free for 14 days.
B. Gu, Dongyun Deng (1993)
Inversion of Acousticl Velocity with Moment Multi-Grid Algorithm
A. Nachman (1988)
Reconstructions from boundary measurementsAnnals of Mathematics, 128
V. Burov, O. Rumiantseva (1996)
Influence of the Scattering Data Redundancy on Uniqueness and Stability in Reconstruction of Strong and Complicated Scatterers
R. Novikov (1986)
Construction of two-dimensional Schrödinger operator with given scattering amplitude at fixed energyTheoretical and Mathematical Physics, 66
Preprint No. R. G. Novikov and G. M. Khenkin (1986)
(Inst. of Physics
O. D. Rumiantseva (1992)
Ill-Posed Problems in Natural Sciences
S. Johnson, Y. Zhou, M. Tracy, M. Berggren, Frank Stenger (1984)
Inverse Scattering Solutions by a Sinc Basis, Multiple Source, Moment Method -- Part III: Fast AlgorithmsUltrasonic Imaging, 6
P. Grinevich, R. Novikov (1995)
Transparent potentials at fixed energy in dimension two. Fixed-energy dispersion relations for the fast decaying potentialsCommunications in Mathematical Physics, 174
A. V. Saskovets (1989)
Inverse Scattering Problems in Acoustics
V. Burov, M. Rychagov, A. Saskovets (1992)
Account of Multiple Scattering in Acoustic Inverse Problems of Tomographic Type
V. Burov, O. Rumiantseva (1992)
Functional-analytical methods for the scalar inverse-scattering problems, 1843
A. Devaney (1978)
Nonuniqueness in the inverse scattering problemJournal of Mathematical Physics, 19
R. G. Newton (1983)
Proceedings of Conference on Inverse Scattering: Theory and Applications
A. N. Sivov (1977)
Generalized Method of Natural Oscillations in the Diffraction Theory
R. Weder (1991)
Global uniqueness at fixed energy in multidimensional inverse scattering theoryInverse Problems, 7
A. Ramm (1987)
Completeness of the products of solutions to PDE and uniqueness theorems in inverse scatteringInverse Problems, 3
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.
Acoustical Physics – Springer Journals
Published: Sep 1, 2003
Keywords: Acoustics
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.