Accession Number : ADA305113

Title :   Inverse Scattering via Heisenberg's Uncertainty Principle.

Descriptive Note : Research rept.,

Corporate Author : YALE UNIV NEW HAVEN CT DEPT OF COMPUTER SCIENCE

Personal Author(s) : Chen, Yu

PDF Url : ADA305113

Report Date : FEB 1996

Pagination or Media Count : 53

Abstract : We present a stable method to recursively linearize the acoustic inverse scattering problem. It turns out that the ill posedness of the problem can be beneficially used to solve it. It means that, due to ill-posedness, not all equations in the nonlinear system are strongly nonlinear, and that when solved recursively in a proper order, they can be reduced to a collection of linear problems. Our method requires solution of a series of forward scattering problems with ascending wave numbers (or frequencies). At each frequency, a linear least-squares problem is solved to obtain an approximate forward model which produces the prescribed scattering data. The robustness of the procedure is demonstrated by several numerical examples in the inversion of the Helmholtz equation in two dimensions.

Descriptors :   *NONLINEAR DIFFERENTIAL EQUATIONS, *ACOUSTIC SCATTERING, UNCERTAINTY, RECURSIVE FUNCTIONS, LEAST SQUARES METHOD, DIFFERENTIAL EQUATIONS, INVERSE SCATTERING, FORWARD SCATTERING, RICCATI EQUATION, S MATRIX, HELMHOLTZ EQUATIONS.

Subject Categories : Acoustics

Distribution Statement : APPROVED FOR PUBLIC RELEASE