Inversion of Generalized Parabolic Projections
Abstract
The niultidimensional inverse scattering problem for all acoustic medium is considered within the homogeneous background Born approximation. A constant density acoustic medium is probed by a wideband plane wave source, and the scattered field is observed along a receiver array located outside the medium. The inversion problem is formulated as a generalized tomographic problem It is shown that the observed scattered field can be appropriately filtered so as to obtain generalized projections of the scattering potential. For a 2-D experimental geometry, these projections are weighted integrals of the scattering potential over regions of parabolic support. The inversion problem is therefor similar to that of x-ray tomography, except that instead of being given projections of the object to be reconstructed along straight lines, projections along parabolas are given. The inversion procedure that we propose is similar to the x-ray solution, in the sense that it consists of a back projection operation followed by 2-D space invariant filtering. A "Projection-Slice Theorem" is derived relating the generalized projections and the scattering potential in the Fourier transform domain.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1987
- Accession Number
- ADA459603
Entities
People
- Ali Oebek
- Bernard C. Lévy
Organizations
- Massachusetts Institute of Technology