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Inverse Wave Imaging Through Operator Decomposition
PDE Seminar| Speaker: | Sean Lehman, Lawrence-Livermore National Laboratory |
| Location: | 0 Kerr |
| Start time: | Thu, Nov 4 2004, 1:40PM |
Description
on-invasive wave imaging is a technique to "look into" an object or
medium whose internal structure cannot be exposed. It is used to form
images of certain physical properties of the object. Examples include
using ultrasound to image breasts for cancer detection, ground
penetrating radar to search for land mines, and acoustic techniques
to look for buried hazardous wastes.
In inverse wave imaging, a wave (acoustic or electromagnetic) is
launched into an object or medium under evaluation. The scattered
field is measured on a surface about it. The goal is to invert
mathematically the scattering process and reconstruct the internal
structure of the object using the measured scattered field. Operator
decomposition is a class of inverse scattering techniques in which
the forward scattering operator is decomposed via a singular value
decomposition or eigenvalue/eigenvector expansion into an orthogonal
set of basis vectors. Using the mathematics of linear algebra, the
basis vectors are used to backpropagate the measured scattered field
to form an image of the scattering structure.
Two specific examples will be given: time-reversal and Hilbert space
decomposition, along with examples.