## EECS CSPL SEMINAR SERIES

FALL TERM 1995

Andrew Yagle
# Andrew Yagle

### Department of Electrical Engineering and Computer Science

### University of Michigan

November 14, 1995

###
Feasibility Conditions for Impulse Reflection Response Data
for Inverse Scattering of 2-D and Absorbing 1-D Media

Abstract -

Layer stripping algorithms for inverse scattering problems
are very fast, but have the reputation of being numerically
unstable, especially when applied to noisy data. This
presentation provides feasibility conditions on the impulse
reflection response data which, if fulfilled, produces a
stable reconstruction. We determine when layer stripping
algorithms are numerically stable, explain why they are stable,
and specify exactly the (discrete) problem they solve when
they are stable. We consider two problems: (1) 1-D
(layered) absorbing medium probed from both above and below,
as in nondestructive testing (this problem is equivalent
to the reconstruction of a lossy LCRG transmission line);
and (2) the 2-D Schrodinger equation inverse scattering problem.
Numerical examples show how the new results render noisy data
feasible and stabilize reconstructions.

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