November 14, 1995
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.