ISSN:
1572-9036
Keywords:
35P25
;
47B35
;
65M25
;
86.34
;
93E10
;
Inverse scattering
;
two-component wave equations
;
scattering matrix
;
fast Cholesky recursions
;
Schur algorithm
;
inverse seismic problem
;
linear estimation
;
ladder filters
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The Schur algorithm and its time-domain counterpart, the fast Cholseky recursions, are some efficient signal processing algorithms which are well adapted to the study of inverse scattering problems. These algorithms use a layer stripping approach to reconstruct a lossless scattering medium described by symmetric two-component wave equations which model the interaction of right and left propagating waves. In this paper, the Schur and fast Chokesky recursions are presented and are used to study several inverse problems such as the reconstruction of nonuniform lossless transmission lines, the inverse problem for a layered acoustic medium, and the linear least-squares estimation of stationary stochastic processes. The inverse scattering problem for asymmetric two-component wave equations corresponding to lossy media is also examined and solved by using two coupled sets of Schur recursions. This procedure is then applied to the inverse problem for lossy transmission lines.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00047331
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