Abstract
This paper examines an implementation of a layer-peeling method to inverse scattering problems in the time domain, which is applied here to the case of one-dimensional lossless discontinuous medium. The method is based on the fast Schur recursion applied directly to the discrete problem. The method is tested on several numerical examples in order to compare its performance to the standard invariant imbedding algorithm. The reconstructions of media from both synthetic data and measured data are presented. The layer-peeling method is shown to be considerably faster than the invariant imbedding method without the loss of precision.
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