Discrete layer-stripping algorithms and feasibility conditions for the 2D inverse conductivity problem

We develop a discrete layer-stripping algorithm for the 2D inverse conducti vity problem. Unlike previous algorithms, this algorithm transforms the pro blem into a time-varying ID Schrodinger equation inverse scattering problem , discretizes this problem and then solves the discrete problem exactly. Th is approach has three advantages: (i) the poor conditioning inherent in the problem is concentrated in the solution of a linear integral transform at the beginning of the problem, to which standard regularization techniques m ay be applied and (ii) feasibility conditions on the transformed data are o btained, satisfaction of which ensures that (iii) the solution of the discr ete nonlinear inverse scattering problem is exact and stable. Other contrib utions include solution of discrete Schrodinger equation inverse potential problems with rime-varying potentials by both layer-stripping algorithms an d solution of nested systems of equations which amount to a time-varying di screte version of the Gel'fand-Levitan equation. An analytic and numerical example is supplied to demonstrate the operation of the algorithm.