Reconstruction of a potential from the impedance boundary map
Mikhail Isaev (CMAP), Roman Novikov (CMAP)
TL;DR
This paper develops formulas and methods to reconstruct the potential in a Schrödinger equation from impedance boundary data, advancing inverse scattering techniques for bounded domains at fixed energy.
Contribution
It introduces new formulas linking impedance boundary maps to scattering data and proposes efficient reconstruction methods for the potential.
Findings
Formulas for generalized scattering data from impedance boundary maps
Efficient potential reconstruction methods at fixed energy
Enhanced inverse scattering techniques for bounded domains
Abstract
We give formulas and equations for finding generalized scattering data for the Schr\"odinger equation in open bounded domain at fixed energy from the impedance boundary map (or Robin-to-Robin map). Combining these results with results of the inverse scattering theory we obtain efficient methods for reconstructing potential from the impedance boundary map.
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Taxonomy
TopicsNumerical methods in inverse problems · Spectral Theory in Mathematical Physics · Microwave Imaging and Scattering Analysis