Modified Sampling Method with Near Field Measurements
Abstract
This paper investigates the inverse scattering problems using sampling methods with near field measurements. The near field measurements appear in two classical inverse scattering problems: inverse scattering for obstacles and interior inverse scattering for cavities. We propose modified sampling methods to treat these two classical problems using near field measurements without making any asymptotic assumptions on the distance between the measurement surface and the scatterers. We provide theoretical justifications based on the factorization of the near field operator in both the symmetric factorization case and the nonsymmetric factorization case. Furthermore, we introduce a data completion algorithm which allows us to apply the modified sampling methods to treat the limited-aperture inverse scattering problems. Finally, numerical examples are provided to illustrate the modified sampling methods with both full- and limited-aperture near field measurements.
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© 2022, Society for Industrial and Applied Mathematics.
History
Submitted: 8 July 2021
Accepted: 11 October 2021
Published online: 27 January 2022
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Youth Innovation Promotion Association https://doi.org/10.13039/501100012492
National Key Research and Development Program of China Stem Cell and Translational Research https://doi.org/10.13039/501100013290 : 2018YFA0702502
National Natural Science Foundation of China https://doi.org/10.13039/501100001809 : 11971471
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