MODIFIED SAMPLING METHOD WITH NEAR FIELD MEASUREMENTS

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.

Automated summary

This paper investigates the use of sampling methods with near field measurements to solve inverse scattering problems, including inverse scattering for obstacles and interior inverse scattering for cavities. Modified sampling methods are proposed and theoretical justifications are provided. A data completion algorithm is introduced to deal with limited-aperture inverse scattering problems. Numerical examples are used to validate the effectiveness of the modified sampling methods.