Near field imaging of small isotropic and extended anisotropic scatterers

• Main Authors: Harris, Isaac, Rome, Scott
• Format: Journal Article
• Language: English
• Published: 12-01-2016
• Subjects: Mathematics - Analysis of PDEs; Mathematics - Mathematical Physics; Physics - Mathematical Physics
• DOI: 10.48550/arxiv.1601.02993

In this paper, we consider two time-harmonic inverse scattering problems of
reconstructing penetrable inhomogeneous obstacles from near field measurements.
First we appeal to the Born approximation for reconstructing small isotropic
scatterers via the MUSIC algorithm. Some numerical reconstructions using the
MUSIC algorithm are provided for reconstructing the scatterer and piecewise
constant refractive index using a Bayesian method. We then consider the
reconstruction of an anisotropic extended scatterer by {a modified linear
sampling method and the factorization method applied }to the near field
operator. This provides a rigorous characterization of the support of the
anisotropic obstacle in terms of a range test derived from the measured data.
Under appropriate assumptions on the material parameters, the derived
factorization can be used to determine the support of the medium without
a-priori knowledge of the material properties.