Direct sampling method for imaging small dielectric inhomogeneities: analysis and improvement

TL;DR

This paper provides a detailed analysis of the direct sampling method (DSM) for imaging small dielectric inhomogeneities, identifies its limitations, and proposes an improved version to enhance imaging performance in complex scenarios.

Contribution

The paper offers the first full analytical characterization of DSM in 2D, revealing its limitations and introducing an improved DSM that better handles inhomogeneities with varying sizes and permittivities.

Findings

Analytical expression of DSM indicator function in terms of Bessel functions.

Limitations of DSM when inhomogeneities are smaller or have lower permittivity.

Improved DSM effectively overcomes these limitations.

Abstract

The direct sampling method (DSM) has been introduced for non-iterative imaging of small inhomogeneities and is known to be fast, robust, and effective for inverse scattering problems. However, to the best of our knowledge, a full analysis of the behavior of the DSM has not been provided yet. Such an analysis is proposed here within the framework of the asymptotic hypothesis in the 2D case leading to the expression of the DSM indicator function in terms of the Bessel function of order zero and the sizes, shapes and permittivities of the inhomogeneities. Thanks to this analytical expression the limitations of the DSM method when one of the inhomogeneities is smaller and/or has lower permittivity than the others is exhibited and illustrated. An improved DSM is proposed to overcome this intrinsic limitation in the case of multiple incident waves. Then we show that both the traditional and improved DSM are closely related to a normalized version of the Kirchhoff migration. The theoretical elements of our proposal are supported by various results from numerical simulations with synthetic and experimental data.