Imaging of 3D objects with experimental data using orthogonality sampling methods

Abstract

This paper is concerned with imaging of 3D scattering objects with experimental data from the Fresnel database. The first goal of the paper is to investigate a modified version of the orthogonality sampling method (OSM) by Harris and Nguyen [SIAM J. Sci. Comput., 42, B72--B737, 2020] for the imaging problem. The advantage of the modified OSM over its original version lies in its applicability to more types of polarization vectors associated with the electromagnetic scattering data. We analyze the modified OSM using the factorization analysis for the far field operator and the Funk-Hecke formula. The second goal is to verify the performance of the modified OSM, the OSM, and the classical factorization method for the 3D Fresnel database. The modified OSM we propose is able to invert the sparse and limited-aperture real data in a fast, simple, and efficient way. It is also shown in the real data verification that the modified OSM performs better than its original version and the factorization method.

A new sampling indicator function for stable imaging of periodic scattering media

“…This is not a surprise since the evanescent modes are typically sensitive with noise but the sampling method only uses propagating modes. The great robustness against noise in the data was also seen in the orthogonality sampling methods studied in [12,19,26].…”

A stable sampling method for inverse scattering from periodic media

“…This is not a surprise since the evanescent modes are typically sensitive with noise but the sampling method only uses propagating modes. The great robustness against noise in the data was also seen in the orthogonality sampling methods studied in [10,17,24].…”

“…The numerical study also shows that the proposed sampling method is more robust than the factorization method and more efficient than the orthogonality sampling method in reconstructing periodic scattering media. We also want to mention that although the orthogonality sampling method has been studied for inverse scattering from bounded objects [8,[10][11][12]14,17,24], its application to the inverse scattering problem for periodic media is still not known.…”

Application of a mild data-driven technique to Lippmann–Schwinger inverse scattering in variable-exponent Lebesgue spaces for microwave imaging

“…On the one hand, qualitative approaches aim at providing a reconstruction of only some features of the scenario under test, such as position and dimension of targets. In these cases, linearized formulations and/or simplified models are often adopted [8][9][10][11][12][13][14][15], although regularization is still needed to face the ill-posedness of the problem. On the other hand, quantitative techniques may allow retrieving the full distributions of the dielectric properties (e.g.…”