Stable Reconstruction of Anisotropic Objects from Near-Field Electromagnetic Data

2023/09/22 by Tran H. Lan, Lan, Tran H., Dinh-Liem Nguyen +1 · 1 citation
Engineering · Mathematics · #Electrical and Bioimpedance Tomography #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical Analysis (math.NA) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2309.12606

openalex publication_date 2023/09/22 · openalex created_date 2023/09/26 · openalex updated_date 2026/07/28

Abstract

This paper addresses the electromagnetic inverse scattering problem of determining the location and shape of anisotropic objects from near-field data. We investigate both cases involving the Helmholtz equation and Maxwell's equations for this inverse problem. Our study focuses on developing efficient imaging functionals that enable a fast and stable recovery of the anisotropic object. The implementation of the imaging functionals is simple and avoids the need to solve an ill-posed problem. The resolution analysis of the imaging functionals is conducted using the Green representation formula. Furthermore, we establish stability estimates for these imaging functionals when noise is present in the data. To illustrate the effectiveness of the methods, we present numerical examples showcasing their performance.

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• A direct imaging method for inverse scattering problem of biharmonic wave with phased and phaseless data

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