A globally convergent numerical method for a 1-d inverse medium problem\n with experimental data

2016/02/29 by Michael V. Klibanov, Klibanov, Michael V., Loc H. Nguyen +5
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Electromagnetic Scattering and Analysis #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1602.09092

openalex publication_date 2016/02/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, a reconstruction method for the spatially distributed\ndielectric constant of a medium from the back scattering wave field in the\nfrequency domain is considered. Our approach is to propose a globally\nconvergent algorithm, which does not require any knowledge of a small\nneighborhood of the solution of the inverse problem in advance. The\nQuasi-Reversibility Method (QRM) is used in the algorithm. The convergence of\nthe QRM is proved via a Carleman estimate. The method is tested on both\ncomputationally simulated and experimental data.\n

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