2014/12/20 by Abdul Wahab, Wahab, Abdul
Engineering · Mathematics · #35L05 #35R30 #47A52 #65J20 #74B05 #Electrical and Bioimpedance Tomography #FOS: Mathematics #Non-Destructive Testing Techniques #Numerical methods in inverse problems #Optimization and Control (math.OC) #Welding Techniques and Residual Stresses #math.OC #msc:35L05 #msc:35R30 #msc:47A52 #msc:65J20 #msc:74B05
paper · pdf · doi:10.48550/arxiv.1412.6667
30 pages
openalex publication_date 2014/12/20 · arxiv created 2015/04/09 · arxiv updated 2015/04/10 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
The aim of this article is to elaborate and rigorously analyze a topological derivative based imaging framework for locating an electromagnetic inclusion of diminishing size from boundary measurements of the tangential component of scattered magnetic field at a fixed frequency. The inverse problem of inclusion detection is formulated as an optimization problem in terms of a filtered discrepancy functional and the topological derivative based imaging functional obtained therefrom. The sensitivity and resolution analysis of the imaging functional is rigorously performed. It is substantiated that the Rayleigh resolution limit is achieved. Further, the stability of the reconstruction with respect to measurement and medium noises is investigated and the signal-to-noise ratio is evaluated in terms of the imaginary part of free space fundamental magnetic solution.