Topological optimality condition for the identification of the center of an inhomogeneity. (12th February 2018)

• Record Type: Journal Article
• Authors: Cakoni, Fioralba; Kovtunenko, Victor A
• Is Part Of: Inverse problems. Volume 34:Number 3(2018:Mar.)
• Publication Date: 2018-02-12
• Subjects: inverse problem for inhomogeneous media -- topology optimization -- topological derivative -- zero-order optimality condition -- asymptotic analysis; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aaa997
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: The inverse scattering problem for inhomogeneous media is considered within the topology optimization framework. Varying the complex-valued refractive index we derive a zero-order necessary optimality condition in minimizing the L 2 misfit cost functional of the far-field measurement. The topology asymptotic expansion of the optimality condition leads to an imaging operator, which is used to identify the center of the unknown inhomogeneity using few far-field measurements. Numerical tests show high precision and stability in the reconstruction using our optimality condition based imaging both in two and three dimensions.