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Article Dans Une Revue Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Année : 2016

A full-field image conversion method for the inverse conductivity problem with internal measurements

Cédric Bellis

Résumé

This article investigates a Fourier-based algorithm for computing heterogeneous material parameter distributions from internal measurements of physical fields. Within the framework of the periodic scalar conductivity model, a pair of dual Lippmann– Schwinger integral equations is derived for the sought constitutive parameters based on full intensity or current density field measurements. A numerical method based on the fast Fourier transform and fixed-point iterations is proposed. Convergence, stability and approximation quality of the method are analysed. For materials with small contrast, a first-order Born-like approximation is also obtained. Overall, the proposed reconstruction approach enables a direct conversion of full-field measurement images, possibly noisy, into maps of material conductivity. A set of numerical results is presented to illustrate the performance of the method.

Dates et versions

hal-01323124 , version 1 (30-05-2016)

Identifiants

Citer

Cédric Bellis, Hervé Moulinec. A full-field image conversion method for the inverse conductivity problem with internal measurements. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2016, 472 (2187), ⟨10.1098/rspa.2015.0488⟩. ⟨hal-01323124⟩
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