Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 472, Issue 2187, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rspa.2015.0488
Keywords
inverse problems; full-field measurements; fast Fourier transform-based method
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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 LippmannSchwinger 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.
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