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

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.