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Electrical impedance tomography using level set representation and total variational regularization. (English) Zbl 1072.65143
Summary: We propose a numerical scheme for the identification of piecewise constant conductivity coefficient for a problem arising from electrical impedance tomography. The key feature of the scheme is the use of level set method for the representation of interface between domains with different values of coefficients. Numerical tests show that our method can recover sharp interfaces and can tolerate a relatively high level of noise in the observation data. Results concerning the effects of number of measurements, noise level in the data as well as the regularization parameters on the accuracy of the scheme are also given.
MSC:
65N21Inverse problems (BVP of PDE, numerical methods)
35R30Inverse problems for PDE
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)