Numerical Determination of Anomalies in Multifrequency Electrical Impedance Tomography

Habib Ammari (1) , Faouzi Triki (2) , Chun-Hsiang Tsou (2)

1 ETH-SAM - Seminar for Applied Mathematics
2 EDP - Equations aux Dérivées Partielles

The multifrequency electrical impedance tomography consists in retrieving the conductivity distribution of a sample by injecting a finite number of currents with multiple frequencies. In this paper we consider the case where the conductivity distribution is piecewise constant, takes a constant value outside a single smooth anomaly, and a frequency dependent function inside the anomaly itself. Using an original spectral decomposition of the solution of the forward conductivity problem in terms of Poincaré variational eigenelements, we retrieve the Cauchy data corresponding to the extreme case of a perfect conductor, and the conductivity profile. We then reconstruct the anomaly from the Cauchy data. The numerical experiments are conducted using gradient descent optimization algorithms.

Mots clés: multifrequency electric impedance tomography; anomalies reconstruction; inverse problems

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Physique mathématique [math-ph]

Habib Ammari, Faouzi Triki, Chun-Hsiang Tsou. Numerical Determination of Anomalies in Multifrequency Electrical Impedance Tomography. European Journal of Applied Mathematics, 2019, 30 (3), pp.481-504. ⟨10.1017/S0956792518000244⟩. ⟨hal-01509354⟩