Numerical determination of anomalies in multifrequency electrical impedance tomography
This work addresses the inverse problem of anomaly detection in electrical impedance tomography for medical or industrial imaging, but the results are preliminary with no quantitative benchmarks.
The paper develops a method to reconstruct anomalies in multifrequency electrical impedance tomography using a spectral decomposition of the forward problem, achieving successful numerical reconstruction via gradient descent.
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.