Inversion of Electrical Capacitance Tomography Data by Simulated Annealing: Non-linear versus Linearized Forward Modeling

In this work we apply the simulated annealing (SA) inversion method to the reconstruction of permittivity images from electrical capacitance tomography (ECT) data. We test the SA inversion method using static physical models simulating some typical distribution patterns of two and three-component flows. The SA-based permittivity inversions have some advantages over other approaches based on linear least-squares inversion: they can find good solutions starting with poor initial models, can more easily implement complex a priori information, and do not introduce smoothing effects in the final permittivity distribution model. A major disadvantage comes from the fact that SA is computationally intensive and lead to relatively slow reconstructions. We establish comparisons between two variations of the SA inversion method: a first one where computation of the forward problem (i.e., to find the mutual capacitance data for a given permittivity distribution inside the sensor) is made in a non-linear fashion by using a finite-volume method (FVM); and a second one, where we employed a linearized numerically improved forward model based on the use of a sensitivity matrix. We found this last approach to be faster and more accurate than traditional linear methods. Finally, results of this work provided us some insight about the effects on permittivity estimation from ECT data caused by linearization of the forward model.