Reconstruction of permittivity images from capacitance tomography data by using very fast simulated annealing

In this paper we introduce an image reconstruction technique for imaging permittivity distributions using electrical capacitance tomography, based on global optimization by very fast simulated annealing. Electrical capacitance measurement data are obtained between electrodes placed around the outer wall of an electrically insulating pipe. Such data are used to infer material distributions inside the pipe. The data are processed in order to reconstruct an image of the spatial distribution of the relative electrical permittivity (also known as dielectric constant) inside the pipe, which reflects a material distribution. In the very fast simulated annealing method, the permittivity image is reconstructed by minimizing iteratively a cost function related to the difference between the measured data and those calculated for an estimated permittivity distribution that is repeatedly updated, in a semi-random search process that mimics the thermodynamic phenomena of annealing (as metals slowly cool down) or crystallization (as liquids freeze). The images are refined until their calculated capacitance data match the measured data, in which case it is considered that such images properly resemble the permittivity distribution that produced the measured capacitance data.