A review of reconstruction techniques for capacitance tomography

Capacitance tomography has been used to image several processes, such as liquid/gas pipe flow, oil/water/gas gravity separation, pneumatic conveying, fluidized beds and flame combustion. The nature of the capacitance sensors is such that reconstruction algorithms well developed for medical tomography are not applicable. The main problem is that the relationship between the measured quantity (capacitance) and the parameter of interest (distribution of the dielectric constant) is nonlinear. Furthermore, it is impossible to establish an explicit expression which relates the dielectric constant distribution to the measured capacitance. Also it should be pointed out that the number of measurements in capacitance tomography is small (typically less than 100) compared to medical tomography. For these reasons the first tested algorithm in capacitance tomography was based on the crude back projection algorithm. This algorithm has over the years been enhanced for use with a capacitance tomograph. In addition other techniques, such as various iterative methods, algorithms based on artificial neural networks and 'look-up' tables have been developed and tested. This paper outlines the working principles for the different techniques and presents the main results.