The main thrust of the work to date on improving the accuracy of the concentration measurement has focused on the development of new software algorithms to calculate the permittivity distribution inside the pipe from the measurements of capacitances between pairs of electrodes located around the outside of the pipe. This has required work in two areas, namely the computation of new more accurate sensitivity maps and the development of high-speed image reconstruction algorithms.
For the sensitivity maps, two approaches have been used, one based on the use of an analytical solution for the electric field and the other based on the use of finite element techniques. New sensitivity maps have been calculated using both of these methods.
We had already shown, prior to the commencement of the current project, that it is possible to dramatically improve the accuracy of ECT images using iterative methods. This technique produces images by successively correcting an approximate initial image, but it is a relatively slow method which is not suitable for use in real-time. We have now succeeded in obtaining images of similar quality to those obtained by iteration in a single calculation, which involves no more computational effort than our existing approximate method. The process involves calculating a new transformation matrix from the sensitivity map and then using this matrix instead of the original sensitivity map in the image reconstruction algorithm. We have developed Matlab software which can generate the required transformation matrices from any set of compatible sensitivity maps, for both the Landweber and Tikhonov image reconstruction methods.
These new transforms can now be used with both versions of our existing on-line software to produce high-accuracy images on-line.