Developments of 3-D Reconstruction Algorithms for ERT

P.A.T. Pinheiro, W.W. Loh and R.C. Waterfall

Process Tomography Unit,

Department of Electrical Engineering and Electronics, UMIST

P.O. Box 88, Manchester, M60 1QD, United Kingdom

Abstract - Electrical resistance tomography (ERT), is an imaging tool for process and clinical applications, in which maps of the electric conductivity distribution of a body are formed from the current-to-voltage map of the body?s surface. ERT is inherently a three-dimensional problem, as the current lines do not remain localised in a plane. The transposition of two-dimensional (2-D) ERT to three-dimensional (3-

D) ERT is a challenging task and imposes significant increase in computational power demands and storage requirements. In this work, it is demonstrated that 3-D ERT is a viable off-line technique for use today and can be implemented using a low-cost Pentium powered PC. The 3-D image reconstruction algorithm implemented is based on the Newton?s method in which optimal experiments are used for the reconstruction process. More importantly, the algorithm incorporates 3- D forward modelling, 3-D data collection and reconstruction. A ?fast? reconstruction algorithm is also implemented and yields a reduced set of equations, which has the advantage of no longer being ill conditioned at expense of a loss in the image resolution. The reconstruction algorithm was applied to a 2.7m3 mixing tank at plant scale and the resulting images analysed.

Keywords : Finite element method, forward problem, inverse problem, 3-D tomography