Fast and robust 3D electrical capacitance tomography

Electrical capacitance tomography (ECT) is well established for 2D imaging of multiphase flow. Increasingly, ECT is now being used to image in 3D. In this paper we examine the challenges of 3D image reconstruction using simulations of a 24 electrode (4 planes of 6 electrodes each) sensor. In particular, we demonstrate that the changes in capacitance in a 3D sensor can be as much as an order of magnitude less than in a 2D sensor and that the condition number for 3D imaging can be of the order of 106. We show that the condition number for 3D imaging with this sensor is dominated by the contributions from the most widely separated electrodes. If these pairs of electrodes are eliminated the condition number can be reduced by up to four orders of magnitude. Interestingly, although cross-plane measurements are essential for accurate reconstruction of 3D images, measurements from the widely separated electrodes are shown to have little influence on the quality of images that can be reconstructed, even in the noise-free case. This finding leads us to propose a new sampling strategy for 3D ECT in which only those capacitance measurements from nearby electrodes are included. This sampling approach leads to a reduction in acquisition time for each ECT data set by 40%, with no degradation in image quality and increased robustness to noise. We demonstrate our findings using experimental measurements on a 3D sensor.