Abstract-Electrical capacitance tomography (ECT) is a relatively mature non-invasive imaging technique that attempts to map dielectric permittivity of materials. ECT has become a promising monitoring technique in industrial process tomography especially in fast flow visualization. One of the most challenging tasks in further development of ECT for real applications are the computational aspects of the ECT imaging. Recently, 3D ECT has gained interest because of its potential to generate volumetric images. Computational time of image reconstruction in 3D ECT makes it more difficult for real time applications. In this paper, we present a robust and computationally efficient 4D image reconstruction algorithm applied to real ECT data. The method takes advantage of temporal correlation between 3D ECT frames to reconstruct movies 4D of dielectric maps. Image reconstruction results are presented for the proposed algorithms for experimental ECT data of a rapidly moving object.Corresponding author: M. Soleimani (m.soleimani@bath.ac.uk). 172Soleimani et al.

Abstract-Electrical Capacitance Tomography (ECT) is a noninvasive and non-destructive imaging technique that uses electrical capacitance measurements at the periphery of an object to generate map of dielectric permittivity of the object. This visualization method is a relatively mature industrial process tomography technique, especially in 2D imaging mode. Volumetric ECT is a new method that poses major computational challenges in image reconstruction and new challenges in sensor design. This paper shows a nonlinear image reconstruction method for 3D ECT based on a validated forward model. The method is based on the finite element approximation for the complete sensor model and the solution of the inverse problem with nonlinear iterative reconstruction. The nonlinear algorithm has been tested against some complicated experimental test cases, and it has been demonstrated that by using an improved forward model and nonlinear inversion method, very complex shaped samples can be reconstructed. The reconstruction of very complex geometry with objects in the shape of letters H, A, L and T is extremely promising for the applications of 3D ECT.Corresponding author: M. Soleimani (m.soleimani@bath.ac.uk). 220Banasiak et al.

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Tomographic techniques have been widely accepted as a valuable tool for process control and monitoring. The classic tomographic approach is to reconstruct a 2D image of a process cross section. However, most processes take place in 3D space. Effective imaging in 3D process space can be achieved using 3D image reconstruction in two ways. The first (called 2.5D by the authors) is to use a few independent 2D images and to interpolate them into a 3D image. This method has been widely used in medical applications of tomography for many years already. The second method and the subject of this paper is ‘real’ three-dimensional reconstruction, where sensors provide three-dimensional measurements and a 3D image is directly obtained during the reconstruction process. The latter method has evolved from classic 2D cross-sectional definition to real and direct 3D imaging. The paper presents the authors' work on a 3D capacitance tomography system including issues such as sensor layout, measurement protocol, data simulation, reconstruction algorithm and 3D visualization.