Acceleration of Electrical Capacitance Volume Tomography Imaging by Fourier-Based Sparse Representations

Electrical capacitance tomography (ECT) is a non-invasive and non-intrusive imaging modality that utilizes mutual capacitance measurements between electrode plates to reconstruct the cross-sectional spatial electrical permittivity distribution inside a region of interest (RoI). Increasing attention has been given in recent years to the extension of ECT to volumetric imaging, also known as electrical capacitance volume tomography (ECVT). Most of the desirable properties of ECT carry over to ECVT. However, the speed of reconstruction is reduced in ECVT due to an increase in the number of measurements and in the number of voxels used to represent the permittivity distribution in the RoI. In this paper, we adopt a Fourier basis representation as a means to accelerate the speed of image reconstruction in ECVT. By considering only spatial frequency components below certain threshold, we show that the number of unknowns can be greatly reduced and the overall reconstruction process significantly accelerated. We present both numerical and experimental results to corroborate our findings.