An explicit conditioning method for image reconstruction in electrical capacitance tomography

• A new invertible linear model is developed for conducting capacitance tomography.
• The new method allows for instantaneous image reconstructions.
• Image reconstructions using the method are superior to other comparably fast methods.
• The method is used to determine the optimum electrode density for an ECT system.

A new electrical capacitance tomography (ECT) image reconstruction method, termed Sensitivity Factor Regularization (SFR), is developed. The SFR method provides an explicit formulation for solving the image reconstruction problem that performs better than other explicit methods, such as linear back-projection and Tikhonov regularization, while providing the same computational efficiency. The computational ease of the SFR method renders it an attractive option for ECT where real-time imaging is required and theoretical statistical evaluation of proposed electrode configurations may readily be performed. A statistical study is conducted using SFR image reconstructions for investigating the impact of electrode density on image quality for a symmetric ECT system characterizing a square cross-section. A larger number of smaller electrodes allows more data to be gathered for use in image reconstruction, but degrades signal-to-noise ratio in the measurements. The statistical study using SFR clearly identifies a theoretical optimum electrode density that minimizes reconstructed image error for a given level of measurement noise.