Image reconstruction using machine-learned pseudoinverse in electrical capacitance tomography

Algorithms based on linear approximation are the primary methods for fast online image reconstruction in electrical capacitance tomography (ECT). One-step reconstruction algorithms use certain inverse matrix approximations, such as the normalized transpose matrix or the Moore-Penrose pseudoinverse matrix used in the linear back-projection (LBP) algorithm or mean square optimization, respectively. For the first time, we proposed the use of a machine-learned pseudoinverse matrix (ML-pseudoinverse) as an alternative to these matrices. So far, multivariate linear regression has been used to identify a sensitivity matrix of the forward problem in tomography. Experiments were performed using a cylindrical ECT sensor with sixteen electrodes and flow image patterns typical for two-phase flow monitoring. Training datasets consisting of images of various test objects and their corresponding measurements were generated using numerical simulation of measurements carried out in the MATLAB environment and the ECTsim toolkit. Real measurements were performed using the EVT4 data acquisition system. Reconstructed images were analyzed using selected image quality norms. The reconstruction results obtained for the validation dataset of two-phase flow images showed that the one-step linear reconstruction algorithm achieved better results when using ML-pseudoinverse than LBP normalized transposition or Moore-Penrose pseudoinverse. The proposed approach can be a good solution for a fast reconstruction algorithm for dynamic processes in online monitoring using ECT. Machine-learned pseudoinverse can be applied to numerous engineering problems, including nonlinear inverse problems. • A machine-learned pseudoinverse matrix for single-step image reconstruction in ECT. • The ML-pseudoinverse outperforms LBP transposition and Moore-Penrose pseudoinverse. • The method's performance validated using simulated and real measurement data. • Fast one-step ECT image reconstruction for monitoring dynamic processes.