ECT for flow imaging: total least squares for image reconstruction algorithm

For the problem that noise has a great impact on the measurement data during the electrical capacitance tomography data acquisition process, a denoising method based on the truncated singular value decomposition combined with the total least squares model is proposed. Soft threshold is performed on the effective value of the truncated singular value decomposition to remove the influence of external noise interference in the measurement data, and as far as possible to retain the original characteristics of the data. For the problem of different errors in the measurement data and the coefficient matrix, a mathematical model is introduced based on total least squares. It is used to improve the total least squares iterative method and reduce both the measurement error and the coefficient matrix error. To solve the problems of slow convergence speed and low efficiency caused by the ill-posedness of the equation during the iteration, adaptive correction parameters are introduced, which effectively avoids the occurrence of local convergence and improves the speed of convergence and imaging accuracy. To solve the ill-condition of the total least squares model, a regularization matrix is added so that the imaging results can achieve the goal of overall optimization. For 12-electrode electrical capacitance tomography system, the simulation experiments are carried out based on four typical flow patterns. The results show that the algorithm effectively increases the robustness of reconstruction and improves the accuracy of the reconstructed images.