Planar ECT Image Reconstruction Based on Solving the Bayesian Model by Combining Fast Iterative Adaptive Shrinkage-Thresholding Algorithm and GMM

Planar electrical capacitance tomography (ECT) is a method to visualize the permittivity distribution and is promising in the field of nondestructive testing of composite materials. Image reconstruction is the core of planar ECT, but it is often a nonlinear underdetermined problem and easily affected by noise, which limits the quality of image reconstruction. Therefore, this article proposes an image reconstruction method based on solving the Bayesian model by combining the fast iterative adaptive shrinkage-thresholding (FIAST) algorithm and the Gaussian mixture model (GMM). First, the original planar ECT problem is transformed into an optimization problem through Bayesian inference and maximum likelihood estimation. Second, the adaptive support-driven Bayesian reweighting (ASDBR) model provides sparse prior knowledge and transforms the optimization problem into a series of iteratively weighted subproblems. Then, adaptive shrink thresholding is introduced and the FIAST algorithm is used to solve these suboptimization problems. Finally, GMM is used to classify the normalized permittivity, determine the optimal threshold, and perform threshold processing on the normalized permittivity to further improve the image reconstruction quality. Simulation and static experimental results show that compared with the Landweber algorithm, L1 (FISTA) algorithm, L1 (FIASTA-GMM) algorithm, ASDBR (FISTA) algorithm, and SBL algorithm, the ASDBR (FIASTA-GMM) algorithm has the best average correlation coefficient (CC) and average relative error (RE) in the simulation, respectively, are 0.9 and 0.062. It can also provide the best and most stable imaging results in noise experiment, regularization experiment, and static experiment.