ECT Image Reconstruction Based on Alternating Direction Approximate Newton Algorithm

To solve the underdetermined problem and the mismatches of position and size of the objects caused by the ill-posed sensitivity matrix in electrical capacitance tomography (ECT) image reconstruction, an alternating direction approximate newton (ADAN) method is developed. Based on the alternating direction method of multipliers (ADMMs), this algorithm utilizes the Bregman operator splitting (BOS) algorithm to segment the total variation (TV) regularization model. An approximation to Newton's method, in which a term in Newton's hessian is replaced by a Barzilai-Borwein (BB) approximation, is used to solve the subproblems after segmentation, and the complete convergence proof and the stability analysis of the algorithm are provided. The quantitative analysis of reconstruction results of the ADAN, Landweber, modified Landweber, Newton, and ${l}_{1}$ regularization methods shows that the average relative error (RE) of ADAN in the reconstruction of ten flow images is 0.2199, which is lower than that of reconstructed by the other four algorithms. The average correlation coefficient (CC) of the reconstructed images of ADAN is higher than that reconstructed by the ${l}_{1}$ regularization, Newton, modified Landweber, and Landweber methods, which are 0.8539, 0.6792, 0.6251, 0.6545, 0.6665, and 0.6614, separately. Moreover, under the same iteration stopping condition, the iteration time of ADAN is the shortest.