Image Reconstruction of Electrical Capacitance Tomography Based on ADMM-Net

This article proposes a method that combines the alternating direction method of multipliers (ADMMs) algorithm with neural networks based on the compressed sensing principle to improve the quality and speed of image reconstruction while solving the parameter selection problem. First, the ADMM algorithm is used to solve the sparse electrical capacitance tomography (ECT) model and obtain the corresponding iterative process. Then, the iterative process is sequentially constructed as a reconstruction layer, convolution layer, nonlinear activation layer, and multiplier update layer to form the ADMM-Net network model. Finally, the limited-BFGS (L-BFGS) algorithm is used to optimize the parameters of the network through end-to-end training. Compared with a single network model, this method encapsulates the mathematical reasoning process in the form of a network for image reconstruction, enhancing the interpretability of the network. At the same time, using network optimization to adjust the parameters avoids the uncertainty of traditional ADMM algorithm parameter selection. To verify the effectiveness of this method, simulations, static experiments, and comparisons with the commonly used Landweber algorithm, Tikhonov regularization algorithm, conjugate gradient (CG) algorithm, and iterative hard thresholding (IHT) algorithm are conducted. The results show that the proposed method outperforms the other five algorithms in terms of reconstruction accuracy, convergence speed, and robustness.