## 1 Introduction
### Related Work  
During the process of solving the inverse problem of EIT, the amount of measured data is significantly smaller than the amount of data to be solved. As a result, the reconstructed image often has a poor resolution. The traditional Tikhonov regularization method, which is based on the L2-norm [8], leads to blurred reconstructed images because it produces overly smooth solutions. To address this issue, [PERSON] et al. proposed an electrical impedance imaging method that utilizes parameter level sets [9]. Their method greatly improves the resulting image quality by reducing the number of unknown quantities. An effective implementation of the merged total variation and Gauss-Newton algorithm has been accomplished to reconstruct the image in the field of two-dimensional EIT [10]. For this investigation, the process of reconstructing images relied on the utilization of 16 electrodes crafted from copper (Cu) and a neighboring technique for data collection. [PERSON] et al. proposed a spatially adaptive TV regularization method [11]. Their method utilizes the difference curvature, an effective spatial feature metric, to identify planar and edge regions. It also employs various image-reconstruction metrics to quantitatively evaluate the obtained reconstruction results, resulting in better robustness and improved resolution for the reconstructed images [12]. In recent years, the development of neural networks has led to the emergence of intelligent algorithms that can selectively train on targeted samples for specific tasks. This approach allows for the utilization of prior knowledge obtained from training, thereby improving the accuracy of model estimation and enhancing the quality of the obtained images [13; 14]. In terms of the speed of image reconstruction, although training the model can be time consuming, once the model is trained, the actual image reconstruction process is a one-step imaging technique, which also enhances the imaging speed of the model [15; 16]. However, as the demand continues to increase, the cost of training its related models is also rising. This makes it impractical to directly implement these models in clinics and general hospitals. The EIT electric field distribution is characterized by its soft field nature, resulting in a nonlinear relationship between the boundary measurement voltage and the conductivity distribution in the measured object field. Therefore, the inverse EIT problem is nonlinear [5]. Due to the nonlinearity of the EIT image-reconstruction problem, many solution algorithms, such as the conjugate gradient method [17], attempt to linearly approximate this nonlinear problem. However, this often leads to significant distortion in the resulting image. On the other hand, although the least-squares method utilizes a nonlinear approach to solve the problem, it is still a local optimization method. Consequently, it tends to encounter local minimization problems, resulting in distortion in the reconstructed images [18]. To tackle this problem, the Huber equation is employed to reconstruct the high-order total variation (HOTV) optimization equation [19]. [PERSON] et al. modified the Finite Element Method (FEM) framework for EIT reconstruction by integrating total generalized variation (TGV) regularization. They conducted reconstructions using both simulation and clinical data. The initial findings suggested that, when compared to TV regularization, TGV regularization enhances the generation of more-authentic images [20]. Additionally, auxiliary variables and generalized Lagrange multipliers are introduced to decompose the optimization equation into two simpler subproblems. The fast alternating direction multipliers method is then used to solve the problem. The algorithm demonstrates relatively fast convergence and produces visually improved images while better preserving details, such as edges.