## 1 Introduction
[16] presented a spatio-temporal structure-aware sparse Bayesian learning (SA-SBL) framework that explores and exploits intra-frame spatial clustering and inter-frame temporal continuity in an unsupervised manner, using a hierarchical Bayesian model and structure-aware priors. [PERSON] et al. [17] introduced a novel spatio-temporal total variation regularization method to utilize the sparsity in 4D space and time and adopted voxel-to-voxel cross-correlation to measure the flow profile. [PERSON] et al. [18] proposed a nonlinear weighted anisotropic total variation (NWATV) regularization technique that incorporates internal inhomogeneity information into the EIT reconstruction process, successfully preserving and improving the characteristics of internal inhomogeneity. [PERSON] et al. [19] considered modifying the TV regularization term with higher-order differential operators during the image reconstruction process and applied the total generalized variation (TGV) regularization to the finite element model (FEM) framework for EIT reconstruction, thereby improving the ill-posedness of the inverse problem. [PERSON] et al. [20] proposed an improved non-convex-L1-norm-penalized total generalized variation (NCP-TGV) model to solve the inverse problem. They developed an iteratively reweighted L1 algorithm that transforms the non-convex model into a convex function, offering advantages in reducing staircase effects and preserving edges simultaneously. On the other hand, some research teams have integrated computer vision and image processing techniques with EIT technology to process the raw reconstructed EIT images using methods like image segmentation, thereby obtaining more accurate regions of interest (ROIs). For example, [PERSON] et al. [21] developed a novel strategy for ECT image reconstruction that combines images reconstructed using two different algorithms through image segmentation methods. This approach retains the advantages of each algorithm for specific imaging regions and improves the overall image reconstruction quality. [PERSON] et al. [22] proposed a method to estimate lung area using functional tidal images or active contour methods, achieving accurate estimation of lung area through image processing. [PERSON] et al. [23] introduced the Otsu thresholding method for the automatic detection of ROIs and used a nonlinear diffusion imaging method to simultaneously estimate the initial values and differences in conductivity. Different regularization schemes were applied to the background and ROIs to improve image reconstruction performance. [PERSON] et al. [24] proposed a standardized method for evaluating and comparing cardiac EIT images based on automated segmentation. They designed an automated solution to segment and extract features from the images, accurately capturing various cardiac ROIs and extracting features. [PERSON] et al. [10] developed an automatic lung segmentation model using deep learning with the U-Net architecture. This model enables automatic, robust, and fast lung segmentation in EIT images without the need for prior information, thus defining appropriate ROIs. However, due to the \"soft field\" effect and the ill-posedness of the inverse problem in EIT, the performance of image reconstruction algorithms is still far from perfect. Therefore, more efforts are needed to develop better reconstruction algorithms. In this paper, we propose a region segmentation algorithm with a relaxation factor based on the traditional maximum entropy thresholding method. By adjusting the relaxation factor parameter, we can control the degree of preserving edge artifacts in the reconstructed image. This algorithm not only serves as an effective post-processing method for identifying regions of interest in EIT images but also complements the reduced-order Tikhonov regularization algorithm. Based on the segmentation results obtained from the soft-threshold region segmentation algorithm, the background region unrelated to the regions of interest is excluded from the solution process in the reduced-order operation.