## 1 Introduction  
With the improvement and development of global navigation satellite systems (GNSS), a large number of ground-based GNSS receivers now provide observation data for most of the global land areas and a small number of ocean areas. Based on ground-based GNSS observation data, the center for ionospheric analysis of the international GNSS service (IGS) developed the global ionospheric map (GIM) product, which can provide the global distribution of the total electron content (TEC) of the ionosphere. However, GIM provides only TEC products, which cannot show the vertical variation of the ionosphere. Computerized ionospheric tomography (CIT) can be based on GNSS observation data and reconstruct ionospheric electron density (IED) information with the help of certain mathematical methods. CIT can portray the three-dimensional (3D) fine structure of the ionosphere, and provide data support for improving the navigation and positioning performance of GNSS and analyzing the relevant physical phenomena and laws of the ionosphere. The successful application of computed tomography (CT) to ionospheric electron density reconstruction was first demonstrated by [PERSON] et al. [1] and [PERSON] et al. [2]. Since then, two main types of inversion models have been developed for the CIT technique: voxel-based models and function-based models. The voxel-based model divides the tomography region into equally spaced or unequally spaced voxels along the longitude, latitude, and altitude directions, and reconstruct the IED by discrete inversion algorithms. The function-based model solves the coefficients of a specified function base by using a parametric method, and then reconstructs the IED. For the voxel-based model, the main inversion algorithms include the algebraic reconstruction technique (ART), the multiplicative algebraic reconstruction technique (MART), the simultaneous algebraic reconstruction technique (SART) in iterative algorithms and Kalman filtering, singular value decomposition (SVD), and regularization methods in non-iterative algorithms. When reconstructing the IED based on the discrete inversion theory, the sparse and non-uniform distribution of ground based GNSS and the lack of horizontal observation information leads to the presence of more discrete voxels with no observation data, which in turn creates the ill-posed problem. Many scholars have improved the strategies and algorithms in voxel-based models to improve this ill-posed problem in CIT. [PERSON] and [PERSON] [3] verified the optimal voxel size of \(5^{\circ}\times 5^{\circ}\times 50\) km (longitude \(\times\) latitude \(\times\) altitude) for low-latitude regions in India based on the ART and MART algorithms. [PERSON] et al. [4] verified the CIT through a checkerboard test resolution, optimized the voxel size and spacing, and reconstructed the 3D distribution of IED with sparse GPS data. According to the distribution characteristics of voxel sizes at different altitudes, CIT methods based on variable voxel sizes and multiple scales have been successively proposed [5; 6; 7; 8]. [PERSON] et al. [9] combined the iterative algorithms and non-iterative advantages, and proposed a hybrid reconstruction algorithm (HRA), which first uses the truncated singular value decomposition (TSVD) method to obtain the initial value of the IED, and then brings the initial value of the IED into the ART algorithm for iterative computation, which significantly improves the reconstruction quality of the IED. [PERSON] et al. [10] established a set of relaxation factors related to the variation of the IED on the basis of the ART, which weakened the effect of noise on the CIT results. [PERSON] et al. [11] proposed an extended SART method for the joint contribution of the intercepts of the intravoxel rays and the electron densities in a specific voxel, which improved the accuracy of the CIT; in particular, it reconstructed the peak electron density (NmF2) more accurately. [PERSON] et al. [12] proposed a two-step method for reconstructing IED with high temporal resolution.