## 1 Introduction  
The ionosphere is the ionized portion of the Earth's upper atmosphere, where a large number of free electrons is present, which affects the radio waves propagating through it. Modeling the electron density of the ionosphere has been a long-standing topic for researchers across the world. Due to the limitation of geographical location, it is difficult to deploy fixed ionospheric observation equipment at the sea, which leads to insufficient ionospheric observation data over sea areas. However, ship positioning and communication will be affected by ionospheric perturbation, so more ionospheric observation means are needed for the ocean region. By using AIS signals, we can obtain electron density information over the ocean area, which can provide auxiliary information for the improvement of the global electron density model, and long-term observations and research into ionosphere variation over ocean areas can also provide a guarantee for maritime communication. Computerized ionospheric tomography (CIT) has been an effective method for reconstructing the three-dimensional structure of ionospheric electron density since [PERSON] first introduced computerized tomography to ionospheric observation. They demonstrated the feasibility of computerized tomography in 2D electron density reconstruction by simulating STECs along a polar-orbiting satellite and five and three ground stations [1]. Researchers have further developed this technique for electron density reconstruction in the ionosphere using various measured data to improve reconstruction quality [2; 3; 4]. [PERSON] et al. validated the computerized tomography technique using measured data to reconstruct 2D electron density over a region with 57-73\({}^{\circ}\) latitude [2]. [PERSON] et al. proposed utilizing GPS satellite occultations and extreme ultraviolet (EUV) observations to provide horizontal integration path information, thereby enhancing the accuracy of CIT [3]. [PERSON] et al. proposed an improved CIT model by fusing 3D multisource ionospheric data to study the evolution of magnetic storms [4]. In the early stage, only signals from polar-orbiting satellites could be used; therefore, the signal rays could only be in the latitude-altitude plane, and the electron density could only be reconstructed on the latitude-altitude plane. The three-dimensional CIT was not realized until the advent of global position satellites (GPSs), when the selection of ground station became more flexible [5; 6; 7], and CIT has become more popular in ionospheric research since then. [PERSON] et al. conducted ionospheric imaging using a global positioning system (GPS) and low earth orbit (LEO) satellites [5]. A new method based on a residual minimization training neural network (RMTNN) was reported by [PERSON] et al. to reconstruct 3D electron density distribution using GPS and ionosonde observation data [6]. More research about the development of voxel-based computerized ionospheric tomography (CIT) technology based on global navigation satellite system (GNSS) ground receivers was introduced by [PERSON] et al. [7]. Algebraic reconstruction technology (ART) [2; 8] and multiplicative algebraic reconstruction technology (MART) [9; 10] are voxel-based methods that always adopt iterative reconstruction algorithms, and both are widely used techniques in CIT [11]. In both ART and MART iteration process, the coefficient matrix and the initial value of electron density are two main factors that can affect the achievement of CIT. From the point of view of the iterative formula, all attempts to achieve better 3D CIT are aimed at improving the rank of the coefficient matrix and the initial value. The coefficient matrix is a matrix of interception length of every signal ray in every voxel within the reconstruction area, and it usually is low-ranked, which will cause the ill-posed problem in CIT [12].