A New Neural Network Approach Integrating Prior Knowledge for Dynamic Three-Dimensional Tomographic Reconstruction of the Earth's Magnetosphere

The energy transfer and coupling between the solar wind and Earth’s magnetosphere are central issues in geophysics. Solar wind charge exchange (SWCX) generates soft X-ray emissions (0.1–2 keV) through interactions between highly charged solar wind ions and neutral atoms in the terrestrial exosphere, providing a new means to globally observe magnetospheric structures. The Solar wind–Magnetosphere–Ionosphere Link Explorer (SMILE), jointly developed by the Chinese Academy of Sciences (CAS) and the European Space Agency (ESA), will carry the Soft X-ray Imager (SXI) and is scheduled for launch soon. SXI will, for the first time, enable continuous global imaging of key large-scale magnetospheric structures, including the bow shock, magnetopause, and cusps, through multi-angle scanning observations.

Three-dimensional tomographic reconstruction requires multi-angle projection data to invert line-of-sight radiative integrals and recover volumetric emissivity distributions. Unlike conventional surface-based imaging, magnetospheric soft X-ray emissions originate from optically thin volume emission produced by SWCX, and their line-of-sight integration conforms to the Radon transform framework. Each SXI pixel represents the integral of X-ray emissivity along its viewing direction. In principle, three-dimensional emissivity distributions can be reconstructed by solving large linear systems. However, the orbital geometry of SMILE severely limits angular coverage, resulting in sparse projections and a strongly ill-posed inverse problem. In addition, the nominal SXI imaging cadence of approximately 5 minutes limits the ability to resolve rapid magnetospheric dynamics.

To address these challenges, this study proposes a progressive deep-learning-driven framework for high-precision three-dimensional and dynamic magnetospheric reconstruction from limited-angle SXI observations. First, a Deep Sparse Coding Estimation Network (DSCE-Net), combining deep learning with sparse representation theory, is developed to suppress instrumental and background noise, significantly improving signal-to-noise ratio and preserving structural integrity in the X-ray images. Second, to compensate for missing projection data caused by restricted viewing angles, a three-dimensional conditional Generative Adversarial Network (3D-CGAN) incorporating multi-scale feature extraction and magnetospheric physical prior constraints is introduced to generate physically consistent projections, effectively alleviating the ill-posedness of limited-angle tomography. Based on the completed projection set, iterative tomographic algorithms are then applied to reconstruct high-accuracy static three-dimensional emissivity distributions, substantially improving the localization and morphology of key structures such as the bow shock and magnetopause. Furthermore, to overcome temporal resolution limitations, an Adaptive X-ray Dynamic Image Estimator (AXDI-Estimator) is designed to fuse 1-minute OMNI solar wind parameters with low-cadence SXI observations, driving simulations to generate continuous minute-scale X-ray image sequences and enabling dynamic tomographic reconstruction with spatiotemporal consistency.

Numerical validation using MHD and Jorgensen–Sun models demonstrates that the proposed framework significantly outperforms traditional methods in image quality, structural fidelity, and dynamic tracking capability. The subsolar magnetopause standoff distance error is constrained within 0–0.4 Re under nominal conditions and remains below 2.4 Re under extreme solar wind conditions. The results meet SMILE mission requirements for spatial resolution, localization accuracy, and dynamic reconstruction, providing an effective solution for three-dimensional dynamic imaging of space plasmas under limited observational geometries.