A Kriging Interpolation-enhanced MART for Non-uniform Observational Data in Geosynchronous SAR-based Computerized Ionospheric Tomography

The ionosphere affects spaceborne synthetic aperture radar (SAR) and Global Navigation Satellite System (GNSS) missions, and reflects solar activity and Earth magnetic field, making its monitoring essential. Computerized ionospheric tomography (CIT) is a key technique for this application, using total electron content (TEC) along signal paths to reconstruct electron density. Unlike GNSS-based CIT using ground receivers, and low Earth orbit (LEO) SAR-based CIT limited by coverage and revisit time, geosynchronous (GEO) SAR-based CIT directly reconstructs ionospheric electron density using TEC from ground permanent scatterer (PS) points. The high orbit, wide coverage, and short revisit time of GEO SAR enable observation of the full vertical ionosphere structure and larger areas with better time resolution. However, GEO SAR-based CIT faces challenges due to the non-uniform distribution of PS points, leading to significant spatial differences in tomographic quality, making it difficult to provide reliable data support for subsequent research. To address this, a Kriging interpolation-enhanced multiplicative algebraic reconstruction technique (MART) is proposed. This proposed method embeds Kriging interpolation into the conventional MART iteration, utilizing the spatial correlation of electron density to compensate for voxels with sparse TEC data, while still incorporating the voxel's own TEC data. This improves the electron density reconstruction accuracy and robustness. Finally, both simulation and real GNSS data experiments demonstrate that the proposed method significantly improves reconstruction in data-sparse voxels and reduces spatial differences in electron density estimation quality compared to conventional method, albeit with a slight trade-off in accuracy for a small number of voxels.