GEO Spatial Correlation SAR Imaging Framework Using MBO2D-SC Algorithm for Sea Surface Wave Imaging under Prolonged Synthetic Aperture Time

Sea surface waves provide critical information about wind patterns, ocean currents, and underwater topography. Geosynchronous orbit synthetic aperture radar (GEO SAR) is particularly well-suited for large-scale, continuous monitoring of sea surface waves due to its wide imaging coverage and persistent observation capabilities. Nevertheless, prolonged synthetic aperture durations in GEO SAR systems amplify decorrelation artifacts induced by the spatially heterogeneous and temporally evolving nature of wave motions, posing significant challenges for accurate imaging. Existing GEO SAR moving target imaging techniques rely on analyzing time-frequency signatures to distinguish moving objects from the background. These approaches work well for high-contrast targets such as vessels but are less effective for sea surface waves, where motion is distributed across the entire scene. To address this challenge, this study presents the geosynchronous orbit spatial correlation SAR (GEOSC-SAR) framework, a novel imaging framework that integrates model-based optimized 2-D spatial correlation (MBO2D-SC). Three key innovations drive our methodology: 1) a blockwise first-order two-dimensional (BFOTD) kinematic model that parameterizes space-variant wave velocity and acceleration fields; 2) the MBO2D-SC algorithm that dynamically computes phase correction coefficients through adaptive spatial correlation processing; and 3) a closed-loop optimization architecture combining genetic algorithm-driven parameter estimation with a custom wave imaging quality evaluation factor. The framework establishes a self-consistent correction mechanism where motion parameter refinement enhances correlation restoration, while phase compensation reduces residual errors. We analyzed GEOSC-SAR from multiple aspects, including a sensitivity analysis to precisely assess the influence of wind speed and wave amplitude on imaging, imaging performance under superimposed flow fields, the exploration of applications for high-wavenumber truncation mitigation, and computational efficiency analysis. Numerical simulations demonstrate that GEOSC-SAR achieves sub-13% relative error (8.3% in image contrast, 7.6% in grayscale modulation, and 12.1% in grayscale modulation balance) compared to original wave surfaces, outperforming existing methods. It demonstrates robustness across conditions (2-12-m/s wind speeds and 0.5-4.5-m wave amplitudes), with superior imaging at high wave amplitudes and low wind speeds, effectively handles superimposed flow fields, and accurately reconstructs wave spectrum in low-wavenumber regions while improving spectrum reconstruction in high-wavenumber regions versus existing methods. Despite increased computational complexity, efficiency enhancements via leveraging temporal patterns in sea surface motion are underway for large-scale, real-time sea surface monitoring.