IHL-SC: A High-Likelihood-Constrained Spatial-Correlation Framework for Continuous GEOSC-SAR Imaging of Sea-Surface Waves

This study addresses continuous geosynchronous orbit (GEO) synthetic aperture radar (SAR) imaging through the formation of a temporally ordered, motion-compensated SAR-observable wave-pattern intensity image sequence over a selected beam-accessible ocean scene. The ultralong aperture integration amplifies motion-induced phase errors and azimuth decorrelation. GEO spatial-correlation SAR (GEOSC-SAR) based on model-based optimal 2-D spatial correlation (MBO2D-SC) enables single-frame focused imaging by optimizing blockwise motion parameters and synthesizing a motion-dependent spatial-correlation kernel for phase compensation. In continuous imaging of sea-surface waves, however, frame-to-frame motion evolution makes the previously optimized kernel mismatched for subsequent frames, leading to residual phase errors, spurious correlation responses, and temporal defocusing. Reoptimizing from a broad global domain at every frame avoids reuse-induced mismatch but incurs substantial computational cost and unstable convergence in a highly nonconvex landscape. We propose interframe high-likelihood spatial-correlation (iHL-SC) processing, a high-likelihood-constrained framework that converts framewise cold-start optimization into a closed-loop procedure in a time-variant blockwise first-order 2-D (TV-BFOTD) parameter space. iHL-SC represents interframe uncertainty using an evolving genetic-algorithm (GA) particle-set distribution and predicts a center-radius prior to construct a high-likelihood admissible region for each incoming frame. GA sampling and evolution are performed directly within this region, while any out-of-bound offspring are deterministically repaired via box projection to enforce hard-bound feasibility before signal-level evaluation. Based on the projected feasible state, we further develop MBO2D-HL-SC, which synthesizes a likelihood-conditioned spatial-correlation kernel to suppress mismatch-driven spurious responses. Beyond a Kalman-filter baseline, we develop PointGRU-Former to infer compact yet robust motion priors from historical particle-group evolution by combining Transformer-based global temporal modeling with PointGRU-based local aggregation. Experiments demonstrate improved multiframe focusing quality and processing efficiency with iHL-SC under the adopted geometry and controlled simulation settings and show that PointGRU-Former provides more accurate priors than competing predictors within the same iHL-SC pipeline.