Diffusion-Prior Split Gibbs Sampling for Synthetic Aperture Radar Imaging under Incomplete Measurements

Synthetic aperture radar (SAR) imaging plays a critical role in all-weather, day-and-night remote sensing, yet reconstruction is often challenged by noise, undersampling, and complex scattering scenarios. Conventional methods, including matched filtering and sparsity-based compressed sensing, are limited in capturing intricate scene structures and frequently suffer from artifacts, elevated sidelobes, and loss of fine details. Recent diffusion models have demonstrated superior capability in representing high-order priors; however, existing diffusion-based SAR methods still yield degraded reconstructions due to oversimplified likelihood approximations in guided sampling. In this work, we propose a diffusion-driven split Gibbs sampling framework for SAR reconstruction, rigorously integrating measurement fidelity with learned diffusion priors. By alternately performing likelihood- and prior-driven updates via proximal sampling, this method ensures progressive convergence toward the true posterior while fully leveraging the expressive power of diffusion priors. Extensive experiments on simulated and Sentinel-1A datasets demonstrate substantial performance improvements: over 7 dB average PSNR gain in simulations, along with significant sidelobe suppression (MPLSR +2.96 dB, MISLR +11.5 dB) with respect to the best baseline result. On real-world Sentinel-1A data, the method achieves an average PSNR gain of 1.6 dB while effectively reducing artifacts and preserving scene details, including ridges, edges, and fine textures. These results underscore the potential of the adapted framework as a robust and generalizable solution for high-fidelity SAR imaging across diverse sensing scenarios.