A Differential Lucy–Richardson–Rosen Algorithm for Near-Diffraction-Limited Image Restoration Guided by Wavefront Sensing

The Lucy–Richardson–Rosen algorithm (LR2A) is widely used in astronomical image restoration. However, its performance degrades under large optical aberrations and high noise levels, often leading to slow convergence or failure. To address these limitations, we propose a Differential Lucy–Richardson–Rosen Algorithm (D-LR2A) that enhances robustness and convergence speed. A Hartmann–Shack wavefront sensor is integrated into the imaging system to measure wavefront aberrations and accurately estimate the spatially varying point spread function (PSF). This enables precise non-blind deconvolution for ground- or space-based telescopes with significant optical distortions. Both numerical simulations and experimental results demonstrate that D-LR2A effectively restores images degraded by severe aberrations and noise, outperforming conventional LR2A in restoration quality and computational efficiency. The method is particularly suitable for real-time or near-real-time applications in astronomical observation, where high-fidelity image recovery is critical. This work presents a practical advancement in computational imaging techniques for modern astronomical instrumentation.