A Hybrid Optimization Approach Combining PIO and L-BFGS for Phase Diversity Image Restoration

Phase diversity technology involves obtaining in-focus and defocused images to establish an optimization model for solving the optimal solution of wavefront aberrations. However, existing nonlinear optimization algorithms often suffer from issues such as being trapped in local minima, slow convergence, and poor restoration performance under noise interference. To address these challenges, this paper proposes a hybrid PIO-L-BFGS algorithm that combines the pigeon-inspired optimization (PIO) algorithm with the L-BFGS algorithm for wavefront aberration optimization in phase diversity image restoration. To evaluate the impact of noise on restoration performance, experiments were conducted under various noise conditions, comparing the performance of PIO, L-BFGS, and PIO-L-BFGS. The results demonstrate that PIO-L-BFGS significantly outperforms L-BFGS in high-noise scenarios, exhibiting superior robustness and optimization capability.