Edge-adaptive curvature-based regularization for robust blind image restoration

Blind image deblurring remains challenging in computational imaging due to the unknown blur kernel, often relying on complex priors or heuristic edge selection. This study presents a novel gradient sparsity framework guided by curvature for robust blind image deblurring. By extracting curvature information from image gradients, we design an efficient L₁ regularization term to enhance edge retention and image sharpness while minimizing computational overhead. A spatially adaptive edge-weighting function is introduced to dynamically adjust regularization intensity according to local image characteristics, ensuring robust performance across various regions. The optimization problem is decomposed into two convex sub-problems, which are efficiently solved in closed form via the half-quadratic splitting algorithm. Comprehensive experiments on benchmark datasets demonstrate that our approach outperforms cutting-edge methods in both peak signal-to-noise ratio and structural similarity, producing sharper images with reduced artifacts. This framework provides a computationally efficient and robust solution for blind deblurring, especially in resource-constrained environments. © 2025 Elsevier B.V.