This paper introduces a novel variational framework for image deblurring that leverages a spatially adaptive coupling of regularization terms. The proposed model integrates an edge-adaptive Total Variation (TV) with a non-convex \(L_1/L_2\) gradient-based ratio through a unified spatio-structural mechanism. This hybrid approach enables a flexible diffusion process that effectively suppresses noise in homogeneous regions while mitigating over-smoothing near discontinuities. To solve the resulting non-convex and non-smooth optimization problem, we develop a high-performance numerical scheme based on the Alternating Direction Method of Multipliers (ADMM). Our solver integrates a Hybrid Conjugate Gradient with Anderson Acceleration (HCGAA) for primal updates and the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) for non-smooth subproblems. Crucially, we establish a formal proof of global convergence to a stationary point by leveraging the Kurdyka-Łojasiewicz (KŁ) framework for semi-algebraic functions. Numerical experiments on blurred and noisy images demonstrate that the proposed ADMM–HCGAA–FISTA strategy consistently outperforms state-of-the-art methods, providing superior edge preservation and higher quantitative metrics.
