Efficient Chebyshev-optimized ADMM algorithm for image restoration using Nesterov acceleration

Abstract In this paper, we propose a non-convex total variation image restoration model based on the hyper-Laplacian gradient prior. The proposed model enhances sparsity while preserving image edges. The regularization term is defined as a linear combination of the ℓ p quasi-norm and the squared ℓ 2 norm. It also balances the sparsity promotion in the image gradients and the smoothness in the restored image. We develop an efficient numerical algorithm using the alternating direction method of multipliers (ADMM) combined with a Chebyshev iterative scheme. The proposed method converges rapidly and provides an accurate solution. To further enhance the overall convergence, the Nesterov acceleration method is incorporated into the proposed ADMM framework. We also establish theoretical convergence analysis of the proposed method. Extensive experiments are conducted on grayscale images with varying resolutions. Different blur kernels and noise levels are considered to show the robustness of the proposed methods. The results indicate that the proposed method achieves superior performance among the compared methods, with improved edge preservation and faster convergence.