Adaptive Parameter Selection Scheme for Hybrid Variation-based Image Denoising Model

Regularization methods play a crucial role in addressing the ill-posedness of inverse problems in image denoising. The key to enhance denoising performance lies in the proper selection of regularization terms that effectively encode image priors and regularization parameters that align with the statistical characteristics of images. To tackle these challenges, this paper proposes a hybrid total variation denoising model, which integrates weighted total variation for edge preservation with higher-order total variation for smooth region preservation. The regularization parameter in the proposed model is adaptively determined using Morozov’s discrepancy principle, thereby improving the efficacy of denoising. Since the proposed model is convex and non-smooth, we employ the alternating direction method of multipliers (ADMM) to decompose the problem into computationally tractable subproblems. To enhance the robustness of ADMM, a strategy of norm error correction is introduced for primal variables and dual variables to refine the penalty parameters. Furthermore, since the proposed model and numerical algorithm eliminate the need for manual parameter tuning, they can be formulated as an unsupervised denoising framework based on algorithmic unfolding architecture. Extensive numerical experiments demonstrate that the proposed method not only outperforms several state-of-the-art techniques in overcoming the staircase effect and preserving local structural features but also exhibits competitive performance compared to representative deep learning-based denoising approaches.