Weighted Total Variation for Hyperspectral Image Denoising Based on Hyper-Laplacian Scale Mixture Distribution

Conventional total variation (TV) regularization methods based on Laplacian or fixed-scale Hyper-Laplacian priors impose uniform sparsity penalties on gradients. These uniform penalties fail to capture the heterogeneous sparsity characteristics across different regions and directions, often leading to the over-smoothing of edges and loss of fine details. To address this limitation, we propose a novel regularization Hyper-Laplacian Adaptive Weighted Total Variation (HLAWTV). The proposed regularization employs a proportional mixture of Hyper-Laplacian distributions to dynamically adapt the sparsity decay rate based on image structure. Simultaneously, the adaptive weights can be adjusted based on local gradient statistics and exhibit strong robustness in texture preservation when facing different datasets and noise. Then, we propose an hyperspectral image (HSI) denoising method based on the HLAWTV regularizer. Extensive experiments on both synthetic and real hyperspectral datasets demonstrate that our denoising method consistently outperforms state-of-the-art methods in terms of quantitative metrics and visual quality. Moreover, incorporating our adaptive weighting mechanism into existing TV-based models yields significant performance gains, confirming the generality and robustness of the proposed approach.