Nonlocal Low-Rank Residual Modeling for Hyperspectral Image Mixed Noise Removal

Hyperspectral image (HSI) denoising remains a critical challenge due to noise corruption during acquisition. While nonlocal low-rank (LR) tensor methods leverage spatial–spectral correlations, they usually fail under heavy or complex noise, as directly estimating LR tensors from noisy observations usually leads to residual noise accumulation. To address this limitation, we propose a novel nonlocal low-rank residual (NLRR) approach, which reformulates LR tensor recovery as a progressive residual minimization problem. Unlike conventional methods that exclusively approximate LR tensors directly from degraded observations, the proposed NLRR approach iteratively refines the latent LR tensor structure by minimizing the rank residual, thereby decoupling noise suppression from tensor approximation. This residual-driven framework uniquely integrates two complementary priors: (1) a nonlocal LR residual prior that exploits spatial self-similarity, and (2) a global spectral LR prior that suppresses spectral redundancy. To generalize the proposed NLRR approach to real-world scenarios with mixed noise, we develop the NLRR-robust principal component analysis (NLRR-RPCA) framework, which incorporates the LR residual along with global spectral LR and sparse tensor priors for mixed noise removal. Additionally, to ensure both numerical stability and computational tractability, we develop an adaptive rank-adjusted alternating minimization algorithm, which dynamically adjusts the ranks of the estimated tensors to better handle different noise scenarios. Extensive experiments on both simulated and real HSI datasets demonstrate that our proposed NLRR approach outperforms numerous popular or state-of-the-art methods in both quantitative evaluation and visual perception.