A Novel Truncated Capped Norm Regularization Method for Hyperspectral Image Denoising

Hyperspectral image (HSI) denoising is a critical yet challenging task. While low-rank tensor decomposition methods, such as tensor ring decomposition (TRD), have shown promise in capturing the intrinsic correlations of HSIs, existing TRD-based approaches often rely on simplistic nuclear norm regularizations, leading to suboptimal noise removal or over-smoothing of details. To address these limitations, this letter proposes a novel Hybrid Capped Truncated Nuclear Norm -regularized Tensor Ring Decomposition (HTCN-TRD) framework for HSI denoising. Specifically, the HTCN-TRD model introduces a hybrid regularization into the TRD framework to flexibly balance low-rankness and sparsity while preserving structural integrity. An efficient optimization algorithm is developed under the alternating direction method of multipliers (ADMM) framework, with theoretical convergence guarantees. Extensive experiments on synthetic and real-world datasets demonstrate that HTCN-TRD outperforms state-of-the-art methods in both quantitative metrics and visual quality.