Fast Noise Removal in Hyperspectral Images via Representative Coefficient Total Variation

Mining structural priors in data is a widely recognized technique for hyperspectral image (HSI) denoising tasks, whose typical ways include model-based methods and data-based methods. The model-based methods have good generalization ability, while the runtime can hardly meet the fast processing requirements of the practical situations due to the large size of an HSI ${\mathbf {X}}\in \mathbb {R}^{\textrm {MN}\times B}$ . For the data-based methods, they perform relatively fast on new test data once they have been trained. However, their generalization ability is always insufficient. In this article, we propose a fast model-based approach via a novel regularizer named the representative coefficient total variation (RCTV) to simultaneously characterize the low-rank and local smooth properties. The RCTV regularizer is proposed based on the observation that the representative coefficient matrix ${\mathbf {U}}\in \mathbb {R}^{\textrm {MN}\times R} (R\ll B)$ obtained by orthogonally transforming the original HSI ${\mathbf {X}}$ can inherit the strong local-smooth prior of ${\mathbf {X}}$ . Since $R/B$ is very small, the model based on the RCTV regularizer has lower time complexity. In addition, we find that the representative coefficient matrix ${\mathbf {U}}$ is robust to noise, and thus, the RCTV regularizer can somewhat promote the robustness of the HSI denoising model. Extensive experiments on mixed noise removal demonstrate that the proposed method realizes a perfect compromise between denoising performance and denoising speed compared with other state-of-the-art methods. Remarkably, the denoising speed of our proposed method outperforms all competing model-based techniques and is comparable with the deep learning-based approaches. The code of our algorithm is released at https://github.com/andrew-pengjj/rctv.git .