  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 cannot meet the fast processing
requirements of the practical situations due to the large size of an HSI data $
\mathbf{X} \in \mathbb{R}^{MN\times B}$. For the data-based methods, they
perform very fast on new test data once they have been trained. However, their
generalization ability is always insufficient. In this paper, we propose a fast
model-based HSI denoising approach. Specifically, we propose a novel
regularizer named 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 $\mathbf{U}\in\mathbb{R}^{MN\times R} (R\ll B)$ 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 HSI
denoising model based on the RCTV regularizer has lower time complexity.
Additionally, 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 the superiority of the proposed method both in denoising
performance and denoising speed compared with other state-of-the-art methods.
Remarkably, the denoising speed of our proposed method outperforms all the
model-based techniques and is comparable with the deep learning-based
approaches.
