Fast Noise Removal in Hyperspectral Images via Representative Coefficient Total Variation

TL;DR

This paper introduces a fast hyperspectral image denoising method using a novel regularizer called RCTV, which leverages low-rank and local smoothness priors through representative coefficients, achieving superior speed and performance.

Contribution

The paper proposes the RCTV regularizer based on representative coefficients, enabling faster and more robust hyperspectral image denoising compared to existing methods.

Findings

Outperforms state-of-the-art denoising methods in accuracy.

Achieves faster denoising speed comparable to deep learning approaches.

Demonstrates robustness to mixed noise in hyperspectral images.

Abstract

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.