Intracluster Structured Low-Rank Matrix Analysis Method for Hyperspectral Denoising

Hyperspectral images (HSIs) denoising aims at eliminating the noise generated during the acquisition and transmission of HSIs. Since denoising is an ill-posed problem, utilizing proper knowledge of HSIs as regularization is essential for a good denoiser. Many HSI denoising methods have been proposed to leverage various prior knowledge, e.g., total variation, sparsity, and so on. Among those knowledge, a low-rank property has been shown to be effective for HSI denoising since it has the ability to deal with the missing values. However, most existing low-rank methods seldom consider mining the useful structures inside the low-rank matrix for a better denoising result. In addition, the rank number needs to be assigned manually. To address these problems, we propose an intracluster structured low-rank matrix analysis method for HSI denoising. First, we divide the original HSI into some clusters by taking advantages of both local similarity and nonlocal similarity structures, with which the resulted clusters are simpler and show more obvious low-rank property. Second, with singular value decomposition on the low-rank matrix in each cluster, the structured sparsity is modeled among the singular values to capture the structure of the low-rank matrix. Finally, an efficient optimization method is proposed to learn the structured sparsity adaptively from the data, as well as to inversely estimate the latent clean HSI from the noisy counterpart. The proposed method can not only obtain better denoising results compared with the-state-of-the-art methods but also automatically determine the rank number. Extensive experimental results demonstrate the effectiveness of the proposed method.