PCC-GLR: Pearson correlation coefficient-based graph Laplacian regularization for hyperspectral image denoising

Recently, the graph Laplacian regularization (GLR) has achieved rapid development in the hyperspectral image denoising task, which transforms the hyperspectral image from the original space into a low-dimensional space to better eliminate noise. However, existing spectral graph regularization methods typically regard each spectral band as a vertex and calculate the similarity relationship between each pair of spectral bands by their corresponding index difference. Although this strategy is easy to operate, it is difficult to accurately explore the similarity relationships of the spectral bands. To address this issue, we propose a Pearson correlation coefficient-based graph Laplacian regularization (PCC-GLR), which, to the best of our knowledge, is the first spectral Laplacian regularizer constructed using the Pearson correlation coefficient for hyperspectral image denoising. In particular, we apply the Pearson correlation coefficient instead of the index difference of spectral bands to better capture the similarity relationship between each pair of spectral bands. Compared to the index difference, the Pearson correlation coefficient can better explore the linear correlation between spectral bands to better capture the spectral correlation. In addition, we incorporate mean normalization of the vertex signals when constructing the Laplacian regularization to adapt to the computation rule of the Pearson correlation coefficient. Moreover, we design both global and local spectral Pearson graphs. For the global spectral Pearson graph, we regard each complete spectral band as a vertex and calculate the Pearson correlation coefficients of any pairs of complete spectral bands. For the local spectral Pearson graph, we divide the whole hyperspectral image into several scenes and calculate the Pearson correlation coefficients of any pairs of spectral bands for each scene independently. By combining the two spectral Pearson graphs, we can obtain an accurate adjacency weight matrix for each scene. The experimental results on four hyperspectral images show the superiority of the proposed PCC-GLR over some other traditional and advanced denoising methods. The code is available at: https://github.com/y12050608-code/PCC-GLR.git