Hyperspectral image (HSI) denoising is a significant preprocessing step to improve the performance of subsequent applications. Recently, HSI denoising methods using low rank representation and sparse coding have attracted much attention. In the HSI, there exists strong local correlations between spectral signatures within each full-band patch (FBP), i.e., the subcube containing the same area of all spectral bands, which suggests that spectral signatures within a clean FBP can be represented by

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... small number of bases. Denoising nonlocal similar FBPs jointly is beneficial as extra structure information is brought by the spatial self-similarity. However, there may exist variations among nonlocal similar FBPs and these variations need to be considered. Therefore, we propose a novel HSI denoising method based on group sparse nonnegative matrix factorization (GSNMF). In GSNMF, spectral signatures from nonlocal similar FBPs are assumed to be represented by a small number of bases and the coefficients of linear combination are sparse in nature. With the group sparse regularization term, spectral signatures within an FBP share a common set of bases for reconstruction, indicating the strong local correlation. Spectral signatures across different nonlocal similar FBPs partially share a set of bases, which means that each of them may remain some non-shared bases. Thus, both nonlocal correlation and variation is considered. The effectiveness of the proposed method is validated in both synthetic and real hyperspectral datasets.