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Hyperspectral image (HSI) denoising is an essential preprocess step to improve the performance of subsequent applications. For HSI, there is much global and local redundancy and correlation (RAC) in spatial/spectral dimensions. In addition, denoising performance can be improved greatly if RAC is utilized efficiently in the denoising process. In this paper, an HSI denoising method is proposed by jointly utilizing the global and local RAC in spatial/spectral domains. First, sparse coding is exploited to model the global RAC in the spatial domain and local RAC in the spectral domain. Noise can be removed by sparse approximated data with learned dictionary. At this stage, only local RAC in the spectral domain is employed. It will cause spectral distortion. To compensate the shortcoming of local spectral RAC, low-rank constraint is used to deal with the global RAC in the spectral domain. Different hyperspectral data sets are used to test the performance of the proposed method. The denoising results by the proposed method are superior to results obtained by other state-of-the-art hyperspectral denoising methods.