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Among all enhancement techniques being developed over the past two decades, anisotropic diffusion has received much attention and experienced significant developments, with promising results and applications in various specific domains. The elegant property of the technique is that it can enhance images by reducing undesirable intensity variability within the objects in the image, while improving SNR and enhancing the contrast of the edges in scalar and, more recently, vector-valued images, such as color, multispectral, and hyperspectral imagery. In this paper, we present an alternative hyperspectral anisotropic diffusion scheme that takes into account the recent advances and the specificities of hyperspectral remote sensing. In addition, the proposed anisotropic diffusion algorithm can improve the classification accuracy of hyperspectral imagery by reducing the spatial and spectral variability of the image, while preserving the edges of objects. It is also revealed that the additive operator splitting scheme of our method can increase computer efficiency. Qualitative experiments, based on a real hyperspectral remote sensing image, show significant improvements in visual effects when using our method. Quantitative analyses, based on classification accuracies, confirm the superiority and validity of the proposed diffusion algorithm.