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Anisotropic diffusion in the hypercube is a powerful image restoration and enhancement tool for hyperspectral imagery. Processing hyperspectral images requires special attention to accuracy, in order to preserve the high spectral precision that characterizes this kind of data. Here, we propose alternative implementations of the method with specific regard to the numerical accuracy of the solution in strict sense. We propose and describe how to apply rotationally invariant finite differences and a local filtering scheme. We also test and discuss their performance on several hyperspectral images.