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In this paper, the anisotropic diffusion for image denoising is considered. A new method to construct diffusion tensors is proposed. The tensors obtained by our approach depend on four directional derivatives of the intensity of an image, and hence they are adaptively determined by local image structure. It is shown that the proposed diffusion filter is isotropic in the interior of a region, whereas it is anisotropic at edges. This property of tensors allows us to efficiently remove noise in an image, particularly noise at edges. Several numerical experiments are conducted on both synthetic and real images.