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We propose a new structure-adaptive anisotropic filtering scheme based on the local structure tensor. We utilize the local structure tensor to measure image local anisotropic features and estimate the orientation of image structures, and these informations are then used to shape and control the anisotropic Gaussian kernel. The proposed filter denoises noisy images while image structures such as corners, junctions and edges are well preserved. Our experimental results clearly show that the proposed scheme outperforms some other adaptive filters such as the adaptive Wiener filter, Weickertpsilas edge enhancing diffusion (EED) filter and Yang's structure-adaptive anisotropic filter in terms of both mean square errors (MSE) and visual quality, and the one based on the nonlinear structure tensor (NLST) can give much better denoising results than that based on the linear structure tensor (LST), particularly in edge regions.