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The anisotropic diffusion techniques are in general efficient to preserve image edges when they are used to reduce noise. However, they are not very effective to denoise those images that are corrupted by a high level of noise mainly for the lack of a reliable edge-stopping criterion in the partial differential equation (PDE). In this paper, a new algorithm is developed to tackle this problem. The main contribution of this paper is in the construction of a new regularization method for the PDE by using the over-complete dyadic wavelet transform (DWT). It proposes to perform anisotropic diffusion in the more stationary DWT domain rather than directly in the raw noisy image domain. In the DWT domain, since noise tends to decrease as the scale increases, at each scale, noise has less influence on the PDE than that in the raw noisy image domain. As a result, the edge-stopping criterion and other partial derivative measurements in the PDE become more reliable. Furthermore, there is no need to do Gaussian smoothing or any other smoothing operations. Experiment results show that the proposed algorithm can significantly reduce noise while preserving image edges. [ABSTRACT FROM AUTHOR]