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This paper introduces a novel perceptually adaptive approach to image denoising using anisotropic non-local means. In the classical non-local means image denoising approach, the value of a pixel is determined based on the weighted average of other pixels, where the weights are determined based on a fixed isotropically weighted similarity function between the local neighborhoods. In the proposed algorithm, we demonstrate that noticeably improved perceptual quality can be achieved through the use of adaptive anisotropically weighted similarity functions between local neighborhoods. This is accomplished by adapting the similarity weighing function in an anisotropic manner based on the perceptual characteristics of the underlying image content derived efficiently based on the Mexican Hat wavelet. Experimental results show that the proposed method can be used to provide improved perceptual quality in the denoised image both quantitatively and qualitatively when compared to existing methods.