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Images often contain noise due to imperfections in various image acquisition techniques. Noise should be removed from images so that the details of image objects (e.g., blood vessels, inner foldings, or tumors in the human brain) can be clearly seen, and the subsequent image analyses are reliable. With broad usage of images in many disciplines—for example, medical science—image denoising has become an important research area. In the literature, there are many different types of image denoising techniques, most of which aim to preserve image features, such as edges and edge structures, by estimating them explicitly or implicitly. Techniques based on explicit edge detection usually require certain assumptions on the smoothness of the image intensity surface and the edge curves which are often invalid especially when the image resolution is low. Methods that are based on implicit edge detection often use multiresolution smoothing, weighted local smoothing, and so forth. For such methods, the task of determining the correct image resolution or choosing a reasonable weight function is challenging. If the edge structure of an image is complicated or the image has many details, then these methods would blur such details. This article presents a novel image denoising framework based on local clustering of image intensities and adaptive smoothing. The new denoising method can preserve complicated edge structures well even if the image resolution is low. Theoretical properties and numerical studies show that it works well in various applications.

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This is an Accepted Manuscript of an Article published in Journal of Computational and Graphical Statistics, 2015, available online at: 10.1080/10618600.2013.870074

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