A generalization of non-local means via kernel regression

13 years 6 months ago

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The Non-Local Means (NLM) method of denoising has received considerable attention in the image processing community due to its performance, despite its simplicity. In this paper, we show that NLM is a zero-th order kernel regression method, with a very specific choice of kernel. As such, it can be generalized. The original method of NLM, we show, implicitly assumes local constancy of the underlying image data. Once put in the context of kernel regression, we extend the existing Non-Local Means algorithm to higher orders of regression which allows us to approximate the image data locally by a polynomial or other localized basis of a given order. These extra degrees of freedom allow us to perform better denoising in texture regions. Overall the higher order method displays consistently better denoising capabilities compared to the zero-th order method. The power of the higher order method is amply illustrated with the help of various denoising experiments.

Priyam Chatterjee, Peyman Milanfar

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