Non-local means and optimal weights for noise removal

Abstract : In this paper, a new denoising algorithm to deal with the additive white Gaussian noise model is described. In the line of work of the Non-Local means approach, we propose an adaptive estimator based on the weighted average of observations taken in a neighborhood with weights depending on the similarity of local patches. The idea is to compute adaptive weights that best minimize an upper bound of the pointwise L 2 risk. In the framework of adaptive estimation, we show that the " oracle " weights are optimal if we consider triangular kernels instead of the commonly-used Gaussian kernel. Furthermore, we propose a way to automatically choose the spatially varying smoothing parameter for adaptive denoising. Under conventional minimal regularity conditions, the obtained estimator converges at the usual optimal rate. The implementation of the proposed algorithm is also straightforward and the simulations show that our algorithm improves significantly the classical NL-means and is competitive when compared to the more sophisticated NL-means filters both in terms of PSNR values and visual quality.
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SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2017
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Soumis le : lundi 21 août 2017 - 19:22:27
Dernière modification le : jeudi 29 novembre 2018 - 16:51:31

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Qiyu Jin, Ion Grama, Charles Kervrann, Quansheng Liu. Non-local means and optimal weights for noise removal. SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2017. 〈hal-01575918〉

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