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Nonlocal means and optimal weights for noise removal. (English) Zbl 1401.62100

Summary: In this paper, a new denoising algorithm to deal with the additive white Gaussian noise model is described. Following the nonlocal (NL) 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 significantly improves the classical NL means and is competitive when compared to the more sophisticated NL means filters, both in terms of peak signal-to-noise ratio values and visual quality.

MSC:

62H35 Image analysis in multivariate analysis
68U10 Computing methodologies for image processing

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AWS
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