2017
DOI: 10.1137/16m1080781
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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 w… Show more

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Cited by 33 publications
(34 citation statements)
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“…In this section we briefly review the Optimal Weights Filter in order to adapt it for removing the impulse noise. Based on similarities among local patches, the Optimal Weights Filter [25] was initially introduced to deal with the Gaussian noise model,…”
Section: 2mentioning
confidence: 99%
See 4 more Smart Citations
“…In this section we briefly review the Optimal Weights Filter in order to adapt it for removing the impulse noise. Based on similarities among local patches, the Optimal Weights Filter [25] was initially introduced to deal with the Gaussian noise model,…”
Section: 2mentioning
confidence: 99%
“…The Optimal Weights Filter is constructed by minimizing a tight bound of the quadratic risk. It is shown in [25] that the optimal weights are given by the formula (6) via the triangular kernel (7). This minimization procedure gives also an exact formula for the bandwidth a as stated below.…”
Section: 2mentioning
confidence: 99%
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