2017 **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…

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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,…”

confidence: 99%

“…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,…”

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.…”

confidence: 99%