  A new image denoising algorithm to deal with the additive Gaussian white
noise model is given. Like the non-local means method, the filter is based on
the weighted average of the observations in a neighborhood, with weights
depending on the similarity of local patches. But in contrast to the non-local
means filter, instead of using a fixed Gaussian kernel, we propose to choose
the weights by minimizing a tight upper bound of mean square error. This
approach makes it possible to define the weights adapted to the function at
hand, mimicking the weights of the oracle filter. Under some regularity
conditions on the target image, we show that the obtained estimator converges
at the usual optimal rate. The proposed algorithm is parameter free in the
sense that it automatically calculates the bandwidth of the smoothing kernel;
it is fast and its implementation is straightforward. The performance of the
new filter is illustrated by numerical simulations.
