SURE-Based Non-Local Means

Non-local means (NLM) provides a powerful framework for denoising. However, there are a few parameters of the algorithm-most notably, the width of the smoothing kernel-that are data-dependent and difficult to tune. Here, we propose to use Stein´s unbiased risk estimate (SURE) to monitor the mean square error (MSE) of the NLM algorithm for restoration of an image corrupted by additive white Gaussian noise. The SURE principle allows to assess the MSE without knowledge of the noise-free signal. We derive an explicit analytical expression for SURE in the setting of NLM that can be incorporated in the implementation at low computational cost. Finally, we present experimental results that confirm the optimality of the proposed parameter selection.