<p>In this work, a new nonlocal means filter for single-look speckled data using the Shannon and Rényi entropies is proposed. The measure of similarity between a central window and patches of the image is based on a statistical test for comparing if two samples have the same entropy and hence have the same distribution.</p><p>The results are encouraging, as the filtered image has better signal-to-noise ratio, it preserves the mean, and the edges are not severely blurred.</p>