Reducing the dimension of local descriptors in images is useful to perform pixels comparison faster. We show here that, for enhancing and optimising the computation of the NL-means denoising filter, image patches can be favourably replaced by a vector of spatial derivatives (local jet), to compute the similarity between pixels. First, we present the basic, limited range implementation, and compare it with the original NL-means. We use a fast estimation of the noise variance to automatically adjust the main parameter of the filter. Next, we present an unlimited range implementation using nearest neighbours search in the local jet space, based on a binary search tree representation.