  In this letter, we note that the denoising performance of Non-Local Means
(NLM) at large noise levels can be improved by replacing the mean by the
Euclidean median. We call this new denoising algorithm the Non-Local Euclidean
Medians (NLEM). At the heart of NLEM is the observation that the median is more
robust to outliers than the mean. In particular, we provide a simple geometric
insight that explains why NLEM performs better than NLM in the vicinity of
edges, particularly at large noise levels. NLEM can be efficiently implemented
using iteratively reweighted least squares, and its computational complexity is
comparable to that of NLM. We provide some preliminary results to study the
proposed algorithm and to compare it with NLM.
