2012/07/31 by Kunal N. Chaudhury, K. N. Chaudhury, Amit Singer +1
Computer Science · Engineering · Mathematics · #Advanced Statistical Methods and Models #Computational complexity theory #Euclidean distance #Euclidean distance matrix #Euclidean geometry #Image and Signal Denoising Methods #Median #Noise (video) #Noise reduction #Outlier #Simple (philosophy) #Sparse and Compressive Sensing Techniques #cs.CV #cs.DS
paper · pdf · doi:10.1109/lsp.2012.2217329
published as IEEE Signal Processing Letters, vol. 19(11), pp. 745 - 748, 2012 · 6 figures, 1 table
arxiv created 2012/08/24 · openalex publication_date 2012/09/05 · arxiv updated 2015/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this letter, we note that the denoising performance of Non-Local Means (NLM) can be improved at large noise levels 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.