Non-local euclidean medians

Kunal N. Chaudhury, Amit Singer

Research output: Contribution to journalArticlepeer-review

65 Scopus citations


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.

Original languageEnglish (US)
Article number6295644
Pages (from-to)745-748
Number of pages4
JournalIEEE Signal Processing Letters
Issue number11
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Applied Mathematics
  • Electrical and Electronic Engineering


  • Euclidean median
  • Weiszfeld algorithm
  • image denoising
  • iteratively reweighted least squares (IRLS)
  • non-local means


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