Journal of Mathematical Imaging and Vision

, Volume 61, Issue 4, pp 458–481 | Cite as

RNLp: Mixing Nonlocal and TV-Lp Methods to Remove Impulse Noise from Images

  • Julie Delon
  • Agnès DesolneuxEmail author
  • Camille Sutour
  • Agathe Viano


We propose a new variational framework to remove random-valued impulse noise from images. This framework combines, in the same energy, a nonlocal \(L^p\) data term and a total variation regularization term. The nonlocal \(L^p\) term is a weighted \(L^p\) distance between pixels, where the weights depend on a robust distance between patches centered at the pixels. In a first part, we study the theoretical properties of the proposed energy, and we show how it is related to classical denoising models for extreme choices of the parameters. In a second part, after having explained how to numerically find a minimizer of the energy thanks to primal-dual approaches, we show extensive denoising experiments on various images and noise intensities. The denoising performance of the proposed methods is on par with state-of-the-art approaches, and the remarkable fact is that, unlike other successful variational approaches for impulse noise removal, they do not rely on a noise detector.


Image denoising Impulse noise Variational methods Patch-based methods Convex optimization 



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Authors and Affiliations

  1. 1.MAP5Université Paris DescartesParisFrance
  2. 2.CMLA, CNRSENS Paris-SaclayCachanFrance
  3. 3.Deloitte FranceParisFrance

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