A Unified Framework for the Restoration of Images Corrupted by Additive White Noise

  • Alessandro Lanza
  • Federica Sciacchitano
  • Serena MorigiEmail author
  • Fiorella Sgallari
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10302)


We propose a robust variational model for the restoration of images corrupted by blur and the general class of additive white noises. The solution of the non-trivial optimization problem, due to the non-smooth non-convex proposed model, is efficiently obtained by an Alternating Directions Method of Multipliers (ADMM), which in particular reduces the solution to a sequence of convex optimization sub-problems. Numerical results show the potentiality of the proposed model for restoring blurred images corrupted by several kinds of additive white noises.


Variational image restoration Additive white noise Total Variation Non-convex non-smooth optimization ADMM 



This work was supported by the “National Group for Scientific Computation (GNCS-INDAM)” and by ex60% project by the University of Bologna “Funds for selected research topics”.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Alessandro Lanza
    • 1
  • Federica Sciacchitano
    • 2
  • Serena Morigi
    • 1
    Email author
  • Fiorella Sgallari
    • 1
  1. 1.Department of MathematicsUniversity of BolognaBolognaItaly
  2. 2.Department of MathematicsUniversity of GenovaGenovaItaly

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