An Adaptive Norm Algorithm for Image Restoration

  • Daniele Bertaccini
  • Raymond H. Chan
  • Serena Morigi
  • Fiorella Sgallari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6667)


We propose an adaptive norm strategy designed for the re-storation of images contaminated by blur and noise. Standard Tikhonov regularization can give good results with Gaussian noise and smooth images, but can over-smooth the output. On the other hand, L 1-TV (Total Variation) regularization has superior performance with some non-Gaussian noise and controls both the size of jumps and the geometry of the object boundaries in the image but smooth parts of the recovered images can be blocky. According to a coherence map of the image which is obtained by a threshold structure tensor, and can detect smooth regions and edges in the image, we apply L 2-norm or L 1-norm regularization to different parts of the image. The solution of the resulting minimization problem is obtained by a fast algorithm based on the half-quadratic technique recently proposed in [2] for L 1-TV regularization. Some numerical results show the effectiveness of our adaptive norm image restoration strategy.


Image Restoration Impulse Noise Smooth Region Recovered Image Gaussian Blur 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Daniele Bertaccini
    • 1
  • Raymond H. Chan
    • 2
  • Serena Morigi
    • 3
  • Fiorella Sgallari
    • 3
  1. 1.Department of MathematicsUniversity of Roma “Tor Vergata”RomeItaly
  2. 2.Department of MathematicsThe Chinese University of Hong KongHong KongP.R. China
  3. 3.Department of Mathematics-CIRAMUniversity of BolognaBolognaItaly

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