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An Adaptive Norm Algorithm for Image Restoration

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Scale Space and Variational Methods in Computer Vision (SSVM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6667))

Abstract

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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Roma “Tor Vergata”, Rome, Italy

    Daniele Bertaccini

  2. Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, P.R. China

    Raymond H. Chan

  3. Department of Mathematics-CIRAM, University of Bologna, Bologna, Italy

    Serena Morigi & Fiorella Sgallari

Authors
  1. Daniele Bertaccini
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  2. Raymond H. Chan
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  3. Serena Morigi
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  4. Fiorella Sgallari
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Editor information

Editors and Affiliations

  1. Computer Science Department, Technion — Israel Institute of Technology, 718 Taub Building Technion, 32000, Haifa, Israel

    Alfred M. Bruckstein

  2. Department of Biomedical Engineering, Biomedical Image Analysis and Interpretation, Eindhoven University of Technology, Den Dolech 2 – WH 2.101, 5600 MB, Eindhoven, The Netherlands

    Bart M. ter Haar Romeny

  3. Faculaty of Engineering, School of Electrical Engineering, Tel Aviv University, Ramat Aviv, 69978, Israel

    Alexander M. Bronstein

  4. Institute of Computationa Science, Faculty of Informatics SI-109, Università della Svizzera Italiana, Via Giuseppe Buffi 13, 6904, Lugano, Switzerland

    Michael M. Bronstein

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© 2012 Springer-Verlag Berlin Heidelberg

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Bertaccini, D., Chan, R.H., Morigi, S., Sgallari, F. (2012). An Adaptive Norm Algorithm for Image Restoration. In: Bruckstein, A.M., ter Haar Romeny, B.M., Bronstein, A.M., Bronstein, M.M. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2011. Lecture Notes in Computer Science, vol 6667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24785-9_17

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  • DOI: https://doi.org/10.1007/978-3-642-24785-9_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24784-2

  • Online ISBN: 978-3-642-24785-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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