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A Novel Framework for Nonlocal Vectorial Total Variation Based on ℓp,q,r −norms

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Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 8932))

Abstract

In this paper, we propose a novel framework for restoring color images using nonlocal total variation (NLTV) regularization. We observe that the discrete local and nonlocal gradient of a color image can be viewed as a 3D matrix/or tensor with dimensions corresponding to the spatial extend, the differences to other pixels, and the color channels. Based on this observation we obtain a new class of NLTV methods by penalizing the ℓp,q,r norm of this 3D tensor. Interestingly, this unifies several local color total variation (TV) methods in a single framework. We show in several numerical experiments on image denoising and deblurring that a stronger coupling of different color channels – particularly, a coupling with the ℓ ∞  norm – yields superior reconstruction results.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Universitat de les Illes Balears, Cra. de Valldemossa km. 7.5, 07122, Palma, Spain

    Joan Duran & Catalina Sbert

  2. Department of Mathematics and Computer Science, Technische Universität München, Boltzmannstrasse 3, 85748, Garching, Germany

    Joan Duran, Michael Moeller & Daniel Cremers

Authors
  1. Joan Duran
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  2. Michael Moeller
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  3. Catalina Sbert
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  4. Daniel Cremers
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Bergen, 7800, Bergen, Norway

    Xue-Cheng Tai

  2. Department of Mathematics, University of California, Los Angeles, CA, USA

    Egil Bae

  3. The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, S.A.R.

    Tony F. Chan

  4. Telemark University College, Postboks 203, 3901, Porsgrunn, Norway

    Marius Lysaker

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© 2015 Springer International Publishing Switzerland

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Duran, J., Moeller, M., Sbert, C., Cremers, D. (2015). A Novel Framework for Nonlocal Vectorial Total Variation Based on ℓp,q,r −norms. In: Tai, XC., Bae, E., Chan, T.F., Lysaker, M. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2015. Lecture Notes in Computer Science, vol 8932. Springer, Cham. https://doi.org/10.1007/978-3-319-14612-6_11

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  • DOI: https://doi.org/10.1007/978-3-319-14612-6_11

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-14611-9

  • Online ISBN: 978-3-319-14612-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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