Skip to main content
SpringerLink
Log in

A TGV Regularized Wavelet Based Zooming Model

  • Conference paper
Scale Space and Variational Methods in Computer Vision (SSVM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7893))

Abstract

We propose and state a novel scheme for image magnification. It is formulated as a minimization problem which incorporates a data fidelity and a regularization term. Data fidelity is modeled using a wavelet transformation operator while the Total Generalized Variation functional of second order is applied for regularization. Well-posedness is obtained in a function space setting and an efficient numerical algorithm is developed. Numerical experiments confirm a high quality of the magnified images. In particular, with an appropriate choice of wavelets, geometrical information is preserved.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bredies, K.: Recovering piecewise smooth multichannel images by minimization of convex functionals with total generalized variation penalty. SFB Report 2012-006 (2012), http://math.uni-graz.at/mobis/publications.html

  2. Bredies, K., Holler, M.: Artifact-free decompression and zooming of JPEG compressed images with total generalized variation. In: Csurka, G., et al. (eds.) VISIGRAPP 2012. CCIS, vol. 359, pp. 242–258. Springer, Heidelberg (2013)

    Google Scholar 

  3. Bredies, K., Kunisch, K., Pock, T.: Total generalized variation. SIAM J. Imag. Sci. 3(3), 492–526 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bredies, K., Kunisch, K., Valkonen, T.: Properties of L 1 − TGV2: The one-dimensional case. J. Math. Anal. Appl. 389(1), 438–454 (2013)

    Article  MathSciNet  Google Scholar 

  5. Bredies, K., Valkonen, T.: Inverse problems with second-order total generalized variation constraints. In: Proceedings of SampTA, Singapore, (2011)

    Google Scholar 

  6. Chambolle, A.: An algorithm for total variation minimization and applications. J. Math. Imaging Vis. 20, 88–97 (2004)

    Article  MathSciNet  Google Scholar 

  7. Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40, 120–145 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Cohen, A., Daubechies, I., Feauveau, J.-C.: Biorthogonal bases of compactly supported wavelets. Commun. Pur. Appl. Math. 45(5), 485–560 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  9. Cohen, A., Daubechies, I., Vial, P.: Wavelets on the interval and fast wavelet transforms. Appl. Comput. Harmon. Anal. 1(1), 54–81 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  10. Daubechies, I.: Ten Lectures on Wavelets. CBMS-NSF Lecture Notes, vol. 61. SIAM (1992)

    Google Scholar 

  11. Duchon, C.E.: Lanczos Filtering in One and Two Dimensions. J. Appl. Meteor. 18(8), 1016–1022 (1979)

    Article  Google Scholar 

  12. Kaulgud, N., Desai, U.B.: Image zooming: Use of wavelets. The International Series in Engineering and Computer Science, vol. 632, pp. 21–44. Springer (2002)

    Google Scholar 

  13. Malgouyres, F., Guichard, F.: Edge direction preserving image zooming: A mathematical and numerical analysis. SIAM J. Numer. Anal. 39, 1–37 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  14. Young, R.M.: An Introduction to Nonharmonic Fourier Series. Academic Press (2001)

    Google Scholar 

  15. Zhang, X., Chan, T.F.: Wavelet inpainting by nonlocal total variation. Inverse Probl. Imag. 4, 191–210 (2010)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Scientific Computing, University of Graz, Heinrichstraße 36, A-8010, Graz, Austria

    Kristian Bredies & Martin Holler

Authors
  1. Kristian Bredies
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Martin Holler
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Fraunhofer Gesellschaft, Institut für Graphische Datenverarbeitung, Fraunhoferstraße 5, 64283, Darmstadt, Germany

    Arjan Kuijper

  2. Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010, Graz, Austria

    Kristian Bredies

  3. Institute for Computer Graphics and Vision, Graz University of Technology, Inffeldgasse 16, 8010, Graz, Austria

    Thomas Pock  & Horst Bischof  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bredies, K., Holler, M. (2013). A TGV Regularized Wavelet Based Zooming Model. In: Kuijper, A., Bredies, K., Pock, T., Bischof, H. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2013. Lecture Notes in Computer Science, vol 7893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38267-3_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38267-3_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38266-6

  • Online ISBN: 978-3-642-38267-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation