Skip to main content

Regularization for Super-Resolution Image Reconstruction

  • Conference paper
Knowledge-Based Intelligent Information and Engineering Systems (KES 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4252))

Abstract

Super-resolution image reconstruction estimates a high-resolution image from a sequence of low-resolution, aliased images. The estimation is an inverse problem and is known to be ill-conditioned, in the sense that small errors in the observed images can cause large changes in the reconstruction. The paper discusses application of existing regularization techniques to super-resolution as an intelligent means of stabilizing the reconstruction process. Some most common approaches are reviewed and experimental results for iterative reconstruction are presented.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Chaudhuri, S.: Super-Resolution Imaging, p. 279. Kluwer Academic Publishers, Dordrecht (2001)

    Google Scholar 

  2. Hardie, R.C., et al.: High-Resolution Image Reconstruction from a Sequence of Rotated and Translated Frames and It’s Application to an Infrared Imaging System. Optical Engineering 37(1), 247–260 (1998)

    Article  Google Scholar 

  3. Tikhonov, A.N., et al.: Numerical Methods for the Solution of Ill-Posed Problems. Kluwer Academic, Netherlands (1995)

    MATH  Google Scholar 

  4. Tikhonov, A.N., Arsenin, V.Y.: Solutions of Ill-Posed Problems. John Wiley & Sons, Washington (1977)

    MATH  Google Scholar 

  5. Morozov, V.A.: Regularization Methods for Ill-Posed Problems. English (ed.). CRC Press, Boca Raton (1993)

    Google Scholar 

  6. Tikhonov, A.N. (ed.): Ill-Posed Problems in Natural Sciences. TVP, Sci. Publishers, Moscow (1991)

    Google Scholar 

  7. Tikhonov, A.N.: Regularization of Incorrectly Posed Problems. Soviet Math. Dokl. 4, 1624–1627 (1963)

    MATH  Google Scholar 

  8. Tikhonov, A.N.: Solution of Incorrectly Formulated Problems and the Regularization Method. Soviet Math. Dokl 4, 1035–1038 (1963)

    Google Scholar 

  9. Hadamard, J.: Sur les problèmes aux dérivées partielles et leur signification physique (On the problems with the derivative partial and their physical significance), pp. 49–52. Princeton University Bulletin (1902)

    Google Scholar 

  10. Groetsch, C.W.: The Theory of Tikhonov Regulaization for Fredholm Equations of the First Kind. Research Notes in Mathematics, vol. 105. Pitman, Boston (1984)

    Google Scholar 

  11. Engl, H.W.: Regularization methods for the stable solution of Inverse Problems. Surveys on Mathematics for Industries 3, 77–143 (1993)

    MathSciNet  Google Scholar 

  12. Hanke, M., Hansen, P.C.: Regularization Methods For Large-Scale Problems. Surveys on Mathematics for Industries 3, 253–315 (1993)

    MATH  MathSciNet  Google Scholar 

  13. Hansen, P.C.: Numerical tools for analysis and solution of Fredholm integral equations of the first kind. Inverse Problems 8, 849–872 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  14. Galatsanos, N.P., Katsaggelos, A.K.: Methods for choosing the Regularization Parameter and Estimating the Noise Variance in Image Restoration and Their Relation. IEEE Transactions on Image Processing 1(3), 322–336 (1992)

    Article  Google Scholar 

  15. Morozov, V.A.: On the Solution of Functional Equations by the method of Regularization. Soviet Math. Dokl. 7, 414–417 (1966)

    MATH  MathSciNet  Google Scholar 

  16. Golub, G.H., Heath, M.T., Wahba, G.: Generalized Cross-Validation as a method for choos-ing a good Ridge Parameter. Technometrics 21, 215–223 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  17. Wahba, G.: Spline Model for Observational Data. In: CBMS-NSF regional conference series in applied mathematics, vol. 59, Society for Industrial and Applied Mathematics, Philadelphia (1990)

    Google Scholar 

  18. Hansen, P.C.: Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion. SIAM, Philadelphia (1998)

    Book  Google Scholar 

  19. Varah, J.M.: Pitfalls in the Numerical Solution of Linear Ill-Posed Problems. SIAM J. Sci. Stat. Comput. 4(2), 164–176 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  20. Hansen, P.C.: Analysis of Discrete Ill-Posed Problems by means of the L-Curve. Siam Review 34(4), 561–580 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  21. Hansen, P.C., O’Leary, D.P.: The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems. Siam J. Sci. Comput. 14(6), 1487–1503 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  22. Lawson, C.L., Hanson, R.J.: Solving least squares problems. Prentice Hall, Englewood Cliffs (1974)

    MATH  Google Scholar 

  23. Zhuang, X., Ostevold, E., Haralick, M.: A Differential Equation Approach To Maximum Entropy Image Reconstruction. IEEE Trans. Acoust. Speech, Signal Processing ASSP-35(2), 208–218 (1987)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bannore, V. (2006). Regularization for Super-Resolution Image Reconstruction. In: Gabrys, B., Howlett, R.J., Jain, L.C. (eds) Knowledge-Based Intelligent Information and Engineering Systems. KES 2006. Lecture Notes in Computer Science(), vol 4252. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11893004_5

Download citation

  • DOI: https://doi.org/10.1007/11893004_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46537-9

  • Online ISBN: 978-3-540-46539-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics