Skip to main content

Orthogonality Based Stopping Condition for Iterative Image Deconvolution Methods

  • Conference paper
Computer Vision – ACCV 2010 (ACCV 2010)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6495))

Included in the following conference series:

  • 2319 Accesses

Abstract

Deconvolution techniques are widely used for image enhancement from microscopy to astronomy. The most effective methods are based on some iteration techniques, including Bayesian blind methods or Greedy algorithms. The stopping condition is a main issue for all the non-regularized methods, since practically the original image is not known, and the estimation of quality is based on some distance between the measured image and its estimated counter-part. This distance is usually the mean square error (MSE), driving to an optimization on the Least-Squares measure. Based on the independence of signal and noise, we have established a new type of error measure, checking the orthogonality criterion of the measurement driven gradient and the estimation at a given iteration. We give an automatic procedure for estimating the stopping condition. We show here its superiority against conventional ad-hoc non-regularized methods at a wide range of noise models.

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. Sarder, P., Nehorai, A.: Deconvolution methods for 3-d fluorescence microscopy images. IEEE In Signal Processing Magazine 23, 32–45 (2006)

    Article  Google Scholar 

  2. Lucy, L.: An iterative technique for rectification of observed distributions. The Astronomical Journal 79, 745–765 (1974)

    Article  Google Scholar 

  3. Richardson, W.: Bayesian-based iterative method of image restoration. JOSA 62, 55–59 (1972)

    Article  Google Scholar 

  4. Agard, D.: Optical sectioning microscopy: Cellular architecture in three dimensions. Ann. Rev. Biophys. Bioeng. 13, 191–219 (1984)

    Article  Google Scholar 

  5. Biggs, D.S.C., Andrews, M.: Acceleration of iterative image restoration algorithms. Appl. Opt. 36, 1766–1775 (1997)

    Article  Google Scholar 

  6. Hanisch, R.J., White, R., Gilliland, R.: Deconvolutions of hubble space telescope images and spectra. In: Jansson, P.A. (ed.) Deconvolution of Images and Spectra, 2nd edn., Academic Press, CA (1997)

    Google Scholar 

  7. Erhardt, A., Zinser, G., Komitowski, D., Bille, J.: Reconstructing 3-d light-microscopic images by digital image processing. Appl. Opt. 24, 194–200 (1985)

    Article  Google Scholar 

  8. McNally, J.: Three-dimensional imaging by deconvolution microscopy. Methods 19, 373–385 (1999)

    Article  Google Scholar 

  9. Tikhonov, A.N., Arsenin, V.Y.: Solutions of ill-posed problems. Scripta series in mathematics, Winston, Washington (1977)

    Google Scholar 

  10. Ayers, G.R., Dainty, J.C.: Iterative blind deconvolution method and its applications. Opt. Lett. 13, 547–549 (1988)

    Article  Google Scholar 

  11. Markham, J., Conchello, J.A.: Parametric blind deconvolution: a robust method for the simultaneous estimation of image and blur. J. Opt. Soc. Am. A 16, 2377–2391 (1999)

    Article  Google Scholar 

  12. Pankajakshan, P., Zhang, B., Blanc-Féraud, L., Kam, Z., Olivo-Marin, J.C., Zerubia, J.: Blind deconvolution for thin-layered confocal imaging. Appl. Opt. 48, 4437–4448 (2009)

    Article  Google Scholar 

  13. Jang, K.E., Ye, J.C.: Single channel blind image deconvolution from radially symmetric blur kernels. Opt. Express 15, 3791–3803 (2007)

    Article  Google Scholar 

  14. Kundur, D., Hatzinakos, D.: Blind image deconvolution. IEEE Signal Processing Magazine 13, 43–64 (1996)

    Article  Google Scholar 

  15. Verbeeck, J., Bertoni, G.: Deconvolution of core electron energy loss spectra. Ultramicroscopy 109, 1343–1352 (2009)

    Article  Google Scholar 

  16. Dey, N., Blanc-Fraud, L., Zimmer, C., Kam, Z., Roux, P., Olivo-Marin, J., Zerubia, J.: Richardson-lucy algorithm with total variation regularization for 3d confocal microscope deconvolution. Microscopy Research Technique 69, 260–266 (2006)

    Article  Google Scholar 

  17. van Kempen, G., van Vliet, L.: The influence of the regularization parameter and the first estimate on the performance of tikhonov regularized nonlinear image restoration algorithms. J. Microsc. 198, 63–75 (2000)

    Article  Google Scholar 

  18. You-Wei Wen, A.M.Y.: Adaptive parameter selection for total variation image deconvolution. Numer. Math. Theor. Meth. Appl. 2, 427–438 (2009)

    MathSciNet  MATH  Google Scholar 

  19. Kovács, L., Szirányi, T.: Focus area extraction by blind deconvolution for defining regions of interes. IEEE Tr. Pattern Analysis and Machine Intelligence 29, 1080–1085 (2007)

    Article  Google Scholar 

  20. Papoulis, A.: Probability, Random Variables ad Stochastic Processes. McGraw-Hill, New York (1984)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Szolgay, D., Szirányi, T. (2011). Orthogonality Based Stopping Condition for Iterative Image Deconvolution Methods. In: Kimmel, R., Klette, R., Sugimoto, A. (eds) Computer Vision – ACCV 2010. ACCV 2010. Lecture Notes in Computer Science, vol 6495. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19282-1_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-19282-1_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-19281-4

  • Online ISBN: 978-3-642-19282-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics