Skip to main content

Bayesian Methods of Deconvolution and Shape Classification

  • Chapter

Abstract

Formal Bayesian methods have only a little history in astronomical applications, yet they have recently become the favorite methodology for statisticians studying image analysis. The “prior distributions” used are spatial stochastic processes which aim to encapsulate the relevant features of the images which are known from past experience. We describe two recent applications of these methods by the author and his colleagues to deconvolution of CCD images blurred by atmospheric motion, and to automatically “sketching” spiral galaxies as a prelude to classification. The deconvolution compares favorably with Maximum Entropy in speed, fit to the data, lack of artifacts, and visual acceptability (at least to our astronomer colleagues). The sketching process produces consistent sketches from quite faint spirals.

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Buonanno, G. Buscema, C.E. Corsi, I. Ferraro, and G. Iannicola. Automated photographic photometry of stars in globular clusters. Astron. Astrophys., 126:278–282, 1983.

    ADS  Google Scholar 

  2. J. Besag. On the statistical analysis of dirty pictures (with discussion). J. Roy. Statist Soc. B, 48:259–302, 1986.

    MathSciNet  MATH  Google Scholar 

  3. Y. Chow, U. Grenander, and D.M. Keenan. Hands. A pattern theoretic study of biological shapes. Technical report, Division of Applied Mathematics, Brown Univ., Providence, R.I., 1989.

    Google Scholar 

  4. D. Geman. Random fields and inverse problems in imaging. St. Flour Lectures 1988. Lecture Notes in Mathematics, Springer-Verlag, New York 1991.

    Google Scholar 

  5. S. Geman and D. Geman. Gibbs distributions and the Bayesian restoration of images. IEEE Trans. Pat. Anal. Mach. Int 6:721–741, 1984.

    Article  MATH  Google Scholar 

  6. U. Grenander. Tutorial in pattern theory. Technical report, Division of Applied Mathematics, Brown Univ., Providence, R.I., 1983.

    Google Scholar 

  7. S.F. Gull and J. Skilling. The entropy of an image. In C.R. Smith and W.T. Gandy Jr. editors, Maximum-Entropy and Bayesian Methods in Inverse Problems. Reidel, Dordrecht, 1985, pp. 287–301.

    Google Scholar 

  8. A.E. Gelfand and A.F.M. Smith. Samping-based approaches to calculating marginal densities. J. Amer. Statist. Assoc, 85:390–409, 1990.

    MathSciNet  Google Scholar 

  9. F.R. Hampel, E.M. Ronchetti, P.J. Rousseeuw, and W.A. Stahel. Robust Statistics: The Approach Based on Influence Functions. Wiley, New York, 1986.

    MATH  Google Scholar 

  10. P.J. Huber. Robust Statistics. Wiley, New York, 1981.

    Book  MATH  Google Scholar 

  11. H.R. Kiinsch. Intrinsic autoregressions and related models on the two-dimensional lattice. Biometrika, 74:517–524, 1987.

    MathSciNet  Google Scholar 

  12. J.L. Marroquin, S. Mitter, and J. Poggio. Probabilistic solution of ill-posed problems in computational vision. J. Amer. Statist. Assoc, 82:76–89, 1987.

    Article  MATH  Google Scholar 

  13. A.F.J. Moffat. A theoretical investigation of focal stellar images in the photographic emulsion and application to photographic photometry. Astron. Astrophys., 3:455–462, 1969.

    ADS  Google Scholar 

  14. R. Molina, A. del Olmo. J, Perea, and B.D. Ripley. Bayesian deconvolution in optical astronomy. Part I. Introduction and applications. Astrom. J., 103:666–675, 1991.

    Article  ADS  Google Scholar 

  15. R. Molina, N. Pérez de la Bianca, and B.D. Ripley. Statistical restoration of astronomical images. In V.D. Di Gesu, L. Scarsi, P. Crane. J.H. Friedman, S. Levialdi, and M.C. Maccarone, editors, Data Analysis in Astronomy III. Plenum, New York, 1989, pp. 75–82.

    Google Scholar 

  16. R. Molina and B.D. Ripley. Using spatial models as priors in image analysis. J. Appl. Statist., 16:193–206, 1989.

    Article  Google Scholar 

  17. R. Molina, B.D. Ripley, and A. Sutherland. Bayesian deconvolution in optical astronomy. Part II. Theory and implementation. Astrom. J., 1991 (submitted for publication).

    Google Scholar 

  18. B.D. Ripley. Spatial Statistics. Wiley, New York, 1981.

    Book  MATH  Google Scholar 

  19. B.D. Ripley. Statistics, images and pattern recognition. Canad. J. Statist, 14:83–111, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  20. B.D. Ripley. Stochastic Simulation. Wiley, New York, 1987.

    Book  MATH  Google Scholar 

  21. B.D. Ripley. Statistical Inference for Spatial Processes. Cambridge Univ. Press, New York 1988.

    Google Scholar 

  22. B.D. Ripley. Recognizing organisms from their shapes — a case study in image analysis. In Proceedings XVth International Biometrics Conference. Budapest invited papers volume. 1990. pp. 259–263.

    Google Scholar 

  23. B.D. Ripley. The uses of spatial models as image priors. In A. Possolo, editor, Spatial Statistics & Imaging. Institute of Mathematical Statistics Lecture Notes, 1991.

    Google Scholar 

  24. B.D. Ripley and M.D. Kirkland. Iterative simulation methods. J. Comput Appi Math., 31:165–172, 1990.

    Article  MATH  Google Scholar 

  25. B.D. Ripley and A.I. Sutherland. Finding spiral structures in images of galaxies. Phil. Trans. Roy. Soc. A, 332:477–485, 1990.

    Article  ADS  Google Scholar 

  26. J. Skilling and S.F. Gull. Algorithms and applications. In C.R. Smith and W.T. Gandy Jr, editors, Maximum-Entropy and Bayesian Methods in Inverse Problems, Reidel, Dordrecht, 1985, pages 83–132.

    Google Scholar 

  27. J. Skilling and S.F. Gull. Bayesian maximum entropy image reconstruction. In A. Possolo, editor, Spatial Statistics & Imaging. Institute of Mathematical Statistics Lecture Notes, 1991.

    Google Scholar 

  28. D. Stoyan, W.S. Kendall, and J. Mecke. Stochastic Geometry and Its Applications. Akademie & Wiley, Berlin & Chichester, 1987.

    MATH  Google Scholar 

  29. B. Takase, K. Kodaira, and S. Okamura. An Atlas of Selected Galaxies. Univ. of Tokyo Press, Tokyo, 1984.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag New York, Inc.

About this chapter

Cite this chapter

Ripley, B.D. (1992). Bayesian Methods of Deconvolution and Shape Classification. In: Feigelson, E.D., Babu, G.J. (eds) Statistical Challenges in Modern Astronomy. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9290-3_38

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-9290-3_38

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9292-7

  • Online ISBN: 978-1-4613-9290-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics