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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 29, Iss. 12 — Dec. 1, 2012
  • pp: 2688–2695

Interval estimate with probabilistic background constraints in deconvolution

Zhuo-xi Huo and Jian-feng Zhou  »View Author Affiliations


JOSA A, Vol. 29, Issue 12, pp. 2688-2695 (2012)
http://dx.doi.org/10.1364/JOSAA.29.002688


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Abstract

We present in this article the use of probabilistic background constraints in astronomical image deconvolution to approach a solution as an interval estimate. We elaborate our objective—the interval estimate of the unknown object from observed data and our approach—Monte Carlo experiment and analysis of marginal distributions of image values. One-dimensional observation and deconvolution using the proposed approach are simulated. Confidence intervals revealing the uncertainties due to the background constraint are calculated and significance levels for sources retrieved from restored images are provided.

© 2012 Optical Society of America

OCIS Codes
(100.0100) Image processing : Image processing
(100.1830) Image processing : Deconvolution

ToC Category:
Image Processing

History
Original Manuscript: August 6, 2012
Manuscript Accepted: November 1, 2012
Published: November 30, 2012

Citation
Zhuo-xi Huo and Jian-feng Zhou, "Interval estimate with probabilistic background constraints in deconvolution," J. Opt. Soc. Am. A 29, 2688-2695 (2012)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-12-2688


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References

  1. A. Meister, Deconvolution Problems in Nonparametric Statistics (Springer-Verlag, 2009), p. 2.
  2. G. R. Ayers and J. C. Dainty, “Iterative blind deconvolution method and its applications,” Opt. Lett. 13, 547–549 (1988). [CrossRef]
  3. S. James and L. Harris, “Image evaluation and restoration,” J. Opt. Soc. Am. 56, 569–574 (1966). [CrossRef]
  4. S. Zaroubi, Y. Hoffman, K. B. Fisher, and O. Lahav, “Wiener reconstruction of the large-scale structure,” Astrophys. J. 449, 446 (1995). [CrossRef]
  5. M. G. Löfdahl, “Multiframe deconvolution with space-variant point-spread functions by use of inverse filtering and fast Fourier transform,” Appl. Opt. 46, 4686–4693 (2007). [CrossRef]
  6. R. Puetter, T. Gosnell, and A. Yahil, “Digital image reconstruction: deblurring and denoising,” Annu. Rev. Astron. Astrophys. 43, 139–194 (2005). [CrossRef]
  7. J. A. Högbom, “Aperture synthesis with a non-regular distribution of interferometer baselines,” Astron. Astrophys. 15, 417–426 (1974).
  8. L. Landweber, “An iteration formula for Fredholm integral equations of the first kind,” Am. J. Math. 73, 615–624 (1951). [CrossRef]
  9. W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. 62, 55–59 (1972). [CrossRef]
  10. L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745–754 (1974). [CrossRef]
  11. J. L. Starck, E. Pantin, and F. Murtagh, “Deconvolution in astronomy: A review,” Publ. Astron. Soc. Pac. 114, 1051–1069 (2002). [CrossRef]
  12. D. N. Esch, A. Connors, M. Karovska, and D. A. van Dyk, “An image restoration technique with error estimates,” Astrophys. J. 610, 1213–1227 (2004). [CrossRef]
  13. C. Byrne, “Iterative algorithms for deblurring and deconvolution with constraints,” Inverse Probl. 14, 1455 (1998). [CrossRef]
  14. A. Lannes, S. Roques, and M. J. Casanove, “Stabilized reconstruction in signal and image processing—i. partial deconvolution and spectral extrapolation with limited field,” J. Mod. Opt. 34, 161–226 (1987). [CrossRef]
  15. P. Hansen, “Regularization tools,” Numer. Algorithms 6, 1–35 (1994). [CrossRef]
  16. T.-P. Li and M. Wu, “A direct restoration method for spectral and image analysis,” Astrophys. Space Sci. 206, 91–102 (1993). [CrossRef]
  17. N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, and J. Zerubia, “Richardson–Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (2006). [CrossRef]
  18. G. M. P. van Kempen and L. J. van Vliet, “Background estimation in nonlinear image restoration,” J. Opt. Soc. Am. A 17, 425–433 (2000). [CrossRef]
  19. G. M. Wing, A Primer on Integral Equations of the First Kind: The Problem of Deconvolution and Unfolding (Society for Industrial Mathematics, 1991), pp. 92–103.
  20. I. S. McLean, Electronic Imaging in Astronomy: Detectors and Instrumentation, 2nd ed. (Springer, 2008), pp. 241–313.
  21. J.-L. Starck and F. Murtagh, Astronomical Image and Data Analysis (Springer-Verlag, 2006), pp. 40–41.

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