OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: James C. Wyant
  • Vol. 47, Iss. 34 — Dec. 1, 2008
  • pp: 6350–6356

Analytical determination of the uncertainty and the optimum sampling frequency for one-dimensional images with noise

Luis Miguel Sanchez-Brea and Philip Siegmann  »View Author Affiliations


Applied Optics, Vol. 47, Issue 34, pp. 6350-6356 (2008)
http://dx.doi.org/10.1364/AO.47.006350


View Full Text Article

Enhanced HTML    Acrobat PDF (650 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Kriging is an estimation technique that has been proved useful in image processing since it behaves, under regular sampling, as a convolution. The uncertainty obtained with kriging has also been shown to behave as a convolution for the case of regular sampling. The convolution kernel for the uncertainty exclusively depends on the spatial correlation properties of the image. In this work we obtain, first, analytical expressions for the uncertainty of 1D images with noise using this convolution procedure. Then, we use this uncertainty to propose a new criterion for determining whether a 1D image with noise is correctly sampled.

© 2008 Optical Society of America

OCIS Codes
(100.0100) Image processing : Image processing
(100.2960) Image processing : Image analysis

ToC Category:
Image Processing

History
Original Manuscript: April 21, 2008
Revised Manuscript: October 9, 2008
Manuscript Accepted: October 23, 2008
Published: November 21, 2008

Citation
Luis Miguel Sanchez-Brea and Philip Siegmann, "Analytical determination of the uncertainty and the optimum sampling frequency for one-dimensional images with noise," Appl. Opt. 47, 6350-6356 (2008)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-47-34-6350


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. W. K. Pratt, Digital Image Processing (Wiley, 1978).
  2. H. P. Urbach, “Generalised sampling theorem for band-limited functions,” Math. Comput. Modell. 38, 133-140 (2003). [CrossRef]
  3. C. E. Shannon, “Communication in presence of noise,” Proc. IRE 37, 20-21 (1949). [CrossRef]
  4. A. J. Jerri, “The Shannon sampling theorem--its various extensions and applications,” Proc. IEEE 65, 1565-1596 (1977). [CrossRef]
  5. K. F. Cheung and R. J. Marks II, “Imaging sampling below the Nyquist density without aliasing,” J. Opt. Soc. Am. A 7, 92-105 (1990). [CrossRef]
  6. M. Pawlak and U. Stadmüller, “Recovering band-limited signals under noise,” IEEE Trans. Inf. Theor. 42, 1425-1438(1996). [CrossRef]
  7. M. Unser, “Sampling--50 years after Shannon,” Proc. IEEE 88, 569-587 (2000). [CrossRef]
  8. R. Christiensen, Linear Models for Multivariate, Time Series, and Spatial Data (Springer-Verlag, 1985).
  9. N. Cressie, Statistics for Spatial Data (Wiley, 1991).
  10. E. Bernabeu, I. Serroukh, and L. M. Sanchez-Brea, “A geometrical model for wire optical diffraction selected by experimental statistical analysis,” Opt. Eng. 38, 1319-1325(1999). [CrossRef]
  11. W. Y. V. Leung, P. J. Bones, and R. G. Lane, “Statistical interpolation of sampled images,” Opt. Eng. 40, 547-553 (2001). [CrossRef]
  12. D. Mainy, J. P. Nectoux, and D. Renard, “New developments in data processing of noisy images,” Mater. Charact. 36, 327-334 (1996). [CrossRef]
  13. L. M. Sanchez-Brea and E. Bernabeu, “Determination of the optimum sampling frequency of noisy images by spatial statistics,” Appl. Opt. 44, 3276-3283 (2005). [CrossRef] [PubMed]
  14. L. M. Sanchez-Brea and E. Bernabeu, “Uncertainty estimation by convolution using spatial statistics,” IEEE Trans. Image Process. 15, 3131-3137 (2006). [CrossRef]
  15. ISO, Guide to the Expression of the Uncertainty in Measurement (International Organization for Standardization, 1995).
  16. L. M. Sanchez-Brea and E. Bernabeu, “On the standard deviation in CCD cameras: a variogram-based technique for non-uniform images,” J. Electron. Imaging 11, 121-126(2002). [CrossRef]
  17. Mathematica 5, Wolfram Research, Inc., 100 Trade Center Drive Champaign, Ill., USA, pp. 61820-7237; http://www.wolfram.com.
  18. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “The focus of light--theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B 72, 109-113(2001).
  19. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901(2003). [CrossRef] [PubMed]
  20. J. M. Rico-García, L. M. Sanchez-Brea, and J. Alda, “Application of tomographic techniques to the spatial-response mapping of antenna-coupled detectors in the visible,” Appl. Opt. 47, 768-775 (2008). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited