Determination of the optimum sampling frequency of noisy images by spatial statistics
| dc.contributor.author | Sánchez Brea, Luis Miguel | |
| dc.contributor.author | Bernabeu Martínez, Eusebio | |
| dc.date.accessioned | 2023-06-20T10:46:29Z | |
| dc.date.available | 2023-06-20T10:46:29Z | |
| dc.date.issued | 2005-06-01 | |
| dc.description | © 2005 Optical Society of America. L. M. Sánchez-Brea is contracted by the Universidad Complutense de Madrid within the Ramón y Cajal program, of the Ministerio de Educación y Ciencia of Spain. | |
| dc.description.abstract | In optical metrology the final experimental result is normally an image acquired with a CCD camera. Owing to the sampling at the image, an interpolation is usually required. For determining the error in the measured parameters with that image, knowledge of the uncertainty at the interpolation is essential. We analyze how kriging, an estimator used in spatial statistics, can generate convolution kernels for filtering noise in regularly sampled images. The convolution kernel obtained with kriging explicitly depends on the spatial correlation and also on metrological conditions, such as the random fluctuations of the measured quantity, and the resolution of the measuring devices. Kriging, in addition, allows us to determine the uncertainty of the interpolation, and we have analyzed it in terms of the sampling frequency and the random fluctuations of the image, comparing it with Nyquist criterion. By use of kriging, it is possible to determine the optimum-required sampling frequency for a noisy image so that the uncertainty at interpolation is below a threshold value. | |
| dc.description.department | Depto. de Óptica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Ministerio de Educación y Ciencia (MEC), España | |
| dc.description.sponsorship | Universidad Complutense de Madrid (UCM) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/26737 | |
| dc.identifier.doi | 10.1364/AO.44.003276 | |
| dc.identifier.issn | 1559-128X | |
| dc.identifier.officialurl | http://dx.doi.org/10.1364/AO.44.003276 | |
| dc.identifier.relatedurl | http://www.opticsinfobase.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/51196 | |
| dc.issue.number | 16 | |
| dc.journal.title | Applied Optics | |
| dc.language.iso | eng | |
| dc.page.final | 3286 | |
| dc.page.initial | 3276 | |
| dc.publisher | The Optical Society Of America | |
| dc.relation.projectID | Programa Ramón y Cajal | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 535 | |
| dc.subject.keyword | Shannon | |
| dc.subject.keyword | Theory | |
| dc.subject.ucm | Óptica (Física) | |
| dc.subject.unesco | 2209.19 Óptica Física | |
| dc.title | Determination of the optimum sampling frequency of noisy images by spatial statistics | |
| dc.type | journal article | |
| dc.volume.number | 44 | |
| dcterms.references | 1. W. K. Pratt, Digital Image Processing (Wiley, New York, 1978). 2. H. P. Urbach, “Generalised sampling theorem for band-limited functions”, Math. Comput. Modell. 38, 133–140 (2003). 3. A. Stern, B. Javidi, “Sampling in the light of Wigner distribution”, J. Opt. Soc. Am. A 21, 360–366 (2004). 4. A. Stern, B. Javidi, “Analysis of practical sampling and reconstruction from Fresnel fields”, Opt. Eng. 43, 239–250 (2004). 5. C. E. Shannon, “Communication in presence of noise”, Proc. IRE 37, 20–21 (1949). 6. G. C. Holst, CCD Arrays, Cameras, and Displays (SPIE, Bellingham, Wash., 1996). 7. A. J. Jerri, “The Shannon sampling theorem—its various extensions and applications”, Proc. IEEE 65, 1565–1596 (1977). 8. K. F. Cheung, R. J. Marks, “Imaging sampling below the Nyquist density without aliasing”, J. Opt. Soc. Am. A 7, 92–105 (1990). 9. M. Pawlak, U. Stadmüller, “Recovering band-limited signals under noise”, IEEE Trans. Inf. Theory 42, 1425–1438 (1996). 10. M. Unser, “Sampling—50 years after Shannon”, Proc. IEEE 88, 569–587 (2000). 11. P. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969). 12. ISO, Guide to the Expression of the Uncertainty in Measurement (International Organization for Standardization, Geneva, Switzerland, 1995). 13. R. Christiensen, Linear Models for Multivariate, Time Series, and Spatial Data (Springer-Verlag, Berlin, 1985). 14. N. Cressie, Statistics for Spatial Data (Wiley, New York, 1991). 15. E. Bernabéu, I. Serroukh, L. M. Sanchez-Brea, “A geometrical model for wire optical diffraction selected by experimental statistical analysis”, Opt. Eng. 38, 1319–1325 (1999). 16. D. Mainy, J. P. Nectoux, D. Renard, “New developments in data processing of noisy images”, Mater. Charact. 36, 327–334 (1996). 17. W. Y. V. Leung, P. J. Bones, R. G. Lane, “Statistical interpolation of sampled images”, Opt. Eng. 40, 547–553 (2001). 18. T. D. Pham, M. Wagner, “Image enhancement by kriging and fuzzy sets”, Int. J. Pattern Recognit. 14, 1025–1038 (2000). 19. G. Y. Hu, R. F. O’Connell, “Analytical inversion of symmetric tridiagonal matrices”, J. Phys. A 29, 1511–1513 (1996). 20. G. S. Ammar, W. B. Gragg, “Superfast solution of real positive definite Toeplitz systems”, SIAM J. Matrix Anal. Appl. 9, 61–76 (1988). 21. W. H. Press, S. A. Teukolski, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, New York, 1992). 22. J. P. Chilès, P. Delfiner, Geostatistics (Wiley, New York, 1999). 23. L. M. Sánchez-Brea, E. Bernabéu, “On the standard deviation in charge-coupled device cameras: a variogram-based technique for nonuniform images”, J. Electron. Imaging 11, 121–126 (2002). 24. G. Cloud, Optical Methods of Engineering Analysis (Cambridge U. Press, Cambridge, UK, 1998). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 72f8db7f-8a25-4d15-9162-486b0f884481 | |
| relation.isAuthorOfPublication.latestForDiscovery | 72f8db7f-8a25-4d15-9162-486b0f884481 |
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