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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

  • Vol. 7, Iss. 1 — Jan. 1, 1990
  • pp: 92–105

Imaging sampling below the Nyquist density without aliasing

Kwan F. Cheung and Robert J. Marks, II  »View Author Affiliations


JOSA A, Vol. 7, Issue 1, pp. 92-105 (1990)
http://dx.doi.org/10.1364/JOSAA.7.000092


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Abstract

For multidimensional band-limited functions, the Nyquist density is defined as that density corresponding to maximally packed spectral replications. Because of the shape of the support of the spectrum, however, sampling multidimensional functions at Nyquist densities can leave gaps among these replications. In this paper we show that, when such gaps exist, the image samples can periodically be deleted or decimated without information loss. The result is an overall lower sampling density. Recovery of the decimated samples by the remaining samples is a linear interpolation process. The interpolation kernels can generally be obtained in closed form. The interpolation noise level resulting from noisy data is related to the decimation geometry. The greater the clustering of the decimated samples, the higher the interpolation noise level is.

© 1990 Optical Society of America

History
Original Manuscript: August 25, 1988
Manuscript Accepted: June 21, 1989
Published: January 1, 1990

Citation
Kwan F. Cheung and Robert J. Marks, "Imaging sampling below the Nyquist density without aliasing," J. Opt. Soc. Am. A 7, 92-105 (1990)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-7-1-92


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References

  1. R. J. Marks, “Multidimensional-signal sample dependency at Nyquist densities,” J. Opt. Soc. Am. A 3, 268–273 (1986). [CrossRef]
  2. D. E. Dudgeon, R. M. Meresereau, Multidimensional Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1984).
  3. D. P. Petersen, D. Middleton, “Sampling and reconstruction of wave-number limited functions in N-dimensional Euclidean spaces,” Inf. Control 5, 279–323 (1962). [CrossRef]
  4. C. E. Shannon, “Communication in the presence of noise,” IRE Proc. 37, 10–21 (1948). [CrossRef]
  5. E. Dubois, “The sampling and reconstruction of time-varying imagery with application in video systems,” IEEE Proc. 23, 502–522 (1985). [CrossRef]
  6. K. F. Cheung, “Image sampling density below that of Nyquist,” Ph.D. dissertation (Department of Electrical Engineering, University of Washington, Seattle, Wash., 1988).
  7. D. S. Chen, J. P. Allebach, “Analysis of error in reconstruction of two-dimensional signals from irregularly spaced samples,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 173–180 (1987). [CrossRef]
  8. J. L. Yen, “On the nonuniform sampling of bandwidth limited signals,” IRE Trans. Circuit Theory 3, 251–257 (1956). [CrossRef]
  9. H. K. Ching, “Truncation effects in the estimation of two-dimensional continuous bandlimited signals,” master’s thesis (Department of Electrical Engineering, University of Washington, Seattle, Wash., 1985).
  10. R. E. Crochiere, L. R. Rabiner, Multirate Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1983).
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  12. P. K. Rajan, “A study on the properties of multidimensional fourier transforms,” IEEE Trans. Circuits Syst. CAS-31, 748–750 (1984).
  13. R. N. Bracewell, The Fourier Transform and Its Application (McGraw-Hill, New York, 1965).
  14. J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, New York, 1978).
  15. A. V. Oppenheim, R. W. Shafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).
  16. A. Papoulis, “Error analysis in sampling theory,” Proc. IEEE 54, 947–955 (1966). [CrossRef]
  17. R. J. Marks, D. Radbel, “Error of linear estimation of lost samples in an oversampled bandlimited signal,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 648–654 (1985).
  18. D. Radbel, “Noise and truncation effects in the estimation of sampled bandlimited signals,” master’s thesis (Department of Electrical Engineering, University of Washington, Seattle, Wash., 1983).
  19. D. Radbel, R. J. Marks, “An FIR estimation filter based on the sampling theorem,” IEEE Trans. Acoust. Speech Signal Process. ASSP-33, 455–460 (1985). [CrossRef]

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