Nonparametric two-dimensional point spread function estimation for biomedical imaging

  • T. D. Doukoglou
  • I. W. Hunter
  • R. E. Kearney
Medical Physics and Imaging

Abstract

The problem of identifying optical system point spread functions (PSFs) arises frequently in the area of image processing and restoration. The paper presents a method for determining two-dimensional PSFs from input/output image signals. The PSF of the system is determined from a set of linear equations involving elements of the input autocorrelation function and the input/output cross-correlation function. The resulting PSF is the one that minimises the sum of squares difference between the actual output image and the predicted one.

Keywords

Linear system identification Multidimensional Nonparametric Point spread function estimation Toeplitz matrix equation Two-dimensional filter estimation 

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References

  1. Akaike, H. (1973) Block Toeplitz matrix inversion.SIAM J. Appl. Math.,24, 234–241.MATHMathSciNetCrossRefGoogle Scholar
  2. Bhargava, U. K., Kashyap, R. L. andGoodman, D. M. (1988) Two non-parametric techniques for impulse response identification.IEEE Trans.,ASSP-36, 984–995.Google Scholar
  3. Blachut, R. E. (1985)Fast algorithms for digital signal processing. Addison-Wesley, Reading, Massachusetts.Google Scholar
  4. Chiang, H. andNikias, C. L. (1990) Adaptive deconvolution and identification of nonminimum phase FIR systems based on cumulants.IEEE Trans.,AC-35, 36–47.MATHMathSciNetGoogle Scholar
  5. Cunningham, I. A. andFenster, A. (1987) A method for modulation transfer function determination from edge profiles with correction for finite-element differentiation.Med. Phys.,14, 533–537.CrossRefGoogle Scholar
  6. Doukoglou, T. D., Hunter, I. W., Kearney, R. E., Lafontaine, S. andNielsen, P. F. (1988) Deconvolution of laser scanning microscope images using system identification techniques. Proc. Canadian Med. Biol. Eng. Conf.,14, 105–106.Google Scholar
  7. Eykhoff, P. (1974)System identification-parameter and state estimation. John Wiley, New York.Google Scholar
  8. Golub, G. H. andVan Loan, C. F. (1989)Matrix computations, 2nd edn. The Johns Hopkins University Press, Maryland.Google Scholar
  9. Gonzalez, R. C. andWintz, P. (1987)Digital image processing. Addison-Wesley, New York.Google Scholar
  10. Hunter, I. W. andKearney, R. E. (1983) Two-sided linear filter identification.Med. & Biol. Eng. & Comput.,21, 203–209.CrossRefGoogle Scholar
  11. Hunter, I. W., Lafontaine, S., Nielsen, P. F. M. andHunter, P. (1988) An apparatus for laser scanning microscopy and dynamic mechanical testing of muscle cells.Proc. SPIE Conf. Scan. Imag. Technol.,10–28, 152–159.Google Scholar
  12. Kalouptsidis, N., Carayannis, G. andManolakis, D. (1982) On block matrices with elements of special structure. Proc. IEEE Int. Conf. Acoust. Speech and Signal Processing, Paris, 1744–1747.Google Scholar
  13. Levinson, N. (1947) The Wiener RMS error criterion in filter design and prediction.J. Math. Phys.,25, 261–278.MathSciNetGoogle Scholar
  14. Ljung, L. andSöderström, T. (1983)Theory and practice of recursive identification. MIT Press, Cambridge, Massachusetts.Google Scholar
  15. Marple, L. S. (1981) Efficient least squares FIR system identification.IEEE Trans.,ASSP-29, 62–73.Google Scholar
  16. Numerical Algorithms Group (1985)NAG library manuals. Numerical Algorithms Group Ltd., Dowers Grove, Illinois.Google Scholar
  17. Press, W., Flannery, B. P., Teukolsky, S. A. andVetterling, W. T. (1986)Numerical recipes. Cambridge Univ. Press, UK.Google Scholar
  18. Rajan, P. K. andReddy, H. C. (1988) Formulation of 2-D normal equations using 2-D to 1-D form preserving transformations.IEEE Trans.,ASSP-36, 415–419.Google Scholar
  19. Reddy, P. S., Reddy, D. R. andSwamy, M. N. S. (1984) Proof of a modified form of Shank's conjecture on the stability of 2-D planar least square inverse polynomials and its implications. —Ibid.,CAS-31, 1009–1015.MATHMathSciNetGoogle Scholar
  20. Robinson, E. A. (1978)Multichannel time series analysis with digital computer programs (revised edition only). Holden-Day, San Francisco.Google Scholar
  21. Sones, R. (1984) A method to measure the MTF of digital X-ray systems.Med. Phys.,11, 166–171.CrossRefGoogle Scholar
  22. Wax, M. andKailath, T. (1983) Efficient inversion of Toeplitzblock Toeplitz matrix.IEEE Trans.,ASSP-31, 1218–1221.MATHMathSciNetGoogle Scholar
  23. Yaroslavsky, L. P. (1985)Digital picture processing. Springer-Verlag, Berlin.Google Scholar

Copyright information

© IFMBE 1993

Authors and Affiliations

  • T. D. Doukoglou
    • 1
  • I. W. Hunter
    • 1
  • R. E. Kearney
    • 1
  1. 1.Department of Biomedical EngineeringMcGill UniversityMontréalCanada

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