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Two-dimensional model-based power spectrum estimation for nonextendible correlation bisequences

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Abstract

The extendibility of estimated correlation bisequences from an available sampled data array is described in terms of the generating functions of associated block Toeplitz with Toeplitz block (BTTB) matrices. The periodogram-based correlation bisequences are shown to be extendible. It is shown that the method of resultants and subresultants is convenient for generating the nonlinear constraints in the optimization problem which is solved iteratively for power spectrum estimation. A nontrivial example illustrates the concepts developed.

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References

  1. H. C. Andrews and B. R. Hunt,Digital Image Restoration, Prentice-Hall, Engelwood Cliffs, NJ, 1977.

    Google Scholar 

  2. N. Balram and J. M. F. Moura, Noncausal Gauss-Markov random fields: Parameter structure and estimation,IEEE Trans. on Inform. Theory, 39(4):1333–1355, July 1993.

    Google Scholar 

  3. S. Barnett,Polynomials and Linear Control Systems, Marcel Dekker, New York, 1983.

    Google Scholar 

  4. J. Besag, Spatial interaction and the statistical analysis of lattice systems,J. Royal Statist. Soc., Series B, 36:192–236, 1974.

    Google Scholar 

  5. N. K. Bose,Applied Multidimensional Systems Theory, Van Nostrand Reinhold, New York, 1982.

    Google Scholar 

  6. N. K. Bose and S. Basu, Tests for polynomial zeros on a polydisc distinguished boundary,IEEE Trans. on Circuits and Systems, CAS-25(9):684–693, September 1978.

    Google Scholar 

  7. N. K. Bose and K. J. Boo, Asymptotic eigenvalue distribution of block-Toeplitz matrices, Technical report, Department of Electrical Engineering, The Pennsylvania State University, University Park, 1996, preprint.

    Google Scholar 

  8. B. M. Brown, On the distribution of the zeros of a polynomial,Quart. J. Math. Oxford, 2(16):241–256, 1965.

    Google Scholar 

  9. R. Chellappa, Y. H. Hu, and S. Y. Kung, On two-dimensional Markov spectral estimation,IEEE Trans. on ASSP, ASSP-31(4):836–841, August 1983.

    Google Scholar 

  10. B. W. Dickinson, Two-dimensional Markov spectrum estimates need not exist,IEEE Trans. on Inform. Theory, IT-26(1): 120–121, January 1980.

    Google Scholar 

  11. G. H. Golub and C. F. Van Loan,Matrix Computation, The Johns Hopkins University Press, Baltimore, MD, 1989.

    Google Scholar 

  12. R. M. Gray, On the asymptotic eigenvalue distribution of Toeplitz matrices,IEEE Trans. on Inform. Theory, IT-18(6):725–730, November 1972.

    Google Scholar 

  13. R. Hettich,Semi-Infinite Programming, Springer-Verlag, New York, 1978.

    Google Scholar 

  14. A. K. Jain, Advances in mathematical models for image processing,Proceedings of the IEEE, 69(5):502–528, May 1981.

    Google Scholar 

  15. E. I. Jury,Inners and Stability of Dynamics Systems, Robert E. Krieger Publishing, Malabar, FL, 1982.

    Google Scholar 

  16. E. I. Jury,Theory and Application of the z-Transform Methods, Robert E. Krieger Publishing, Malabar, FL, 1982.

    Google Scholar 

  17. S. Lakshmanan and H. Derin, Necessary and sufficient conditions on the parameters of 1-D Gaussian Markov processes,IEEE Trans. on Signal Processing, 40(5):1266–1271, May 1992.

    Google Scholar 

  18. S. Lakshmanan and H. Derin, Valid parameter space for 2-D Gaussian Markov random fields,IEEE Trans. on Inform. Theory, 39(2):703–709, March 1993.

    Google Scholar 

  19. S. Lakshmanan and H. Derin, Extendibility tests for multidimensional covariance sequences,IEEE Trans. on Signal Processing, 41(5): 1836–1846, May 1993.

    Google Scholar 

  20. S. W. Lang and J. H. McClellan, Multidimensional MEM spectral estimation,IEEE Trans. on ASSP, ASSP-30(6):880–887, December 1982.

    Google Scholar 

  21. S. W. Lang and J. H. McClellan, Spectral estimation for sensor arrays,IEEE Trans. on ASSP, ASSP-31(2):349–358, April 1983.

    Google Scholar 

  22. H. Lev-Ari, S. R. Parker, and T. Kailath, Multidimensional maximum-entropy covariance extension,IEEE Trans. on Inform. Theory, 35(3):497–508, May 1989.

    Google Scholar 

  23. J. S. Lim,Two-Dimensional Signal and Image Processing, Prentice-Hall, Englewood Cliffs, NJ, 1990.

    Google Scholar 

  24. J. S. Lim and A. V. Oppenheim,Advanced Topics in Signal Processing, Prentice-Hall, Englewood Cliffs, NJ, 1988.

    Google Scholar 

  25. J. M. F. Moura and N. Balram, Recursive structure of noncausal Gauss-Markov random fields,IEEE Trans. on Inform. Theory, 38(2):334–354, March 1992.

    Google Scholar 

  26. J. G. Proakis, C. M. Rader, F. Ling, and C. L. Nikias,Advanced Digital Signal Processing, Macmillan Publishing Company, New York, 1992.

    Google Scholar 

  27. G. Sharma and R. Chellappa, A model-based approach for estimation of two-dimensional maximum entropy power spectra,IEEE Trans. on Inform. Theory, IT-31(l):90–99, January 1985.

    Google Scholar 

  28. G. Strang, A proposal for Toeplitz matrix calculations,Stud. Appl. Math., 74:171–176, 1986.

    Google Scholar 

  29. E. E. Tyrtyshnikov, A unifying approach to some old and new theorems on distribution and clustering,Linear Algebra and Its Applications, 232:1–43, 1996.

    Google Scholar 

  30. P. Whittle, On stationary processes in the plane,Biometrika, 41:434–449, 1954.

    Google Scholar 

  31. J. W. Woods, Two-dimensional Markov spectral estimation,IEEE Trans. on Inform. Theory, IT-22(5):552–559, September 1976.

    Google Scholar 

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Authors and Affiliations

  1. Department of Electrical Engineering, The Spatial and Temporal Signal Processing Center, The Pennsylvania State University, 16802, University Park, Pennsylvania

    K. J. Boo & N. K. Bose

Authors
  1. K. J. Boo
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  2. N. K. Bose
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Additional information

This paper is in memory of Sydney R. Parker.

This work was partly supported by Korea Telecom and partly by HRB Systems.

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Boo, K.J., Bose, N.K. Two-dimensional model-based power spectrum estimation for nonextendible correlation bisequences. Circuits Systems and Signal Process 16, 141–163 (1997). https://doi.org/10.1007/BF01183272

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  • DOI: https://doi.org/10.1007/BF01183272

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