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Abstract

In the preceding chapters, the design and analysis of recursive and nonrecur-sive one-dimensional (1-D) and two-dimensional (2-D) digital filters have been discussed for the case of deterministic input signals. However, in situations such as satellite and radar imaging, knowledge of the original image is not deterministically available. Each pixel is considered as a random variable and the image is thought of as a sample of an ensemble of images. For simplicity in modeling, the image is assumed to have a Gaussian distribution which can be specified uniquely by its first- and second-order moments (mean and covariances). To perform the estimation and filtering process, the image should be represented by an appropriate statistical model.

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References

  1. A. K. Jain and J. R. Jain, Partial difference equations and finite difference methods in image processing—Part 2: image restoration, IEEE Trans. Autom. Control AC-23, 817–833 (1978).

    Article  Google Scholar 

  2. J. W. Woods and C. H. Radewan, Kaiman filtering in two dimensions, IEEE Trans. Inf. Theory IT-23, 473–482 (1977).

    Article  MathSciNet  Google Scholar 

  3. B. R. Suresh and B. A. Shenoi, New results in two-dimensional Kaiman filtering with applications to image restoration, IEEE Trans. Circuits Syst. CAS-28, 307–319 (1981).

    Article  Google Scholar 

  4. M. R. Azimi-Sadjadi and P. W. Wong, Two-dimensional block Kaiman filtering for image restoration, IEEE Trans. Acoust., Speech, Signal Process ASSP-35, 1736–1749 (1987).

    Article  Google Scholar 

  5. E. J. Delp, R. L. Kashyap, and O. R. Mitchell, Image data compression using autoregressive time series models, Pattern Recognition 11, 313–323 (1979).

    Article  Google Scholar 

  6. R. Chellappa and R. L. Kashyap, Texture synthesis using 2-D noncausal autoregressive models, IEEE Trans. Acoust., Speech, Signal Process ASSP-33, 194–202 (1985).

    Article  Google Scholar 

  7. S. Lawrence Marple, Jr., Digital Spectral Analysis with Applications, Prentice-Hall, Engle-wood Cliffs, NJ (1987).

    Google Scholar 

  8. R. Kumar, A fast algorithm for solving a Toeplitz system of equations, IEEE Trans. Acoust., Speech, Signal Process ASSP-33, 254–267 (1985).

    Article  Google Scholar 

  9. P. J. Brockwell and R. A. Davis, Time Series Theory and Methods, Springer-Verlag, Berlin (1987).

    MATH  Google Scholar 

  10. A. K. Jain, Advances in mathematical models for image processing, Proc. IEEE 69, 502–528 (1981).

    Article  Google Scholar 

  11. S. Ranganath and A. K. Jain, Two-dimensional linear prediction models—Part 1: Spectral factorization and realization, IEEE Trans. Acoust., Speech, Signal Process ASSP-33, 280–299 (1985).

    Article  Google Scholar 

  12. R. L. Kashyap, Characterization and estimation of two-dimensional ARMA models, IEEE Trans. Inf. Theory IT-30, 736–745 (1984).

    Article  MathSciNet  Google Scholar 

  13. A. K. Jain, A semicausal model for recursive filtering of two-dimensional images, IEEE Trans. Comput. C-26, 343–350 (1977).

    Article  Google Scholar 

  14. G. C. Verghese, B. C. Levy, and T. Kailath, A generalized state-space for singular systems, IEEE Trans. Autom. Control AC-26, 811–831 (1981).

    Article  MathSciNet  Google Scholar 

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© 1989 Springer Science+Business Media New York

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King, R., Ahmadi, M., Gorgui-Naguib, R., Kwabwe, A., Azimi-Sadjadi, M. (1989). Image Modeling. In: Digital Filtering in One and Two Dimensions. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0918-3_10

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  • DOI: https://doi.org/10.1007/978-1-4899-0918-3_10

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-0920-6

  • Online ISBN: 978-1-4899-0918-3

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