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Image restoration using a conjugate gradient-based adaptive filtering algorithm

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Abstract

A new two-dimensional (2D) sample-based conjugate gradient (SCG) algorithm is developed for adaptive filtering. This algorithm is based on the conjugate gradient method of optimization and therefore has a fast convergence characteristic. The SCG is computationally simpler than the recursive least squares (RLS) algorithm. The SCG algorithm with the equation-error and output-error methods is investigated for application in image restoration. Simulation results show that the new algorithm significantly outperforms existing algorithms in the restoration of noisy images.

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References

  1. M. R. Azimi-Sadjadi and H. Pan, Two-dimensional block diagonal LMS adaptive filtering,IEEE Trans. on Signal Processing, 2420–2429, Sept. 1994.

  2. P. H. Bauer, Finite wordlength effects in m-D digital filters with singularities on the stability boundary,IEEE Trans. Signal Processing, vol. SP-40, 894–900, April 1992.

    Google Scholar 

  3. P. H. Bauer and E. I. Jury, Stability analysis of multidimensional (m-D) direct realization of digital filters under the influence of nonlinearities,IEEE Trans. Acous. Speech, and Signal Process., vol. ASP-36, 1770–1780, Nov. 1988.

    Google Scholar 

  4. G. K. Boray and M. D. Srinath, Conjugate gradient techniques for adaptive filtering,IEEE Trans, Circuits and Syst., vol. CAS-39, 1–10, Jan. 1992.

    Google Scholar 

  5. T. Bose and M. Q. Chen, Conjugate gradient method in adaptive bilinear filtering,IEEE Trans. Signal Processing, vol. SP-43, 1503–1508, June 1995.

    Google Scholar 

  6. T. Bose and D. A. Trautman, Stability of first-order multidimensional digital filters under quantization,IEEE Trans. Signal Processing, vol. SP-41, 387–390, Jan. 1993.

    Google Scholar 

  7. S. G. Chen and Y. A. Kao, A new efficient 2-D LMS adaptive filtering algorithm,Proc. Intl. Symp. on Circuits and Systems, 233–236, May 1994.

  8. Y. S. Chung and M. Kanefsky, On 2-D recursive LMS algorithms using ARMA prediction for ADPCM encoding of images,IEEE Trans, on Image Processing, vol. 1, no. 3, July 1992.

  9. P. M. Clarkson,Optimal and Adaptive Signal Processing, CRC Press, Boca Raton, FL, 1993.

    Google Scholar 

  10. P. L. Feintuch, An adaptive recursive LMS filter,Proc. IEEE, vol. 64, 1622–1624, 1976.

    Google Scholar 

  11. M. M. Hadhoud and D. W. Thomas, The two-dimensional adaptive LMS (TDLMS) algorithm,IEEE Trans. Circuits and Syst., vol. CAS-35, 485–494, May 1988.

    Google Scholar 

  12. S. Haykin,Adaptive Filter Theory, Prentice-Hall, Englewood Cliffs, NJ, 1986.

    Google Scholar 

  13. A. Jenning, Influence of the eigenvalue spectrum on the convergence rate of the conjugate gradient method,J. Inst. Math. Appl., vol. 20, 67–72, 1977.

    Google Scholar 

  14. K. S. Joo, T. Bose, and J. W. Hall, Jr., 2-D nonlinear adaptive filtering for image restoration,Proc. IEEE Workshop on Nonlinear Signal and Image Processing, 1995.

  15. J. N. Lin, X. Nie, and R. Unbehauen, Two-dimensional LMS adaptive filter incorporating a local-mean estimator for image processing,IEEE Trans. Circuits Sys.-II: Analog and Digital Signal Processing, vol. CAS-40, 417–428, July 1993.

    Google Scholar 

  16. D. G. Luenberger,Introduction to Linear andNonlinear Programming, Addison-Wesley, Reading, MA, 1973.

    Google Scholar 

  17. W. B. Mikhail and S. M. Ghosh, Two-dimensional variable-step-size sequential adaptive gradient algorithms with applications,IEEE Trans. Circuits and Syst., vol. CAS-38, 1577–1580, Dec. 1991.

    Google Scholar 

  18. T. Soni, B. D. Rao, J. R. Zeidler, and W. H. Ku, Enhancement of images using the 2-D LMS adaptive algorithm,Proc. IEEE Intl. Conf. Acous., Speech, and Signal Processing, 3029–3032, May 1991.

  19. J. C. Strait and W. K. Jenkins, A fast two-dimensional quasi-Newton adaptive filter. Proc. Intl. Symp. on Circuits and Systems, 149–152, May 1994.

  20. H. Youlal, M. Janati-I, and M. Najim, Two-dimensional joint process lattice for adaptive restoration of images,IEEE Trans. Image Processing, 366–378, July 1992.

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Authors and Affiliations

  1. Department of Electrical Engineering, University of Colorado, Campus Box 110, P.O. Box 173364, 80217-3364, Denver, Colorado

    Kyung Sub Joo, Tamal Bose & Guo Fang Xu

Authors
  1. Kyung Sub Joo
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  2. Tamal Bose
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  3. Guo Fang Xu
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This work was supported in part by a grant from the Colorado Advanced Software Institute.

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Joo, K.S., Bose, T. & Xu, G.F. Image restoration using a conjugate gradient-based adaptive filtering algorithm. Circuits Systems and Signal Process 16, 197–206 (1997). https://doi.org/10.1007/BF01183274

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  • DOI: https://doi.org/10.1007/BF01183274

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