Abstract
An adaptive filtering algorithm is developed for the class of stack filters, which is a class of nonlinear filters obeying a weak superposition property.
The adaptation algorithm can be interpreted as a learning algorithm for a group of decision-making units, the decisions of which are subject to a set of constraints called the stacking constraints. Under a rather weak statistical assumption on the training inputs, the decision strategy adopted by the group, which evolves according to the proposed learning algorithm, can be shown to converge asymptotically to an optimal strategy in the sense that it corresponds to an optimal stack filter under the mean absolute error criterion.
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8. References
P.D. Wendt, E.J. Coyle, and N.C. Gallagher, “Stack Filters,” IEEE Trans. on Acoustics, Speech and Signal Processing, vol. ASSP-34, no. 4, pp. 898–911, August 1986.
J.P. Fitch, E.J. Coyle, and N.C. Gallagher, “Median Filtering by Threshold Decomposition,” IEEE Trans. on Acoustics, Speech and Signal Processing, vol. ASSP-32, no. 6, pp. 1183–89, Dec. 1984.
J.P. Fitch, E.J. Coyle, and N.C. Gallagher, “Threshold decomposition of multi-dimensional rank order operations,” IEEE Trans. on Circuits and Systems, vol. CAS-32, no. 5, May 1985.
J.W. Tukey, “Nonlinear (nonsuperposable) methods for smoothing data,” in Conf. Rec., 1974 EASCON,
T. Nodes and N.C. Gallagher, “Median Filters: Some Modifications and Their Properties,” IEEE Trans. on Acoustics, Speech and Signal Processing, vol. ASSP-30, pp. 739–46, Oct. 1982.
J. Serra, Image Analysis and Mathematical Morphology, New York: Academic Press, 1982.
G. Matheron, Random Sets and Integral Geometry, New York: Wiley, 1975.
P.A. Maragos, R.W. Schafer, “Morphological Filters — Part II: Their Relations to Median, Order-Statistic, and Stack Filters,” IEEE Trans. on Acoustics, Speech and Signal Processing, vol. ASSP-35, no. 8, pp. 1170–84, August 1987.
J. H. Lin and E. J. Coyle, “Optimal Nonlinear Filtering under the Mean Absolute Error Criterion,” Proc. IEEE Int. Conf. on Acoustics, Speech, Signal Processing, New York, NY, April 1988.
P.A. Maragos and R.W. Schafer, “Morphological Filters-Part I: Their Set-Theoretic Analysis and Relations to Linear Shift-Invariant Filters,” IEEE Transactions on Acoustics, Speech and Signal Processing, vol. ASSP-35, no. 8, pp. 1153–69, August 1987.
E.J. Coyle, “Rank order operators and the mean absolute error criterion,” IEEE Trans. on Acoustics, Speech, and Signal Processing, vol. ASSP-36, no. 1, pp. 63–76, Jan. 1988.
E.J. Coyle and J.-H. Lin, “Stack Filters and the Mean Absolute Error Criterion,” IEEE Trans. on Acoustics, Speech and Signal Processing, vol. ASSP-36, no. 8, August 1988.
J.P. Hayes, et al., “Architecture of a Hypercube Supercomputer,” Proceedings 1986 International Conference on Parallel Processing, pp. 653–660, Aug. 1986.
S. T. Alexander, Adaptive Signal Processing: Theory and Application, Springer-Verlag: New York, 1986.
M. L. Honig, D. G. Messerschmitt, Adaptive Filters: Structures, Algorithms, and Applications, Kluwer Academic, 1984.
C. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Prentice Hall: Englewood Cliffs, NY, 1982
B. Hajek, “Hitting-time and Occupation-time Bounds Implied by Drift Analysis with Applications,” Advances in Applied Probability, 14, pp 502–525, 1982.
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© 1989 Springer-Verlag
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Lin, J.H., Sellke, T.M., Coyle, E.J. (1989). Adaptive stack filtering under the mean absolute error criterion. In: Porter, W.A., Kak, S.C. (eds) Advances in Communications and Signal Processing. Lecture Notes in Control and Information Sciences, vol 129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042738
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DOI: https://doi.org/10.1007/BFb0042738
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