Secondarily constrained Boolean filters

Signal Processing

Volumn 71, Issue 3, 1998, Pages 247-263

  Sarca, Octavian V ^a   Dougherty, Edward R ^b   Astola, Jaakko ^a  

^a TAMPERE UNIVERSITY OF TECHNOLOGY   (Finland)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Estimation precision; Image restoration; Linearly separable Boolean functions; Optimal binary image filters

Indexed keywords

ALGORITHMS; BOOLEAN FUNCTIONS; CONSTRAINT THEORY; ERRORS; ESTIMATION; ITERATIVE METHODS; OPTIMIZATION;

BINARY FILTERS; BOOLEAN FILTERS;

DIGITAL FILTERS;

EID: 0032288990     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0165-1684(98)00149-2     Document Type: Article

References (26)

1. S. Agaian, J. Astola, K. Egiazarian, Binary Polynomial Transforms and Nonlinear Digital Filters, Marcel Dekker, New York, NY, 1995.
2. J. Barrera, E.R. Dougherty, N.S. Tomita, Automatic programming of binary morphological machines by design of statistically optimal operators in the context of computational learning theory, J. Electronic Imaging 6 (January 1997) 54-67.
3. A. Cichocki, R. Unbehauen, Neural Networks for Optimization and Signal Processing, Wiley, Chichester, 1993.
4. E.R. Dougherty, Optimal mean-square N-observation digital morphological filters, I. optimal binary filters, J. Comput. Vision Graphics Image Process. 55 (January 1992) 36-54.
5. E.R. Dougherty, J. Barrera, Bayesian design of optimal morphological operators based on prior distributions for conditional probabilities, Acta Stereologica 16 (3) (1997) 167-174.
6. E.R. Dougherty, R.P. Loce, Optimal mean-absolute-error hit-or-miss filters: Morphological representation and estimation of the binary conditional expectation, Opt. Eng. 32 (April 1993) 815-827.
7. E.R. Dougherty, R.P. Loce, Precision of morphologicalrepresentation estimators for translation-invariant binary filters: increasing and nonincreasing, Signal Processing 40 (1994) 129-154.
8. E.R. Dougherty, R.P. Loce, Optimal binary differencing filters: design, logic complexity, precision analysis, and application to digital document processing, J. Electronic Imaging 5 (January 1996) 66-86.
9. J.P. Fitch, E.J. Coyle, N.C. Gallagher, Jr., Median filtering by threshold decomposition, IEEE Trans. Acoust. Speech Signal Process. 32 (December 1984) 1183-1188.
10. J.P. Fitch, E.J. Coyle, N.C. Gallagher, Jr., The analog median filter, IEEE Trans. Acoust. Speech Signal Process. 38 (June 1990) 955-968.
11. R. Fletcher, Practical Methods of Optimization, 2nd ed., Wiley, New York, 1990.
12. S. Haykin, Neural Networks - A Comprehensive Foundation, Macmillan College Publishing Company, New York, 1994.
13. S. Haykin, Adaptive Filter Theory, 3rd ed., Prentice Hall, Upper Saddle River, NJ, 1996.
14. J. Hertz, A. Krogh, R.G. Palmer, Introduction to the Theory of Neural Computation, Addison-Wesley, Redwood City, CA, 1991.
15. M. Ismail, T. Fiez, Analog VLSI - Signal and Information Processing, McGraw-Hill, Singapore, 1994.
16. K.D. Lee, Y.H. Lee, Threshold Boolean filters, IEEE Trans. Signal Process. 42 (August 1994) 2022-2036.
17. R.P. Loce, E.R. Dougherty, Optimal morphological restoration: The morphological filter mean-absolute-error theorem, Visual Comm. Image Repres. 3 (December 1992) 412-432.
18. R.P. Loce, E.R. Dougherty, Design and application of binary differencing filters, Proc. SPIE 2422 (February 1995) 338-349.
19. R.P. Loce, E.R. Dougherty, Enhancement and Restoration of Digital Documents: Statistical Design of Nonlinear Algorithms, SPIE Press, Bellingham, WA, 1997.
20. S. Muroga, Threshold Logic and its Applications, Wiley, New York, 1971.
21. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C - The Art of Scientific Computing, 2nd ed., Cambridge University Press, Cambridge CB2 1RP, UK, 1992.
22. F. Rosenblatt, The perceptron - a perceiving and recognizing automation, Cornell Aeronautical Laboratory Report, January 1957.
23. F. Rosenblatt, Principles of Neurodynamics, Spartan Books, East Lansing, MI, 1962.
24. C.L. Sheng, Threshold Logic, Academic Press, New York, 1969.
25. B. Widrow, S.D. Stearns, Adaptive Signal Processing, Prentice-Hall, Englewood Cliffs, NJ, 1985.
26. L. Yin, J.T. Astola, Y.A. Neuvo, Optimal weighted order statistic filters under the mean absolute error criterion, Proc. IEEE Internat. Conf. Acoust. Speech Signal Processing, vol. 4, May 1991, pp. 2529-2532.