On the asymptotic performance of median smoothers in image analysis and nonparametric regression

Annals of Statistics

Volumn 24, Issue 4, 1996, Pages 1648-1666

  Koch, Inge ^a  

^a NONE

Author keywords

Asymptotic optimality; M estimation; Median smoother

Indexed keywords

EID: 0030364565     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1032298289     Document Type: Article

References (14)

1. BLOOMFIELD, P. and STEIGER, W. L. (1983). Least Absolute Deviations: Theory, Applications, and Algorithms. Birkhäuser, Boston.
2. BOVIK, A. C., HUANG, T. S. and MUNSON, D. C. (1987). The effect of median filtering on edge estimation and detection. IEEE Trans. Pattern Anal. Machine Intell. 9 181-194.
3. CHUNG, K. L. (1974). A Course in Probability Theory. Academic Press, London.
4. CRAMER, H. (1946). Mathematical Methods of Statistics. Princeton Univ. Press.
5. EUBANK, R. L. (1988). Spline Smoothing and Nonparametric Regression. Dekker, New York.
6. GALLAGHER, N. C. and WISE, G. L. (1981). A theoretical analysis of the properties of median filters. IEEE Trans. Acoust., Speech, Signal Processing. 29 1136-1141.
7. HARDLE, W. and GASSER, T. (1984). Robust non-parametric function fitting. J. Roy. Statist. Soc. Ser. B 46 242-251.
8. HUANG, T. S. (1981). Two-Dimensional Signal Processing: Transforms and Median Filters. Springer, New York.
9. HUBER, P. J. (1964). Robust estimation of a location parameter. Ann. Math. Statist. 35 73-101.
10. POLLARD, D. (1984). Convergence of Stochastic Processes. Springer, New York.
11. POLLARD, D. (1990). Empirical Processes: Theory and Applications. IMS, Hayward, CA.
12. PRIESTLEY, M. B. and CHAO, M. T. (1972). Non-parametric function fitting. J. Roy. Statist. Soc. Ser. B 34 385-392.
13. SHORACK, G. R. and WELLNER, J. A. (1986). Empirical Processes with Applications to Statistics. Wiley, New York.
14. YANG, G. J. and HUANG, T. S. (1981). The effect of median filtering on edge location estimation. Computer Graphics and Image Processing 15 224-245.