On stationarizability for nonstationary 2-D random fields using discrete wavelet transforms

IEEE Transactions on Image Processing

Volumn 7, Issue 9, 1998, Pages 1359-1366

  Wu, Bing Fei ^a   Su, Yu Lin ^a  

^a NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

Author keywords

Discrete wavelet transform; Nonstationarity; Random fields

Indexed keywords

BROWNIAN MOVEMENT; MATHEMATICAL MODELS; WAVELET TRANSFORMS;

DISCRETE WAVELET TRANSFORMS (DWT);

IMAGE PROCESSING;

EID: 0032163159     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/83.709667     Document Type: Article

References (19)

1. G. Beylkin et al., Eds., Wavelets and Their Applications. Cambridge, U.K.: Jones and Bartlett, 1992.
2. C. K. Chui, An Introduction to Wavelets. New York: Academic, 1992.
3. I. Daubechies, "The wavelet transform, time-frequency localization and signal analysis," IEEE Trans. Inform. Theory, vol. 36, pp. 961-1005, 1990.
4. I. Daubechies, Ten Lectures on Wavelets. Philadelphia, PA: SIAM, 1992.
5. K. Falconer, Fractal Geometry: Mathematical Foundations And Applications. New York: Wiley, 1990.
6. P. Flandrin, "Wavelet analysis and synthesis of fractional Brownian motion," IEEE Trans. Inform. Theory, vol. 38, pp. 910-917, 1992.
7. S. Kandambe and G. F. Boudreaux-Bartels, "A comparison of wavelet functions for pitch detection of speech signals," in Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing, 1991, pp. 449-452.
8. L. M. Kaplan and C.-C. Kuo, "Fractal estimation from noisy data via discrete fractional Gaussian noise (DFGN) and the Haar basis," IEEE Trans. Signal Processing, vol. 41, pp. 3554-3562, 1993.
9. T. H. Koornwinder, Ed., Wavelets: An Elementary Treatment of Theory and Applications. Singapore: World Scientific, 1993.
10. H. Krim and J.-C. Pesquet, "Multiresolution analysis of a class of nonstationary processes," IEEE Trans. Inform. Theory, vol. 41, pp. 1010-1020, 1995.
11. P. Lancaster and M. Tismenetsky, The Theory of Matrices, 2nd ed. 1985.
12. S. G. Mallat, "A theory for multiresolution signal decomposition: The wavelet representation," IEEE Trans. Pattern Anal. Machine Intell., vol. 11, pp. 674-693, July 1989.
13. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. New York: McGraw-Hill, 1991.
14. H.-O. Peitgen and D. Saupe, Eds., The Science of Fractal Images. Berlin, Germany: Springer-Verlag, 1988.
15. J.-A. Riestra, A Generalized Taylor's Formula for Functions of Several Variables and Certain of Its Applications. Essex, U.K.: Longman House, 1995.
16. O. Rioul and M. Vetterli, "Wavelets and signal processing," IEEE Signal Processing Mag., pp. 14-38, Oct. 1991.
17. A. Rosenfeld and A. C. Kah, Digital Picture Processing, vol. 1, 2nd ed. New York: Academic, 1982.
18. A. H. Tewfik and M. Kim, "Correlation structure of the discrete wavelet coefficients of fractional Brownian motion," IEEE Trans. Inform. Theory, vol. 38, pp. 904-909, 1992.
19. A. M. Yaglom, Correlation Theory of Stationary and Related Random Functions I: Basic Results. Berlin, Germany: Springer-Verlag, 1986.