Estimation of 2-D noisy fractional Brownian motion and its applications using wavelets

IEEE Transactions on Image Processing

Volumn 9, Issue 8, 2000, Pages 1407-1419

  Liu, Jen Chang ^b,c   Hwang, Wen Liang ^c   Chen, Ming Syan ^a,b  

^a IEEE

^b NATIONAL TAIWAN UNIVERSITY   (Taiwan)

^c INSTITUTE OF INFORMATION SCIENCE   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BROWNIAN MOVEMENT; COMPUTER SIMULATION; DIGITAL FILTERS; FRACTALS; IMAGE ANALYSIS; PARAMETER ESTIMATION; REGRESSION ANALYSIS; TWO DIMENSIONAL; WAVELET TRANSFORMS;

DENOISING; FRACTAL IMAGES; FRACTAL PARAMETER ESTIMATION ALGORITHM; FRACTIONAL BROWNIAN MOTION; WIENER FILTER;

IMAGE ENHANCEMENT;

EID: 0034247488     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/83.855435     Document Type: Article

References (25)

1. D. P. Bertsekas, Constrained Optimization and Lagrange Multiplier Methods. New York: Academic, 1982.
2. C. Chen, J. S. Deponte, and M. D. Fox, "Fractal feature analysis in medical imaging," IEEE Trans. Med. Imag., vol. MI-8, pp. 133-142, 1989.
3. N. Delprat, B. Escudie, P. Guillemain, R. Kronland-Martinet, P. Tchamitchian, and B. Torresani, "Asymptotic wavelet and Gabor analysis: Extraction of instantaneous frequencies," IEEE Trans. Inform. Theory, vol. 38, Mar. 1992.
4. P. Flandrin, "On the spectrum of fractional Brownian motions," IEEE Trans. Inform. Theory, vol. IT-353, pp. 197-199, Jan. 1989.
5. P. Flandrin, "Wavelet analysis and synthesis of fractional Brownian motion," IEEE Trans. Inform. Theory, vol. 38, Mar. 1992.
6. W. L. Hwang and S. Mallat, "Characterization of self-similar multifractals with wavelet maxima," Appl. Comput. Harmon. Anal., vol. 1, pp. 316-328, 1994.
7. W. L. Hwang, "Estimation of fractional Brownian motion embedded in a noisy environment using nonorthogonal wavelets," IEEE Trans. Signal Processing, vol. 47, Aug. 1999.
8. L. Kaplan and C.-C. Kuo, "Fractal estimation from noisy measurements via discrete fractional gaussian noise and the Haar basis," IEEE Trans. Signal Processing, vol. 41, Dec. 1993.
9. _, "Texture segmentation via Haar fractal feature estimation," J. Vis. Commun. Image Represent., vol. 6, Dec. 1995.
10. _, "Texture roughness analysis and synthesis via extended self-similar (ESS) model," IEEE Trans. Image Processing, vol. 4, Nov. 1995.
11. _, "An improved method for 2-D self-similar image synthesis, "IEEE Trans. Image Processing, vol. 5, May 1996.
12. T. Lundhal, W. J. Ohley, S. M. Kay, and R. Siffert, "Fractional Brownial motion: An ML estimator and its application to image texture," IEEE Trans. Med. Imag., vol. MI-5, Sept. 1986.
13. S. Mallat and W. L. Hwang, "Singularity detection and processing with wavelets," IEEE Trans. Inform. Theory, vol. 38, Mar. 1992.
14. S. Mallat and S. Zhong, "Characterization of signals from multi-scale edges," IEEE Trans. Pattern Anal. Machine Intell., vol. 14, no. 7, 1992.
15. B. Mandelbrot and H. Van Ness, "Fractional Brownian motions, fractional noises and applications," SIAM Rev., vol. 10, Oct. 1968.
16. A. P. Pentland, "Fractal-based description of natural scenes," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, pp. 661-674, Nov. 1984.
17. K. Perlin, "Hypertexture," Comput. Graph., vol. 23, July 1989.
18. P. J. Rousseeuw, "Least median of squares regression," J. Amer. Statist. Assoc., vol. 79, Dec. 1984.
19. Z. Cvetkovic and M. Vetterli, "Discrete-time wavelet extrema representation: Design and consistent reconstruction," IEEE Trans. Signal Processing, vol. 43, Mar. 1995.
20. G. W. Wornell, "A Karhunen-Loeve-like expansion for 1/f processes via wavelet," IEEE Trans. Inform. Theory, vol. 36, pp. 859-861, July 1990.
21. G. W. Wornell and A. Oppenheim, "Estimation of fractal signals from noisy measurements using wavelet," IEEE Trans. Signal Processing, vol. 40, Mar. 1992.
22. S. Hoefer, F. Heil, M. Pandit, and R. Kumaresan, "Segmentation of textures with different roughness using the model of isotropic two-dimensional fractional Brownian motion," Int. Conf. Acoustics, Speech, Signal Processing, 1993.
23. I. S. Reed, P. C. Lee, and T. K. Truong, "Spectral representation of fractional Brownian motion in n-dimensions and its properties," IEEE Trans. Inform. Theory, vol. 41, p. 1439, Sept. 1995.
24. B. F. Wu and Y. L. Su, "On stationarizability for nonstationary 2-D random fields using discrete wavelet transforms," IEEE Trans. Image Processing, vol. 7, pp. 1359-1366, Sept. 1998.
25. A. Arneodo, N. Decoster, and S. G. Roux, "Intermittency, log-normal statistics, and multifractal cascade process in high-resolution satellite images of cloud structure," Phys. Rev. Lett., vol. 83, pp. 1255-1258, Aug. 1999.