Multiscale autoregressive models and wavelets

IEEE Transactions on Information Theory

Volumn 45, Issue 3, 1999, Pages 828-845

  Daoudi, Khalid ^a   Frakt, Austin B ^a   Willsky, Alan S ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BROWNIAN MOVEMENT; MATHEMATICAL MODELS; REGRESSION ANALYSIS;

FRACTIONAL BROWNIAN MOTION; MULTISCALE AUTOREGRESSIVE (MAR) MODELS;

DIGITAL SIGNAL PROCESSING;

EID: 0032623730     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.761321     Document Type: Article

References (39)

1. P. Abry and F. Sellan The wavelet-based synthesis for fractional Brownian motion proposed by F. Sellan and Y. Meyer: Remarks and fast implementation Appl. Computational Harmonic Anal. vol. 3 pp. 377-383 1996.
2. H. Akaike Stochastic theory of minimal realizations IEEE Trans. Automat. Contr. vol. AC-19 pp. 667-674 Dec. 1974.
3. - Markovian representation of stochastic processes by canonical variables SIAM J. Contr. vol. 13 no. 1 pp. 162-173 Jan. 1975.
4. K. S. Arun and S. Y. Kung Balanced approximation of stochastic systems SIAM J. Matrix Anal. Appl. vol. 11 no. 1 pp. 42-68 Jan. 1990.
5. M. Basseville A. Benveniste K. C. Chou S. A. Golden R. Nikoukhah and A. S. Willsky Modeling and estimation of multiresolution stochastic processes IEEE Trans. Inform. Theory vol. 38 pp. 766-784 Mar. 1992.
6. H. Cheng and C. A. Bouman Trainable context model for multiscale segmentation in Proc. IEEE Int. Conf. Image Processing Chicago IL Oct. 1998.
7. K. C. Chou A. S. Willsky and A. Benveniste Multiscale recursive estimation data fusion and regularization IEEE Trans. Automat. Contr. vol. 39 pp. 46478 Mar. 1994.
8. K. C. Chou A. S. Willsky and R. Nikoukhah Multiscale systems Kaiman filters and Riccati equations IEEE Trans. Automat. Contr. vol. 39 pp. 47992 Mar. 1994.
9. K. Chou A stochastic modeling approach to multiscale signal processing Ph.D. dissertation Massachusetts Institute of Technology May 1991.
10. R. L. Claypoole R. G. Baraniuk and R. D. Nowak Adaptive wavelet transforms via lifting in Trans. Int. Conf. Acoustics Speech and Signal Processing Seattle WA May 1998 pp. 1513-1516.
11. A. Cohen I. Daubechies and P. Vial Wavelet bases on the interval and fast algorithms J. Appl. Computational Harmonic Anal. vol. 1 pp. 54-81 1993.
12. M. S. Grouse and R. G. Baraniuk Simplified wavelet-domain hidden Markov models using contexts in Proc. IEEE Int. Conf. Acoustics Speech and Signal Processing Seattle WA May 1998 pp. 2277-2280.
13. M. S. Grouse R. D. Nowak and R. G. Baraniuk Wavelet-based statistical signal processing using hidden Markov models IEEE Trans. Signal Processing vol. 46 no. 4 pp. 886-902 Apr. 1998.
14. M. Daniel and A. S. Willsky Modeling and estimation of fractional Brownian motion using multiresolution stochastic processes in Fractals in Engineering J. L. Vehel E. Lutton and C. Tricot Eds. New York: Springer 1997 pp. 124-137.
15. ___ A multiresolution methodology for signal-level fusion and data assimilation with applications to remote sensing Proc. IEEE vol. 85 pp. 164-180 Jan. 1997.
16. K. Daoudi A. B. Frakt and A. S. Willsky Multiscale autoregressive models and wavelets: Extended version Tech. Rep. LIDS-P-2437 Massachusetts Institute of Technology Nov. 1998.
17. I. Daubechies Ten Lectures on Wavelets SIAM 1992.
18. I. Daubechies and W. Sweldens Factoring wavelet transforms into lifting steps J. Fourier Analysis Appl. vol. 4 no. 3 pp. 245-267 1998.
19. U. B. Desai and D. Pal A realization approach to stochastic model reduction and balanced stochastic realizations in IEEE Conf. Decision and Control 1982 pp. 1105-1112.
20. E. Fabre New fast smoothers for multiscale systems IEEE Trans. Signal Processing vol. 44 no. 8 pp. 1893-1911 Aug. 1996.
21. P. W. Fieguth and A. S. Willsky Fractal estimation using models on multiscale trees IEEE Trans. Signal Processing vol. 44 pp. 1297-1300 May 1996.
22. P. Flandrin Wavelet analysis and synthesis of fractional Brownian motion IEEE Trans. Inform. Theory vol. 38 pp. 910-917 Mar. 1992.
23. A. B. Frakt A realization theory for multiscale autoregressive stochastic models Ph.D. dissertation proposal Nov. 1997.
24. A. B. Frakt and A. S. Willsky Computationally Efficient Stochastic Realization for Internal Multiscale Autoregressive Models to be published.
25. - Efficient multiscale stochastic realization in Int. Conf. Acoustics Speech and Signal Processing Seattle WA May 1998.
26. W. W. Irving W. C. Karl and A. S. Willsky A theory for multiscale stochastic realization in Proc. 33rd IEEE Conf. Decision and Control Lake Buena Vista FL Dec. 1994 vol. l pp. 655-662.
27. W. W. Irving Multiscale stochastic realization and model identification with applications to large-scale estimation problems Ph.D. dissertation Massachusetts Institute of Technology Sept. 1995.
28. W. W. Irving and A. S. Willsky A canonical correlations approach to multiscale stochastic realization IEEE Trans. Automat. Contr. to be published.
29. H. Krim and J.-C. Pesquet Multiresolution analysis of a class of nonstationary processes IEEE Trans. Inform. Theory vol. 41 pp. 1010-1020 July 1995.
30. A. Lindquist and G. Picci On the stochastic realization problem Siam J. Contr. Optim. vol. 17 no. 3 pp. 365-389 May 1979.
31. M. R. Luettgen and A. S. Willsky Likelihood calculation for a class of multiscale stochastic models with application to texture discrimination IEEE Trans. Image Processing vol. 4 no. 2 pp. 194-207 Feb. 1995.
32. S. Mallat A Wavelet Tour of Signal Processing. New York: Academic 1998.
33. B. B. Mandelbrot and J. W. Van Ness Fractional Brownian motions fractional noises and applications SIAM Rev. vol. 10 pp. 422-137 1968.
34. Y. Meyer Ondelettes et Opérateurs I: Ondeletts II: Opérateurs de Calderôn-Zygmund III: Opérateurs Multilinéaires (with R. Coifman). Paris Hermann 1993.
35. F. Sellan Synthèse de mouvements Browniens fractionnaires àl'aide de la transformation par ondelettes C.R.A.S. Paris Sér. I Math vol. 321 pp. 351-358 1995.
36. G. Strang and T. Nguyen Wavelets and Filter Banks. WellesleyCambridge Press 1996.
37. A. H. Tewfik and M. Kim Corrélation structure of the discrete wavelet coefficients of fractional Brownian motion IEEE Trans. Inform. Theory vol. 38 pp. 904-909 Mar. 1992.
38. H. L. Van Trees Detection Estimation and Modulation Theory Part I. New York: Wiley 1968.
39. J. Zhang and G. Walter A wavelet-based KL-like expansion for widesense stationary random processes IEEE Trans. Signal Processing vol. 42 pp. 1737-1745 July 1994.