An overlapping tree approach to multiscale stochastic modeling and estimation

IEEE Transactions on Image Processing

Volumn 6, Issue 11, 1997, Pages 1517-1529

  Irving, William W ^a,b   Fieguth, Paul W ^a,c   Willsky, Alan S ^a,d  

^a IEEE   (Canada)

^b BAE SYSTEMS   (United Kingdom)

^c UNIVERSITY OF WATERLOO   (Canada)

^d USA   (United States)

Author keywords

Least squares estimation; Multiscale; Quadtrees; Stochastic modeling

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; ESTIMATION; IMAGE RECONSTRUCTION; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; RANDOM PROCESSES; TREES (MATHEMATICS);

IMAGE DOMAIN; MULTISCALE ALGORITHM; OVERLAPPING TREE APPROACH; QUADTREES;

IMAGE ENHANCEMENT;

EID: 0031275764     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/83.641412     Document Type: Article

References (20)

1. H. Akaike, "Markovian representation of stochastic processes by canonical variables," SIAM J. Contr., vol. 13, 1975.
2. M. Basseville et al., "Modeling and estimation of multiresolution stochastic processes," IEEE Trans. Inform. Theory, vol. 38, pp. 766-784, 1992.
3. R. Chellappa and S. Chatterjee, "Classification of textures using Gaussian Markov random fields," IEEE Trans. Acoust., Speech, Signal Processing, vol. 33, pp. 959-963, 1985.
4. K. Chou, A. Willsky, and A. Benveniste, "Multiscale recursive estimation, data fusion, and regularization," IEEE Trans. Automat. Contr., vol. 39, pp. 464-478, 1994.
5. R. Coifman and D. Donoho, "Translation invariant de-noising," in Lecture Notes in Statistics: Wavelets and Statistics. New York: Springer-Verlag, 1995, pp. 125-150.
6. P. Fieguth, A. Willsky, and W. Karl, "Multiresolution stochastic imaging of satellite oceanographic altimetric data," in Proc. 1994 IEEE Int. Conf. Image Processing, vol. II, pp. 1-5.
7. P. Fieguth, W. Karl, A. Willsky, and C. Wunsch, "Multiresolution optimal interpolation and statistical analysis of TOPEX/POSEIDON satellite altimetry," IEEE Trans. Geosci. Remote Sensing, vol. 33, pp. 280-292, 1995.
8. P. Fieguth, A. Willsky, and W. Karl, "Efficient multiresolution counterparts to variational methods for surface reconstruction," Comput. Vis. Image Understanding, to be published.
9. P. Fieguth, "Application of multiscale estimation to large scale multidimensional imaging and remote sensing problems," Ph.D. dissertation, Dept. Electr. Eng. Comput. Sci., Mass. Inst. Technol., Cambridge, 1995.
10. Å. Björck and G. Golub, "Numerical methods for computing angles between linear subspaces," Math. Computat., vol. 27, pp. 579-594, 1973.
11. H. Hotelling, "Relations between two sets of variates," Biometrika, vol. 28, pp. 321-377, 1936.
12. W. Irving, "Multiscale stochastic realization and model identification with applications to large-scale estimation problems," Ph.D. dissertation, Dept. Electr. Eng. Comput. Sci., Mass. Inst. Technol., Cambridge, 1995.
13. W. Irving and A. Willsky, "A canonical correlations approach to multiscale stochastic realization," submitted for publication.
14. B. Kosko, Ed., Neural Networks for Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1992, pp. 37-61.
15. M. Luettgen, W. Karl, and A. Willsky, "Efficient multiscale regularization with applications to the computation of optical flow," IEEE Trans. Image Processing, vol. 3, pp. 41-64, Jan. 1994.
16. M. Luettgen and A. Willsky, "Multiscale smoothing error models," IEEE Trans. Automat. Control, vol. 40, pp. 173-175, 1995.
17. M. Luettgen, W. Karl, A. Willsky, and R. Tenney, "Multiscale representations of Markov random fields," IEEE Trans. Signal Processing, vol. 41, pp. 3377-3396, 1993.
18. M. Luettgen and A. Willsky, "Likelihood calculation for a class of multiscale stochastic models, with application to texture discrimination," IEEE Trans. Image Processing, vol. 4, pp. 194-207, 1995.
19. D. F. Morrison, Multivariate Statistical Methods. New York: McGraw-Hill, 1967.
20. R. J. Muirhead, Aspects of Multivariate Statistical Theory. New York: Wiley, 1982.