Multi-resolution approximation to the stochastic inverse problem

Advances in Applied Probability

Volumn 31, Issue 4, 1999, Pages 1039-1057

  Angulo, J M ^a   Ruiz Medina, M D ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; INTEGRAL EQUATIONS; INVERSE PROBLEMS; LINEAR EQUATIONS; MATHEMATICAL OPERATORS; THEOREM PROVING; WAVELET TRANSFORMS;

COVARIANCE FACTORIZATION; FRACTIONAL SOBOLEV SPACES; MEAN SQUARE LINEAR PREDICTION; MULTIRESOLUTION APPROXIMATION; ORTHOGONAL EXPANSION; ORTHONORMAL WAVELET BASIS; STOCHASTIC INVERSE PROBLEM;

RANDOM PROCESSES;

EID: 85037954414     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0001867800009617     Document Type: Article

References (27)

1. ANGULO, J. M. AND RUIZ-MEDINA, M. D. (1998). A series expansion approach to the inverse problem. J. Appl. Prob. 35, 371-382.
2. ANGULO, J. M., RUIZ-MEDINA, M. D. AND ANH, V. V. (1999a). Wavelet-based orthogonal expansion of fractional generalised random fields. Preprint.
3. ANGULO, J. M., RUIZ-MEDINA, M. D. AND ANH, V. V. (1999b). Estimation and filtering of fractional generalised random fields. Preprint.
4. ANH, V. V., ANGULO, J. M. AND RUIZ-MEDINA, M. D. (1999). Possible long-range dependence in fractional random fields. J. Statist. Planning and Inference 80, 95-110.
5. BHATIA, M., KARL, W. C. AND WILLSKY, A. S. (1997). Tomographic reconstruction and estimation based on multiscale natural-pixel bases. IEEE Trans. Image Processing 6, 463-478.
6. DAUBECHIES, I. (1988). Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math. 41, 909-996.
7. DAUTRAY, R. AND LIONS, J. L. (1985). Mathematical Analysis and Numerical Methods for Science and Technology. Vol. 2. Functional and Variational Methods. Springer, New York.
8. DONOHO, D. L. (1993). Unconditional bases are optimal bases for data compression and for statistical estimation. Appl. Comput. Harmon. Anal. 1, 100-115.
9. DONOHO, D. L. (1995). Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition. Appl. Comput. Harmon. Anal. 2, 101-126.
10. DONOHO, D. L. (1996). Unconditional bases and bit-level compression. Appl. Comput. Harmon. Anal. 3, 388-392.
11. DONOHO, D. L. AND JOHNSTONE, I. M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika 81, 425-455.
12. DONOHO, D. L. AND JOHNSTONE, I. M. (1995). Adapting to unknown smoothness via wavelet shrinkage. J. Amer. Statist. Assoc. 90, 1200-1224.
13. DONOHO, D. L. AND JOHNSTONE, I. M. (1998). Minimax estimation via wavelet shrinkage. Ann. Statist. 26, 879-921.
14. DONOHO, D. L., JOHNSTONE, I. M., KERKYACHARIAN, G. AND PICARD, D. (1995). Wavelet shrinkage: asymptopia? J. Roy. Statist. Soc. B 57, 301-369.
15. DONOHO, D. L., JOHNSTONE, I. M., KERKYACHARIAN, G. AND PICARD, D. (1996). Density estimation by wavelet thresholding. Ann. Statist. 24, 508-539.
16. FIEGUTH, P. W., KARL, W. C. AND WILLSKY, A. S (1998). Efficient multiresolution counterparts to variational-methods for surface reconstruction. Computer Vision and Image Understanding 70, 157-176.
17. KOLACZYK, E. D. (1996). A wavelet shrinkage approach to tomographic image reconstruction. J. Amer. Statist. Assoc. 91, 1079-1090.
18. MEYER, Y. (1992). Wavelets and Operators. Cambridge University Press.
19. MILLER, E. L. AND WILLSKY, A. S. (1995). A multiscale approach to sensor fusion and the solution of linear inverse problems. Appl. Comput. Harmon. Anal. 2, 127-147.
20. MILLER, E. L. AND WILLSKY, A. S. (1996a). A multiscale, statistically based inversion scheme for linearized inverse scattering problems. IEEE Trans. Geosc. Remote Sens. 34, 346-357.
21. MILLER, E. L. AND WILLSKY, A. S. (1996b). Wavelet-based methods for the nonlinear inverse scattering problem using the extended Born approximation. Radio Science 31, 51-65.
22. RAMM, A. G. (1990). Random Fields Estimation Theory. Longman, Essex, UK.
23. RUIZ-MEDINA, M. D., ANGULO, J. M. AND ANH, V. V. (1997). Fractional generalised random fields. Preprint.
24. STEIN, E. M. (1970). Singular Integrals and Differential Properties of Functions. Princeton University Press, Princeton, NJ.
25. TRIEBEL, H. (1978). Interpolation Theory, Function Spaces, Differential Operators. North-Holland, New York.
26. WORNELL, G. W. (1990). A Karhunen-Loève-like expansion for 1/f processes via wavelets. IEEE Trans. Inform. Theory 36, 859-861.
27. ZHANG, J. AND WALTER, G. (1994). A wavelet-based KL-like expansion for wide-sense stationary random processes. IEEE Trans. Signal Processing 42, 1737-1744.