Wavelet decomposition approaches to statistical inverse problems

Biometrika

Volumn 85, Issue 1, 1998, Pages 115-129

  Abramovich, F ^a   Silverman, B W ^b  

^a TEL AVIV UNIVERSITY   (Israel)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

Exact risk analysis; Near minimax estimation; Singular value decomposition; Spatially adaptive estimation; Statistical linear inverse problem; Vaguelette; Wavelet

Indexed keywords

EID: 0000521350     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/85.1.115     Document Type: Article

References (17)

1. CHUI, C. K. (1992). An Introduction to Wavelets. San Diego: Academic Press.
2. DAUBECHIES, I. (1992). Ten Lectures on Wavelets. Philadelphia: Society for Industrial and Applied Mathematics.
3. DONOHO, D. L. (1995). Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition. Appl. Comp. Harm. Anal. 2, 101-26.
4. DONOHO, D. L. & JOHNSTONE, I. M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika 81, 425-55.
5. DONOHO, D. L. & JOHNSTONE, I. M. (1995). Adapting to unknown smoothness via wavelet shrinkage. J. Am. Statist. Assoc. 90, 1200-24.
6. DONOHO, D. L. & JOHNSTONE, I. M. (1998). Minimax estimation via wavelet shrinkage. Ann. Statist. To appear.
7. GOLDENSHLUGER, A. & NEMIROVSKI, A. (1997). On spatial adaptive estimation of nonparametric regression. Math. Meth. Statist. 6, 135-70.
8. JOHNSTONE, I. M. & SILVERMAN, B. W. (1990). Speed of estimation in positron emission tomography and related inverse problems. Ann. Statist. 18, 251-80.
9. JOHNSTONE, I. M. & SILVERMAN, B. W. (1991). Discretization effects in statistical inverse problems. J. Complex. 7, 1-34.
10. JOHNSTONE, I. M. & SILVERMAN, B. W. (1997). Wavelet threshold estimators for data with correlated noise. J. R. Statist. Soc. B 59, 319-51.
11. KOLACZYK, E. D. (1996). A wavelet shrinkage approach to tomographic image reconstruction. J. Am. Statist. Assoc. 91, 1079-90.
12. LEPSKII, O. (1990). On a problem of adaptive estimation in gaussian white noise. Theory Prob. Applic. 35, 454-66.
13. MALLAT, S. G. (1989). A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Patt. Anal. Mach. Intel. 11, 674-93.
14. MEYER, Y. (1992). Wavelets and Operators. Cambridge: Cambridge University Press.
15. NASON, G. P. & SILVERMAN, B. W. (1994). The discrete wavelet transform in S. J. Comp. Graph. Statist. 3, 163-91.
16. O'SULLIVAN, F. (1986). A statistical perspective on ill-posed inverse problems (with Discussion). Statist. Sci. 1, 502-27.
17. TIKHONOV, A. N. & ARSENIN, V. Y. (1977). Solutions of Ill-posed Problems. New York: Wiley.