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References

A, B, C, D, E, F, G, H, I, H, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z.

A

Abramovich, F., & Benjamini, Y. (1996).
Adaptive thresholding of wavelet coefficients. Computat. Stat. Data Anal., 22, 351--361.
Abramovich, F., & Silverman, B.W. (1998).
Wavelet decomposition approaches to statistical inverse problems. Biometrika, 85, 115-129.
Abramovich, F., Sapatinas, T., & Silverman, B.W. (1998).
Wavelet thresholding via a Bayesian approach. J. R. Statist. Soc. B, 60.
Antoniadis, A. (1996).
Smoothing noisy data with tapered Coiflets series. Scand. J. Statist., 23, 313--330.
Antoniadis, A., Gregoire, G., & Nason, G.P. (1999).
Density and hazard rate estimation for right censored data using wavelet methods. J. R. Statist. Soc. B, 61.

B

Barber, S., Nason, G.P., & Silverman, B.W. (2001).
Posterior probability intervals for wavelet thresholding. University of Bristol research report 01:01.
Bruce, A., & Gao, H.-Y. (1996).
Applied Wavelet Analysis with S-Plus. New York: Springer-Verlag.
Buckheit, J.B., & Donoho, D.L. (1995).
Improved linear discrimination using time-frequency dictionaries. Pages 540-551 of: Laine, A.F., Unser, M.A., & Wickerhauser, M.V. (eds), Proc. SPIE. Wavelet Applications in Signal and Image Processing III, vol. 2569. Bellingham, Washington: SPIE.
C
Cavaretta, A.S., Dahmen, W. and Micchelli, C. (1991).
Stationary subdivision. Mem. Amer. Math. Soc., 93, 1-186.
Chen, S.S., Donoho, D.L., and Saunders, M.A. (1996).
Atomic decompositions by basis pursuit. Tech. rept. 479. Department of Statistics, Stanford University, Stanford.
Chipman, H.A., Kolaczyk, E.D., and McCulloch, R.E. (1997).
Adaptive Bayesian Wavelet Shrinkage. J. Am. Statist. Ass., 92, 1413-1421.
Chipman, H.A., & Wolfson, L.J. (1999).
Prior elicitation in the wavelet domain. In "Bayesian Inference in Wavelet-Based Models: Lecture Notes in Statistics 141", Muller, P., & Vidakovic, B. (Eds).
Chui, C.K. (1992).
An Introduction to Wavelets. London: Academic Press.
Clyde, M., Parmigiani, G., & Vidakovic, B. (1998).
Multiple shrinkage and subset selection in wavelets. Biometrika 85, (to appear).
Cohen, A., Daubechies, I. and Vial, P. (1993).
Wavelets on the interval and fast wavelet transforms. Applied and Computational Harmonic Analysis, 1, 54-81. See also this table of computed filter coefficients.
Cohen, A. and Dyn, N. (1996).
Nonstationary subdivision schemes and multiresolution analysis. SIAM J. Math. Anal. 27, 1745-1769.
Cohen, I., Raz, S., & Malah, D. (1997).
Orthonormal shift-invariant wavelet packet decomposition and representation. Sig. Proc., 57, 251-270.
Coifman, R.R., & Donoho, D.L. (1995).
Translation-invariant de-noising. Pages 125--150 of: Antoniadis, A., & Oppenheim, G. (eds), Wavelets and Statistics, Lecture Notes in Statistics 103. New-York: Springer-Verlag.
Coifman, R.R., & Saito, N. (1994).
Constructions of local orthonormal bases for classification and regression. Compt. Rend. Acad. Sci. Paris Ser. A, 319, 191-196.
Coifman, R.R., & Wickerhauser, M.V. (1992).
Entropy-based algorithms for best-basis selection. IEEE Trans. Inf. Theor., 38, 713-718. (see Technical Report Entropy-based algorithms for best basis selection by the same authors).
Crouse, M.S., Nowak, R.D., and Baraniuk, R.G. (1998).
Wavelet-based statistical signal processing using hidden Markov models. IEEE Trans. Sig. Proc., 46, (to appear).
D
Daubechies, I. (1988).
Orthonormal bases of compactly supported wavelets. Comms. Pure Appl. Math., 41, 909-996.
Daubechies, I. (1992).
Ten Lectures on Wavelets. Philadelphia: SIAM.
Delyon, B., & Juditsky, A. (1995).
Estimating wavelet coefficients. Pages 151--168 of: Antoniadis, A., & Oppenheim, G. (eds), Wavelets and Statistics, Lecture Notes in Statistics 103. New-York: Springer-Verlag.
Deslauriers, G. and Dubuc, S. (1989)
Symmetric dyadic interpolation.Constr. Approx., 5, 49-68.
Donoho, D.L. (1992).
Interpolating wavelet transforms. Tech. rept. 408. Department of Statistics, Stanford University, Stanford.
Donoho, D.L. (1995).
Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition. Appl. Comput. Harm. Anal., 2, 101-126. (See Technical Report Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition.
Donoho, D.L., & Johnstone, I.M. (1994a).
Ideal denoising in an orthonormal basis chosen from a library of bases. Compt. Rend. Acad. Sci. Paris Ser. A, 319, 1317-1322. (See Technical Report Ideal denoising in an orthonormal basis chosen from a library of bases.).
Donoho, D.L., & Johnstone, I.M. (1994b).
Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81, 425-455. (See Technical Report, Ideal spatial adaptation by wavelet shrinkage.)
Donoho, D.L., & Johnstone, I.M. (1995).
Adapting to unknown smoothness via wavelet shrinkage. J. Am. Statist. Ass., 90, 1200-1224. (See Technical Report Adapting to unknown smoothness via wavelet shrinkage.
Donoho, D.L., Johnstone, I.M., Kerkyacharian, G., & Picard, D. (1995).
Wavelet shrinkage: asymptopia? (with discussion). J. R. Statist. Soc. B, 57, 301-337.
Donoho, D.L., Johnstone, I.M., Kerkyacharian, G., & Picard, D. (1996).
Density estimation by wavelet thresholding. Ann. Statist., 24, 508-539.
Donovan, G., Geronimo, J.S. and Hardin, D.P. (1996)
Intertwining multiresolution analyses and the construction of piecewise-polynomial wavelets. SIAM J. Math. Anal. 27, 1791-1815.
Downie, T.R. and Silverman, B.W. (1998)
The discrete multiple wavelet transform and thresholding methods IEEE Trans. Sig. Proc., 46, 2558--2561.
F
Fryzlewicz, P. (1999)
Wavelets on the interval --- theory and applications. Technical Report, Department of Mathematics, University of Bristol. [PDF], [PostScript],
G
Gao, H.-Y. (1997).
Choice of thresholds for wavelet shrinkage estimate of the spectrum. J. Time Series Anal., 18, 231-251.
Geronimo, J.S., Hardin, D.P. and Massopust, P.R. (1994)
Fractal functions and wavelet expansions based on several scaling functions.Journal of Approximation Theory, 78, 373-401.
H
Hall, P., & Nason, G.P. (1997).
On choosing a non-integer resolution level when using wavelet methods. Statist. Probab. Lett., 34, 5--11.
Hall, P., & Patil, P. (1995)
Formulae for mean integrated squared error of nonlinear wavelet-based density estimators. Ann. Statist., 23, 905-928.
Hess-Nielsen, N., & Wickerhauser, M.V. (1996).
Wavelets and time-frequency analysis. Proc. IEEE, 84, 523-540.
Hill, I.D. (1976).
Algorithm AS 100: Normal-Johnson and Johnson-Normal transformations. Applied Statistics 25, 190-192.
Hill, I.D., Hill, R., & Holder, R.L. (1976).
Algorithm AS99: Fitting Johnson curves by moments. Applied Statistics 25, 180-189.
J
Jawerth, B., & Sweldens, W. (1994).
An overview of wavelet based multiresolution analyses. SIAM Rev., 36, 377-412.
Johnson, N.L. (1949).
Systems of frequency curves generated by methods of translation. Biometrika 36, 149-176.
Johnstone, I.M., & Silverman, B.W. (1997).
Wavelet threshold estimators for data with correlated noise. J. R. Statist. Soc. B, 59, 319-351.
K
Kovac, A. (1997).
Wavelet thresholding for unequally spaced data. Ph.D. thesis, Department of Mathematics, University of Bristol, Bristol.
Kovac, A. and Silverman, B.W., (2000)
Extending the scope of wavelet regression methods by coefficient-dependent thresholding. J. Am. Statist. Ass., 95, (to appear).
L
Lang, M., Guo, H., Odegard, J.E., Burrus, C.S., & Wells, R.O. (1995).
Nonlinear processing of a shift invariant DWT for noise reduction. Pages 640--651 of: Szu, H.H. (ed), Proc. SPIE. Wavelet Applications II, vol. 2491. Bellingham, Washington: SPIE.
Lawton, W. (1993)
Applications of complex valued wavelet transforms to subband decomposition. IEEE Trans. Sig. Proc. 41, 3566-3568.
Learned, R.E., & Willsky, A.S. (1995).
A wavelet packet approach to transient signal classification. Appl. Comput. Harm. Anal., 2, 265-278.
M
Mallat, S.G. (1989a).
Multiresolution approximations and wavelet orthonormal bases of L^2(R). Trans. Am. Math. Soc., 315, 69-87.
Mallat, S.G. (1989b).
A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattn Anal. Mach. Intell., 11, 674-693.
Mallat, S.G., & Zhang, Z. (1993).
Matching pursuit in a time-frequency dictionary. IEEE Trans. Sig. Proc., 41, 3397-3415.
McCoy, E.J., Percival, D.B., & Walden, A.T. (1995).
Spectrum estimation via wavelet thresholding of multitaper estimators. Tech. rept. TR-95-14. Statistics Section, Imperial College, London.
Meyer, Y. (1992).
Wavelets and Operators. Cambridge: Cambridge University Press.
Mintzer, F. (1982).
On half-band, third-band and Nth band FIR filters and their design. IEEE Trans. Acoust. Speech Sig. Proc., 30, 734-738.
Mintzer, F. (1985).
Filters for distortion-free two-band multirate filter banks. IEEE Trans. Acoust. Speech Sig. Proc., 33, 626-630.
Morgan, R. and Nason, G.P., 1999.
Wavelet shrinkage of itch response data. Revue de Statistique Applique, (to appear).
Moulin, P. (1994).
Wavelet thresholding techniques for power spectrum estimation. IEEE Trans. Sig. Proc., 42, 3126-3136.
N
Nason, G.P. (1996).
Wavelet shrinkage using cross-validation. J. R. Statist. Soc. B, 58, 463-479.
Nason, G.P., & Silverman, B.W. (1994).
The discrete wavelet transform in S. J. Comput. Graph. Statist., 3, 163-191.
Nason, G.P., & Silverman, B.W. (1995).
The stationary wavelet transform and some statistical applications. Pages 281--300 of: Antoniadis, A., & Oppenheim, G. (eds), Wavelets and Statistics, Lecture Notes in Statistics 103. New-York: Springer-Verlag.
Nason, G.P., von Sachs, R., & Kroisandt, G. (1998).
Adaptive estimation of the evolutionary wavelet spectrum.
Nason, G.P., Sapatinas, T. and Sawczenko, A. (1998)
Statistical modelling of time series using non-decimated wavelet representations.
Neumann, M.H., & von Sachs, R. (1997).
Wavelet thresholding in anisotropic function classes and application to adaptive estimation of evolutionary spectra. Ann. Statist., 25, 38-76.
O
Ogden, R.T. (1997).
Essential wavelets for statistical applications and data analysis. Boston: Birkh\"auser.
Ogden, R.T., & Parzen, E. (1996).
Change-point approach to data analytic wavelet thresholding. Statist. Comput., 6, 93-99.
P
Percival, D.B., & Guttorp, P. (1994).
Long-memory processes, the Allan variance and wavelets. Pages 325-344 of: Foufoula-Georgiou, E., & Kumar, P. (eds), Wavelets in Geophysics. San Diego: Academic Press.
Percival, D.B., & Mofjeld, H.O. (1997).
Analysis of subtidal coastal sea level fluctuations using wavelets. J. Am. Statist. Ass., 92, 868-880.
Pesquet, J.C., Krim, H., & Carfantan, H. (1996).
Time-invariant orthonormal wavelet representations. IEEE Trans. Sig. Proc., 44, 1964-1970.
S
Saito, N. (1994).
Local feature extraction and its applications using a library of bases. Ph.D. thesis, Yale University, New Haven.
Saito, N. and Beylkin, G. (1993).
Multiresolution representations using the autocorrelation functions of compactly supported wavelets. IEEE Trans. Sig. Proc., 41, 3584--3590. (see extended abstract.)
Saito, N., & Coifman, R.R. (1996).
On local feature-extraction for signal classification. Z. Angew. Math. Mech., 76, 453-456.
Shensa, M.J. (1992).
Discrete wavelet transforms: wedding the á trous and Mallat algorithms. IEEE Trans. Sig. Proc., 40, 2464-2482.
Smith, M.J.T., & Barnwell, T.P. (1986).
Exact reconstruction techniques for tree-structured subband coders. IEEE Trans. Acoust. Speech Sig. Proc., 34, 434-441.
Strang, G. (1993).
Wavelet transforms versus Fourier transforms. Bull. (New Series) Am. Math. Soc., 28, 288-305.
Strela, V., Heller, P.N., Strang, G., Topiwala, P. and Heil, C. (1999).
The application of multiwavelet filterbanks to image processing. IEEE Trans. Im. Proc., 8, 548-563.
V
Vaidyanathan, P.P. (1990).
Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial. Proceedings of the IEEE, 78, 56--93.
Vidakovic, B. (1998).
Nonlinear wavelet shrinkage with Bayes rules and Bayes factors. J. Am. Statist. Ass., 93, 173-179. See technical report.
von Sachs, R. (1996).
Adaptively wavelet-smoothed Wigner estimates of evolutionary spectra. Z. Angew. Math. Mech., 76, 71-74.
von Sachs, R., & Schneider, K. (1996).
Wavelet smoothing of evolutionary spectra by nonlinear thresholding. Appl. Comput. Harm. Anal., 3, 268-282.
von Sachs, R., Nason, G.P., & Kroisandt, G. (1996).
Spectral representation and estimation for locally-stationary wavelet processes. Proceedings of the workshop ``Spline functions and wavelets'': Montreal. (to appear).
W
Walden, A.T., & Contreras Cristan, A. (1997).
The phase-corrected undecimated discrete wavelet packet transform and the recurrence of high latitude interplanetary shock waves. Tech. rept. TR-97-03. Statistics Section, Imperial College, London.
Wickerhauser, M.V. (1994).
Adapted Wavelet Analysis from Theory to Software. Wellesley, Massachusetts: A.K. Peters.
X
Xia, X.-G., Geronimo, J., Hardin, D. and Suter, B. (1996)
Design of prefilters for discrete multiwavelet transforms. IEEE Trans. Sig. Proc., 44, 25--35.