Local discriminant bases and their applications

R. R. Coifman and N. Saito, ?Constructions of local orthonormal bases for classification and regression,?C. R. Acad. Sci. Paris, Série I, Vol. 319, pp. 191?196, 1994.

N. Saito and R.R. Coifman, ?Local discriminant bases,? inMathematical Imaging: Wavelet Applications in Signal and Image Processing, A.F. Laine and M.A. Unser (eds.),Proc. SPIE 2303, pp. 2?14, 1994.

N. Saito,Local Feature Extraction and Its Applications Using a Library of Bases, Ph.D. Thesis, Dept. of Mathematics, Yale University, New Haven, CT 06520 USA, Dec. 1994.

N. Saito and R.R. Coifman, ?Local feature extraction for classification and regression using a library of bases,? in preparation.

N. Saito and R.R. Coifman, ?Extraction of geological information from acoustic well-logging waveforms using time-frequency atoms,?Geophysics, 1995 (submitted).

R. A. Fisher, ?The use of multiple measurements in taxonomic problems,?Ann. Eugenics, Vol. 7, pp. 179?188, 1936.

L. Breiman, J.H. Friedman, R.A. Olshen, and C.J. Stone,Classification and Regression Trees, Chapman & Hall: New York, 1993. Previously published by Wadsworth & Brooks/Cole in 1984.

T.M. Cover and P. Hart, ?Nearest neighbor pattern classification,?IEEE Trans. Inform. Theory, Vol. IT-13, pp. 21?27, 1967.

B.D. Ripley, ?Statistical aspects of neural networks,? inNetworks and Chaos: Statistical and Probabilistic Aspects, O.E. Barndorff-Nielsen, J.L. Jensen, D.R. Cox, and W.S. Kendall (eds.), Ch. 2, pp. 40?123, Chapman & Hall: New York, 1993.

K. Fukunaga,Introduction to Statistical Pattern Recognition, Academic Press: San Diego, CA, second edition, 1990.

S.M. Weiss and C.A. Kulikowski,Computer Systems That Learn: Classification and Prediction Methods from Statistics, Neural Nets, Machine Learning, and Expert Systems, Morgan Kaufmann: San Francisco, CA, 1991.

G.J. McLachlan,Discriminant Analysis and Statistical Pattern Recognition, John Wiley & Sons: New York, 1992.

S. Watanabe,Pattern Recognition: Human and Mechanical, John Wiley & Sons: New York, 1985.

StatSci,S-PLUS Reference Manual, Vol. 1 & 2, version 3.2, Seattle, WA, Dec. 1993.

R.A. Becker, J.M. Chambers, and A.R. Wilks,The New S Language: A Programming Environment for Data Analysis and Graphics, Chapman & Hall: New York, 1988.

J. M. Chambers and T.R. Hastie,Statistical Models in S, Chapman & Hall: New York, 1992.

J. Rissanen,Stochastic Complexity in Statistical Inquiry, World Scientific: Singapore, 1989.

J. R. Quinlan and R.L. Rivest, ?Inferring decision trees using the minimum description length principle,?Information and Control, Vol. 80, pp. 227?248, 1989.

C.S. Wallace and J.D. Patrick, ?Coding decision trees,?Machine Learning, Vol. 11, pp. 7?22, 1993.

R.R. Coifman and M.V. Wickerhauser, ?Entropy-based algorithms for best basis selection,?IEEE Trans. Inform. Theory, Vol. 38, pp. 713?719, 1992.

Y. Meyer,Wavelets: Algorithms and Applications, SIAM: Philadelphia, PA, 1993. Translated and revised by R.D. Ryan.

N. Saito and G. Beylkin, ?Multiresolution representations using the auto-correlation functions of compactly supported wavelets,?IEEE Trans. Signal Processing, Vol. 41, pp. 3584?3590, 1993.

I. Daubechies,Ten Lectures on Wavelets, SIAM: Philadelphia, PA, 1992.

Y. Meyer,Wavelets and Operators, Cambridge University Press: New York, 1993. Translated by D.H. Salinger.

M.V. Wickerhauser,Adapted Wavelet Analysis from Theory to Software, A.K. Peters: Wellesley, MA, 1994.

R.R. Coifman and Y. Meyer, ?Remarques sur l'analyse de fourier à fenêtre,?C. R. Acad. Sci. Paris, Série I, Vol. 312, pp. 259?261, 1991.

P. Auscher, G. Weiss, and M.V. Wickerhauser, ?Local sine and cosine bases of Coifman and Meyer and the construction of smooth wavelets,? inWavelets: A Tutorial in Theory and Applications C.K. Chui (ed.), pp. 237?256, Academic Press: San Diego, CA, 1992.

H.S. Malvar, ?The LOT: transform coding without blocking effects,?IEEE Trans. Acoust., Speech, Signal Processing, Vol. 37, pp. 553?559, 1989.

H.S. Malvar, ?Lapped transforms for efficient transform/subband coding,?IEEE Trans. Acoust., Speech, Signal Processing, Vol. 38, pp. 969?978, 1990.

K.R. Rao and P. Yip,Discrete Cosine Transform: Algorithms, Advantages, and Applications, Academic Press: San Diego, CA, 1990.

J. Kova?evi? and M. Vetterli, ?Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases forR n,?IEEE Trans. Inform. Theory, Vol. 38, pp. 533?555, 1992.

K. Gröchenig and W.R. Madych, ?Multiresolution analysis, Haar bases, and self-similar tilings ofR n,?IEEE Trans. Inform. Theory, Vol. 38, pp. 556?568, 1992.

M.V. Wickerhauser, ?High-resolution still picture compression,?Digital Signal Processing: A Review Journal, Vol. 2, pp. 204?226, 1992.

N. Otsu, ?Mathematical studies on feature extraction in pattern recognition,? (in Japanese), Researches of the Electrotechnical Laboratory, No. 818, Electrotechnical Laboratory, 1-1-;4, Umezono, Sakura-machi, Niihari-gun, Ibaraki, Japan, July 1981.

C.E. Shannon and W. Weaver,The Mathematical Theory of Communication, The University of Illinois Press: Urbana, IL, 1949.

S. Watanabe, ?Karhunen-Loève expansion and factor analysis: theoretical remarks and applications,? inTrans. 4th Prague Conf. Inform. Theory, Statist. Decision Functions, Random Processes, Prague, 1967, pp. 635?660.

M.V. Wickerhauser, ?Fast approximate factor analysis,? inCurves and Surfaces in Computer Vision and Graphics II, Proc. SPIE 1610, pp. 23?32, 1991.

R.R. Coifman and F. Majid, ?Adapted waveform analysis and denoising,? inProgress in Wavelet Analysis and Applications, Y. Meyer and S. Roques (eds.), pp. 63?76, Editions Frontieres: B.P.33, 91192 Gif-sur-Yvette Cedex, France, 1993.

N. Saito, ?Simultaneous noise suppression and signal compression using a library of orthonormal bases and the minimum description length criterion,? inWavelets in Geophysics, E. Foufoula-Georgiou and P. Kumar (eds.), Ch. XI, pp. 299?324, Academic Press: San Diego, CA, 1994.

M. Basseville, ?Distance measures for signal processing and pattern recognition,?Signal Processing, Vol. 18, pp. 349?369, 1989.

J.N. Kapur and H.K. Kesavan,Entropy Optimization Principles with Applications, Academic Press: San Diego, CA, 1992.

S. Kullback and R.A. Leibler, ?On information and sufficiency,?Ann. Math. Statist., Vol. 22, pp. 79?86, 1951.

P.J. Huber, ?Projection pursuit (with discussion),?Ann. Statist., Vol. 13, pp. 435?525, 1985.

T. Chang and C.-C.J. Kuo, ?Texture analysis and classification with tree-structured wavelet transform,?IEEE Trans. Image Processing, Vol. 2, pp. 429?441, 1993.

P. Brodatz,Textures: A Photographic Album for Artists and Designers, Dover: New York, 1966.

L. Woog,Wavelet-packet based signal enhancement and denoising algorithms, Ph.D. Thesis, Dept. of Comput. Sci., Yale University, 1995, in preparation.

R.R. Coifman and D. Donoho, ?Translation-invariant denoising,? inWavelets and Statistics, A. Antoniadis (ed.), Springer-Verlag: New York, 1995.

L. Breiman, ?Bagging predictors,? Dept. of Statistics, Univ. of California, Berkeley, CA, Tech. Rep. 421, Sep. 1994.

B. Efron and R.J. Tibshirani,An Introduction to the Bootstrap, Chapman & Hall: New York, 1993.

R.R. Coifman and M.V. Wickerhauser, ?Wavelets and adapted waveform analysis,?Wavelets: Mathematics and Applications, J. Benedetto and M. Frazier (eds.), Ch. 10, CRC Press: Boca Raton, FL, 1993.

W.S. Harlan, J.F. Claerbout, and F. Rocca, ?Signal/noise separation and velocity estimation,?Geophysics, Vol. 49, pp. 1869?1880, 1984.