Ridgelets: A key to higher-dimensional intermittency?

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 357, Issue 1760, 1999, Pages 2495-2509

  Candès, Emmanuel J ^a   Donoho, David L ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Edges; Nonlinear approximation; Radon transform; Ridge functions; Singularities; Wavelets

Indexed keywords

EID: 0346727379     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.1999.0444     Document Type: Article

References (15)

1. Barron, A. R. 1993 Universal approximation bounds for superpositions of a sigmoidal function. IEEE Trans. Inform. Theory 39, 930-945.
2. Candès, E. J. 1998 Ridgelets: theory and applications. PhD thesis, Department of Statistics, Stanford University.
3. Candès, E. J. 1999 Harmonic analysis of neural networks. Appl. Comput. Harmon. Analysis 6(2), 197-218.
4. Cybenko, G. 1989 Approximation by superpositions of a sigmoidal function. Math. Control Signals Systems 2, 303-314.
5. Daubechies, I. 1988 Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. 41, 909-996.
6. Donoho, D. L. 1993 Unconditional bases are optimal bases for data compression and for statistical estimation. Appl. Comput. Harmon. Analysis 1, 100-115.
7. Donoho, D. L. 1996 Unconditional bases and bit-level compression. Appl. Comput. Harmon. Analysis 3, 388-392.
8. Donoho, D. L. 1998 Orthonormal ridgelets and linear singularities. Report no. 1998-19, Department of Statistics, Stanford University.
9. Friedman, J. H. & Stuetzle, W. 1981 Projection pursuit regression. J. Am. Statist. Ass. 76, 817-823.
10. Helgason, S. 1986 Groups and geometric analysis. New York: Academic.
11. Jones, L. K. 1992 A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural network training. Ann. Statist. 20, 608-613.
12. Lemarié, P. G. & Meyer, Y. 1986 Ondelettes et bases Hilbertiennes. Rev. Mat. Iberoamericana 2, 1-18.
13. Logan, B. F. & Shepp, L. A. 1975 Optimal reconstruction of a function from its projections. Duke Math. Jl 42, 645-659.
14. Meyer, Y. 1990 Ondelettes et opérateurs. Paris: Hermann.
15. Murata, N. 1996 An integral representation of functions using three-layered networks and their approximation bounds. Neural Networks 9, 947-956.