Orthonormal ridgelets and linear singularities

SIAM Journal on Mathematical Analysis

Volumn 31, Issue 5, 2000, Pages 1062-1099

  Donoho, David L ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Edges; Nonlinear approximation; Radon transform; Ridge function; Ridgelet; Singularities; Thresholding of wavelet coefficients; Wavelets

Indexed keywords

EID: 0034345309     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141098344403     Document Type: Article

References (15)

1. E. J. CANDÈS, Harmonic analysis of neural networks, Appl. Comput. Harmon. Anal., 6 (1999), pp. 197-218.
2. E. J. CANDÈS, Ridgelets: Theory and Applications, Ph.D. Thesis, Department of Statistics, Stanford University, Stanford, CA, 1998.
3. E. J. CANDÈS AND D. L. DONOHO, Ridgelets: The key to high-dimensional intermittency?, Philos. Trans. Roy. Soc. London Ser. A, to appear.
4. I. C. DAUBECHIES, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math., 41 (1988), pp. 909-996.
5. S. R. DEANS, The Radon Transform and Some of Its Applications, Reprinted Ed., Krieger, Malabar, FL, 1991.
6. D. L. DONOHO, I. M. JOHNSTONE, G. KERKYACHARIAN, AND D. PICARD, Wavelet shrinkage: Asymptopia? J. Roy. Statist. Ser. B, 57 (1995), pp. 301-369.
7. D. L. DONOHO, M. VETTERLI, I. DAUBECHIES, AND R. A. DEVORE, Data compression and harmonic analysis, IEEE Trans. Inform. Theory, 44 (1998), pp. 2435-2476.
8. D. L. DONOHO, Orthonormal Ridgelets and Linear Singularities, Technical Report, Department of Statistics, Stanford University, Stanford, CA, 1998; also available online from http://www-stat.stanford.edu/~donoho/Reports/1998/ridge-lin-sing.ps.
9. D. L. DONOHO, Ridge Functions and Orthonormal Ridgelets, Technical Report, Department of Statistics, Stanford University, Stanford, CA, 1998; also available online from http://www-stat.stanford.edu/~donoho/Reports/1998/Ridge-Ridgelet.ps.
10. n, Proc. Nat. Acad. Sci. USA, 96 (1999), pp. 1828-1833.
11. I. M. GEL'FAND AND G. E. SHILOV, Generalized Functions: Properties and Operations, Academic Press, New York, London, 1964.
12. S. HELGASON, Groups and Geometric Analysis, Academic Press, New York, London, 1986.
13. B. F. LOGAN AND L. A. SHEPP, Optimal reconstruction of a function from its projections, Duke Math. J., 42 (1975), pp. 645-659.
14. P. G. LEMARIÉ AND Y. MEYER, Ondelettes et bases Hilbertiennes, Rev. Mat. Iberoamericana, 2 (1986), pp. 1-18.
15. R. STRICHARTZ, A Guide to Distribution Theory and Fourier Transforms, CRC Press, Boca Raton, FL, 1993.