Efficient Computation of Oscillatory Integrals via Adaptive Multiscale Local Fourier Bases

Applied and Computational Harmonic Analysis

Volumn 9, Issue 1, 2000, Pages 19-53

  Averbuch, A ^a   Braverman, E ^b   Coifman, R ^c   Israeli, M ^b   Sidi, A ^b  

^a TEL AVIV UNIVERSITY   (Israel)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^c YALE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002475397     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1006/acha.2000.0305     Document Type: Article

References (22)

1. Alpert B., Beylkin G., Coifman R., Rokhlin V. Wavelet-like bases for the fast solution of second-kind integral equations. SIAM J. Sci. Comput. 14:1993;159-184.
2. Auscher P., Weiss G., Wickerhauser M. V. Local sine and cosine bases of Coifman and Meyer and the construction of smooth wavelets. Chui C. K. Wavelets - A Tutorial in Theory and Applications. 1992;237-256 Academic Press, New York.
3. Averbuch A., Aharoni G., Coifman R., Israeli M. Local cosine transform - A method for the reduction of the blocking effect in JPEG. J. Math. Imaging Vision. 3:1993;7-38.
4. A. Averbuch, F. Meyer, O. Strömberg, R. Coifman, and, A. Vassiliou, Low bit-rate efficient compression for seismic data, in preparation.
5. Beylkin G., Coifman R., Rokhlin V. Fast wavelet transforms and numerical algorithms. Comm. Pure Appl. Math. 44:1991;141-183.
6. Bradie B., Coifman R., Grossman A. Fast numerical computations of oscillatory integrals related to acoustic scattering, I. Appl. Comput. Harmonic Anal. 1:1993;94-99.
7. Cohen A., Daubechies I., Feauveau J. Biorthogonal bases of compactly supported wavelets. Comm. Pure Appl. Math. 45:1996;485-560.
8. Coifman R., Meyer Y. Gaussian bases. Appl. Comput. Harmonic Anal. 2:1995;299-302.
9. R. R. Coifman, and, Y. Meyer, Orthonormal wave packet bases, preprint, Dept. of Mathematics, Yale University, New Haven, 1990.
10. Coifman R. R., Meyer Y. Remarques sur l'analyse de Fourier à fenêtre. C.R. Acad. Sci. Paris I. 312:1991;259-261.
11. Coifman R., Matviyenko G., Meyer Y. Modulated Malvar-Wilson bases. Appl. Comput. Harmonic Anal. 4:1997;58-61.
12. Coifman R. R., Wickerhauser M. V. Entropy-based algorithms for best basis selection. IEEE Trans. Inform. Theory. 38:1992;713-718.
13. Coifman R. R., Meyer Y. Size properties of wavelet packets. Ruskai M. B., Beylkin G., Coifman R., Daubechies I., Mallat S., Meyer Y., Rafael L. Wavelets and Their Applications. 1992;125-150 Jones & Bartlett, Boston.
14. Daubechies I. Orthogonal bases of compactly supported wavelets. Comm. Pure and Appl. Math. 41:1988;909-996.
15. Matviyenko G. Optimized local trigonometric bases. Appl. Comput. Harmonic Anal. 3:1996;301-323.
16. Meyer F. G., Coifman R. R. Brushlets: a tool for directional image analysis and image compression. Appl. Comput. Harmonic Anal. 4:1997;147-187.
17. Ralston A., Rabinowitz P. A First Course in Numerical Analysis. Int. Series in Pure and Appl. Math. XIX:1978;McGraw-Hill KOGAKUSHA, Tokyo.
18. Rokhlin V. Diagonal forms of translation operators for the Helmholtz equation in three dimensions. Appl. Comput. Harmonic Anal. 1:1993;82-93.
19. Sidi A., Israeli M. Quadrature methods for periodic singular and weakly singular Fredholm integral equations. J. Sci. Comput. 3:1988;201-231.
20. Sidi A., Pennline J. A. Improved accuracy of quadrature method solutions of Fredholm integral equations that arise from nonlinear two-point boundary value problems. J. Integral Equations Appl. 11:1999;103-139.
21. Stokes G. G. On the numerical calculation of a class of definite integrals and infinite series. Camb. Philos. Trans. 9:1856;166-187.
22. Watson G. N. The limits of applicability of the principle of stationary phase. Proc. Camb. Philos. Soc. 19:1918;49-55.