Scattering in flatland: Efficient representations via wave atoms

Foundations of Computational Mathematics

Volumn 10, Issue 5, 2010, Pages 569-613

  Demanet, Laurent ^a   Ying, Lexing ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Boundary integral equation; Computational harmonic analysis; Fast algorithm; Wave propagation

Indexed keywords

ACOUSTIC SCATTERING; COMPRESSION STRATEGIES; FAST ALGORITHMS; LOCAL FOURIER BASIS; NUMERICAL EXPERIMENTS; OSCILLATORY KERNELS; SCATTERING PROBLEMS; TIME-FREQUENCY LOCALIZATION;

BOUNDARY INTEGRAL EQUATIONS; RADAR CROSS SECTION; SCATTERING; WAVE PROPAGATION;

ATOMS;

EID: 77955304303     PISSN: 16153375     EISSN: 16153383     Source Type: Journal    
DOI: 10.1007/s10208-010-9070-4     Document Type: Article

References (24)

1. E. Abbott, Flatland: A Romance in Many Dimensions, 3rd edn. (Dover, New York, 1992) (1884).
2. J. P. Antoine, R. Murenzi, Two-dimensional directional wavelets and the scale-angle representation, Signal Process. 52, 259-281 (1996).
3. A. Averbuch, E. Braverman, R. Coifman, M. Israeli, A. Sidi, Efficient computation of oscillatory integrals via adaptive multiscale local Fourier bases, Appl. Comput. Harmon. Anal. 9(1), 19-53 (2000).
4. G. Beylkin, R. Coifman, V. Rokhlin, Fast wavelet transforms and numerical algorithms. I, Commun. Pure Appl. Math. 44(2), 141-183 (1991).
5. B. Bradie, R. Coifman, A. Grossmann, Fast numerical computations of oscillatory integrals related to acoustic scattering, Appl. Comput. Harmon. Anal. 1, 94-99 (1993).
6. 2 singularities, Commun. Pure Appl. Math. 57, 219-266 (2004).
7. H. Cheng, W. Y. Crutchfield, Z. Gimbutas, L. F. Greengard, J. F. Ethridge, J. Huang, V. Rokhlin, N. Yarvin, J. Zhao, A wideband fast multipole method for the Helmholtz equation in three dimensions, J. Comput. Phys. 216, 300-325 (2006).
8. A. Córdoba, C. Fefferman, Wave packets and Fourier integral operators, Commun. PDE3(11), 979-1005 (1978).
9. L. Demanet, L. Ying, Curvelets and wave atoms for mirror-extended images, in Proc. SPIE Wavelets XII Conf., 2007.
10. L. Demanet, L. Ying, Wave atoms and sparsity of oscillatory patterns, Appl. Comput. Harmon. Anal. 23(3), 368-387 (2007).
11. H. Deng, H. Ling, Fast solution of electromagnetic integral equations using adaptive wavelet packet transform, IEEE Trans. Antennas Propag. 47(4), 674-682 (1999).
12. H. Deng, H. Ling, On a class of predefined wavelet packet bases for efficient representation of electromagnetic integral equations, IEEE Trans. Antennas Propag. 47(12), 1772-1779 (1999).
13. B. Engquist, L. Ying, Fast directional multilevel algorithms for oscillatory kernels, SIAM J. Sci. Comput. 29(4), 1710-1737 (2007).
14. B. Engquist, L. Ying, Fast directional computation for the high frequency Helmholtz kernel in two dimensions, Commun. Math. Sci. 7(2), 327-345 (2009).
15. W. L. Golik, Wavelet packets for fast solution of electromagnetic integral equations, IEEE Trans. Antennas Propag. 46(5), 618-624 (1998).
16. D. Huybrechs, S. Vandewalle, A two-dimensional wavelet-packet transform for matrix compression of integral equations with highly oscillatory kernel, J. Comput. Appl. Math. 197(1), 218-232 (2006).
17. S. Kapur, V. Rokhlin, High-order corrected trapezoidal quadrature rules for singular functions, SIAM J. Numer. Anal. 34, 1331-1356 (1997).
18. R. Kress, Minimizing the condition number of boundary integral operators in acoustic and electromagnetic scattering, Q. J. Mech. Appl. Math. 38(2), 323-341 (1985).
19. S. Mallat, A Wavelet Tour of Signal Processing, 2nd edn. (Academic Press, Orlando-San Diego, 1999).
20. F. G. Meyer, R. R. Coifman, Brushlets: a tool for directional image analysis and image compression, Appl. Comput. Harmon. Anal. 4, 147-187 (1997).
21. V. Rokhlin, Rapid solution of integral equations of scattering theory in two dimensions, J. Comput. Phys. 86(2), 414-439 (1990).
22. V. Rokhlin, Diagonal forms of translation operators for the Helmholtz equation in three dimensions, Appl. Comput. Harmon. Anal. 1, 82-93 (1993).
23. L. Villemoes, Wavelet packets with uniform time-frequency localization, C. R. Math. 335(10), 793-796 (2002).
24. G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd edn. (Cambridge University Press, Cambridge, 1966).