3D curvelet transforms and astronomical data restoration

Applied and Computational Harmonic Analysis

Volumn 28, Issue 2, 2010, Pages 171-188

  Woiselle, A ^a,b   Starck, J L ^a   Fadili, J ^c  

^a UNIVERSITÉ PARIS DIDEROT   (France)

^b SAFRAN AIRCRAFT ENGINES   (France)

^c Centre National de la Recherche Scientifique   (France)

Author keywords

3D transform; Astrophysics; Curvelet; Galaxy distribution; Multi resolution representations; Wavelet

Indexed keywords

3D TRANSFORM; CURVELETS; D-TRANSFORM; GALAXY DISTRIBUTION; MULTI RESOLUTION REPRESENTATION;

ASTROPHYSICS; COSMOLOGY; FILAMENTS (LAMP); GALAXIES; TWO DIMENSIONAL;

THREE DIMENSIONAL;

EID: 76149133622     PISSN: 10635203     EISSN: 1096603X     Source Type: Journal    
DOI: 10.1016/j.acha.2009.12.003     Document Type: Article

References (45)

1. Benjamini Y., and Hochberg Y. Controlling the false discovery rate: A practical and powerful approach to multiple testing. J. Roy. Statist. Soc. Ser. B Methodol. 57 1 (1995) 289-300
2. S. Berlemont, A. Bensimon, J.-C. Olivo-Marin, Detection of curvilinear objects in biological noisy image using feature-adapted fast slant stack, in: SPIE Conference Wavelets XII, Special Session on Wavelet in Bioimaging, 2007
3. Candès E.J., and Donoho D.L. Ridgelets: the key to high dimensional intermittency. Philos. Trans. R. Soc. Lond. Ser. A 357 (Sep. 1999) 2495-2509
4. E.J. Candès, D.L. Donoho, Curvelets, multiresolution representation, and scaling laws, in: SPIE Wavelet Applications in Signal and Image Processing, 2000
5. Candès E.J., and Donoho D.L. New tight frames of curvelets and optimal representations of objects with C2 singularities. Comm. Pure Appl. Math. 57 2 (2003) 219-266
6. P. Carre, D. Helbert, E. Andres, 3D fast ridgelet transform, in: International Conference on Image Processing, vol. 1, 2003, pp. 1021-1024
7. V. Chandrasekaran, M.B. Wakin, D. Baron, R.G. Baraniuk, Surflets: A sparse representation for multidimensional functions containing smooth discontinuities, in: Proceedings of the International Symposium on Information Theory, ISIT 2004, July 2004
8. Chandrasekaran V., Wakin M.B., Baron D., and Baraniuk R.G. Representation and compression of multidimensional piecewise functions using surflets. IEEE Trans. Inform. Theory 55 1 (Jan. 2009) 374-400
9. Chen Z., and Ning R. Breast volume denoising and noise characterization by 3D wavelet transform. Comput. Med. Imaging Graph. 28 5 (2004) 235-246
10. Dima A., Scholz M., and Obermayer K. Semiautomatic quality determination of 3D confocal microscope scans of neuronal cells denoised by 3D wavelet shrinkage. In: Szu H.H. (Ed). Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series vol. 3723 (March 1999) 446-457
11. Do M.N., and Vetterli M. The contourlet transform: an efficient directional multiresolution image representation. IEEE Trans. Image Process. 14 12 (Dec. 2005) 2091-2106
12. Donoho D.L., and Huo X. Beamlets and multiscale image analysis. Multiscale and Multiresolution Methods. Lecture Notes in Computational Science and Engineering vol. 20 (2001), Springer, New York 149-196
13. Donoho D.L. Wedgelets: nearly minimax estimation of edges. Ann. Statist. 27 3 (1999) 859-897
14. n. Applied Mathematics. Proc. Natl. Acad. Sci. USA 96 (1999) 1828-1833
15. Donoho D.L., and Levi O. Fast X-ray and beamlet transforms for three-dimensional data. In: Rockmore D., and Healy D. (Eds). Modern Signal Processing (2002) 79-116
16. Elad M., Starck J.-L., Querre P., and Donoho D.L. Simultaneous cartoon and texture image inpainting using morphological component analysis. Appl. Comput. Harmon. Anal. 19 (2005) 340-358
17. Escalera E., Slezak E., and Mazure A. New evidence for subclustering in the Coma cluster using the wavelet analysis. Astronom. Astrophys. 264 (Oct. 1992) 379-384
18. Fadili M.J., Starck J.-L., and Murtagh F. Inpainting and zooming using sparse representations. Comput. J. 52 1 (2007) 64-79
19. Hennenfent G., and Herrmann F.J. Seismic denoising with nonuniformly sampled curvelets. IEEE Comput. Sci. Eng. 8 3 (May 2006) 16-25
20. Y. Lu, M.N. Do, 3-D directional filter banks and surfacelets, in: Proc. of SPIE Conference on Wavelet Applications in Signal and Image Processing XI, San Diego, USA, 2005
21. Lu Y.M., and Do M.N. Multidimensional directional filter banks and surfacelets. IEEE Trans. Image Process. 16 4 (2007) 918-931
22. Martínez V.J., Starck J.-L., Saar E., Donoho D.L., Reynolds S.C., de la Cruz P., and Paredes S. Morphology of the galaxy distribution from wavelet denoising. Astrophys. J. 634 (Dec. 2005) 744-755
23. Martinez V.J., Paredes S., and Saar E. Wavelet analysis of the multifractal character of the galaxy distribution. MNRAS 260 (Jan. 1993) 365-375
24. Miller C.J., Genovese C., Nichol R.C., Wasserman L., Connolly A., Reichart D., Hopkins A., Schneider J., and Moore A. Controlling the false-discovery rate in astrophysical data analysis. Astronom. J. 122 6 (Dec. 2001) 3492-3505
25. G. Peyre, S. Mallat, Discrete bandelets with geometric orthogonal filters, in: Proceedings of ICIP'05, vol. 1, Sept. 2005, pp. 65-68
26. S. Pires, J.-L. Starck, A. Amara, R. Teyssier, A. Refregier, J. Fadili, FASTLens (FAst STatistics for weak Lensing): Fast method for weak lensing statistics and map making, ArXiv e-print, April 2008
27. J.K. Romberg, M. Wakin, R. Baraniuk, Multiscale wedgelet image analysis: fast decompositions and modeling, in: IEEE Int. Conf. on Image Proc., ICIP'02, vol. 3, June 2002, pp. 585-588
28. Romeo A.B., Horellou C., and Bergh J. N-body simulations with two-orders-of-magnitude higher performance using wavelets. MNRAS 342 (June 2003) 337-344
29. Romeo A.B., Horellou C., and Bergh J. A wavelet add-on code for new-generation n-body simulations and data de-noising (jofiluren). MNRAS 354 (Nov. 2004) 1208-1222
30. Rusanovskky D., and Egiazarian K. Video denoising algorithm in sliding 3D DCT domain. Lecture Notes in Comput. Sci. 37 08 (2005) 618-625
31. I.W. Selesnick, K.Y. Li, Video denoising using 2D and 3D dual-tree complex wavelet transforms, in: Proc. of SPIE Conference on Wavelet Applications in Signal and Image Processing X, San Diego, USA, Aug. 2003
32. Sendur L., and Selesnick I.W. Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency. IEEE Trans. Signal Process. 50 11 (Nov. 2002) 2744-2756
33. Sendur L., and Selesnick I.W. Bivariate shrinkage with local variance estimation. IEEE Signal Process. Lett. 9 12 (Dec. 2002) 438-441
34. Slezak E., de Lapparent V., and Bijaoui A. Objective detection of voids and high density structures in the first CfA redshift survey slice. Astrophys. J. 409 (1993) 517-529
35. Starck J.-L., Candès E.J., and Donoho D.L. The curvelet transform for image denoising. IEEE Trans. Image Process. 11 6 (June 2002) 670-684
36. Starck J.-L., and Murtagh F. Astronomical Image and Data Analysis. Astronomy and Astrophysics Library (2006), Springer, Berlin
37. Starck J.-L., Murtagh F., Candès E., and Donoho D.L. Gray and color image contrast enhancement by the curvelet transform. IEEE Trans. Image Process. 12 6 (2003) 706-717
38. Starck J.L., Bijaoui A., Lopez B., and Perrier C. Image reconstruction by the wavelet transform applied to aperture synthesis. Astronom. Astrophys. 283 (1999) 349-360
39. Starck J.L., Donoho D.L., and Candès E. Very high quality image restoration by combining wavelets and curvelets. In: Laine A., Unser M.A., and Aldroubi A. (Eds). SPIE Conference on Signal and Image Processing: Wavelet Applications in Signal and Image Processing IX. San Diego, 1-4 August 2001 (2001), SPIE
40. Starck J.L., Martinez V.J., Donoho D.L., Levi O., Querre P., and Saar E. Analysis of the spatial distribution of galaxies by multiscale methods. EURASIP J. Appl. Signal Process. 15 (Nov. 2005) 2455-2469
41. J.L. Starck, M.K. Nguyen, F. Murtagh, Deconvolution based on the curvelet transform, in: International Conference on Image Processing, vol. II, 2003, pp. 993-996
42. Starck J.L., Nguyen M.K., and Murtagh F. Wavelets and curvelets for image deconvolution: a combined approach. Signal Process. 83 (2003) 2279-2283
43. Zhang B., Fadili J., and Starck J.L. Wavelets, ridgelets, and curvelets for Poisson noise removal. IEEE Trans. Image Process. 17 7 (July 2008) 1093-1108
44. Teyssier R. Cosmological hydrodynamics with adaptive mesh refinement. A new high resolution code called ramses. Astronom. Astrophys. 385 (April 2002) 337-364
45. Ying L., Demanet L., and Candès E. 3D discrete curvelet transform. Appl. Comput. Math. 217 50 (2005)