Ridgelet Decomposition: Discrete implementation and Color denoising

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 6001, Issue , 2005, Pages

  Carré, Philippe ^a   Helbert, David ^a  

^a UNIVERSITÉ DE POITIERS   (France)

Author keywords

Color images; Denoising; Discrete Analytical Lines; Ridgelet Transform

Indexed keywords

ALGORITHMS; DISCRETE FOURIER TRANSFORMS; GAUSSIAN NOISE (ELECTRONIC); REDUNDANCY; THREE DIMENSIONAL; TWO DIMENSIONAL;

COLOR IMAGES; DENOISING; DISCRETE ANALYTICAL LINES; RIDGELET TRANSFORM;

COLOR IMAGE PROCESSING;

EID: 33644633763     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.629569     Document Type: Conference Paper

References (29)

1. E. Candès, Ridgelets: Theory and Applications. PhD thesis. Dpt of Statistics, Stanford University, http://www.acm.caltech.edu/emmanuel/, August 1998.
2. M. Do, Directional Multiresolution Image Representations. PhD thesis, Department of Communication Systems. Swiss Federal Institute of Technology Lausanne, November 2001.
3. A. Flesia, H. Hel-Or, A. Averbuch, E. Candés, R. Coifman, and D. Donoho, "Digital implementation of ridgelet packets," in Beyond Wavelets. J. Stoeckler and G. V. Weiland, eds., Academic Press, 2002.
4. S. Mallat, "A theory for multiresolution signal decomposition : the wavelet transform," IEEE Trans. on PAMI 11, pp. 674-693, 1989.
5. M. Bronstein, A. Bronstein, and M. Zibulevsky, "Applications of non-uniform fft for acoustic diffraction tomography," tech. rep., http://visl.technion.ac.il/bron/works, march 2002.
6. J. Fessier and B. Sutton, "A min-max approach to the multidimensional nonuniform fft: Application to tomographic image reconstruction," To be Published in IEEE Trans, on Signal Processing, 2001.
7. K. Fourmont, "Non-equispaced fast fourier transforms with applications to tomography," tech. rep., Math Department at the University of Muenster, http://www.math.uni-muenster.de, May 2002.
8. F. Natterer. "Numerical methods in tomography," Acta Numerica, 1999.
9. D. Potts and G. Steidl, "A new linogram algorithm for computerized tomography," IMA Journal of Numerical Analysis 21, pp. 769-782, 2001.
10. J. Roerdink and M. Westenberg, "Data-parallel tomographic reconstruction: a comparison of filtered back-projection and direct fourier reconstruction," Parallel Computing 24, pp. 2129-2144, 1998.
11. P. Toft, The Radon Transform: theory and implementation. PhD thesis. Dpt of Mathematical Modelling, Technical University of Denmark, 1996.
12. M. Brady, "A fast discrete approximation algorithm for the radon transform," SIAM J. Computer 27, pp. 107-119, February 1998.
13. F. Matus and J. Flusser, "Image representation via a finite radon transform," IEEE Trans. on Pattern Analysis and Machine Intelligence 15(10), pp. 996-1006, 1993.
14. A. Averbuch, R. Coifman, D. Donoho, M. Israeli, and J. Waiden, "Fast slant stack: A notion of radon transform for data in a cartesian grid which is rapidly computible, algebraically exact, geometrically faithful and invertible," SIAM Scientific Computing to appear, 2001.
15. Y. Shkolnisky, A. Averbuch, and D. Donoho, "2d fourier based discrete radon transform," submitted, Dpt of Statistics, Stanford University, http://www.math.tau.ac.il/amir1/publications.html.
16. J.-L. Starck, E. Candès, and D. Donoho, "The curvelet transform for image denoising," IEEE Transactions on Image Processing 11, pp. 670-684, November 2002.
17. E. Andres, "Modélisation analytique discrète d'objets géométriques," Habilitation, Université de Poitiers, 2000.
18. J.-P. Reveillès, "Géométrie discrète, calcul en nombres entiers et algorithmique," Habilitation. Université Louis Pasteur de Strasbourg, 1991.
19. P. Carré, D.Helbert, and E. Andrès, "3-d fast ridgelet transform," in ICIP'03, IEEE International Conference on Image Processing, (Barcelona, Spain). September 2003.
20. J. Bresenham, "Algorithms for computer control of a digital plotter," IBM Sys. Journal 4, pp. 25-30, January 1965.
21. E. Andres, R. Acharya, and C. Sibata, "Discrete analytical hyperplanes," Graphical Models and Image Processing 59(5), pp. 302-309, 1997.
22. D. Potts, G. Steidl, and M. Tasche, "Fast fourier transforms for nonequispaced data: a tutorial," in Modern Sampling Theory: Mathematics ans Applications, 2001.
23. A. Averbuch and Y. Shkolnisky, "3d discrete x-ray transform," submitted, http://www.math.tau.ac.il/amir1/publications.html.
24. D. Donoho, "Wavelet shrinkage and W.V.D. : a 10-minute tour," tech. rep., Stanford University, 1992.
25. J.-L. Starck, E. Candés, and D. Donoho, "the curvelet transform for image denoising," IEEE Trans. Image Processing 11, pp. 131-141, June 2002.
26. D. Helbert, P. Carré, and E. Andres, "La transformée ridgelet analytique discréte 3D," in GRETSI, (Paris, France), September 2003.
27. P. Carré, D. Helbert, and E. Andres, "3D fast ridgelet transform," in ICIP, (Barcelona, Spain), September 2003.
28. A. Averbuch and Y. Shkolnisky, "3d Fourier based discrete Radon transform," Applied and Computational Harmonic 15, pp. 33-69, 2003.
29. E. Andres, R. Acharya, and C. Sibata, "Discrete analytical hyperplanes.," CVGIP: Graphical Model and Image Processing 59(5), pp. 302-309, 1997.