Generalized discrete radon transforms and their use in the ridgelet transform

Journal of Mathematical Imaging and Vision

Volumn 23, Issue 2, 2005, Pages 145-165

  Colonna, Flavia ^a   Easley, Glenn ^b  

^a GEORGE MASON UNIVERSITY   (United States)

^b System Planning Corporation   (United States)

Author keywords

Curvelet transform; Radon transform; Ridgelet transform; SAR; Speckle reduction

Indexed keywords

CURVELET TRANSFORMS; RADON TRANSFORMS; RIDGELET TRANSFORMS; SPECKLE REDUCTION;

MATRIX ALGEBRA; SYNTHETIC APERTURE RADAR;

WAVELET TRANSFORMS;

EID: 23944461150     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-005-6463-0     Document Type: Article

References (35)

1. H.H. Arsenault and G. April, "Properties of speckle integrated with a finite aperture and logarithmically transformed," J. Opt. Soc. Am., Vol. 66, pp. 1160-1163, 1976.
2. J.J. Benedetto and P.J.S.G. Ferreira (Eds.), Modern Sampling Theory: Mathematics and Applications, Applied and Numerical Harmonic Analysis Series, Birkhauser: Boston, MA, 2001.
3. E.D. Bolker, The finite Radon transform, Integral Geometry (Brunswick, Maine, 1984), Amer. Math. Soc.: Providence, RI, 1987, pp. 27-50.
4. E.J. Candès, "Ridgelets: Theory and applications," Ph.D. Thesis, Dept. of Statistics, Stanford Univ., 1998.
5. W.G. Carrara, R.S. Goodman, and R.M. Majewski, Spotlight Synthetic Aperture Radar-Signal Processing Algorithms, Artech House: Norwell, MA, 1995.
6. V.C. Chen and L. Hao, Time-Frequency Transforms for Radar Imaging and Signal Analysis, Artech House: Norwell, MA, 2002.
7. G.R. Easley and F. Colonna, "Geometric transforms and their applications to SAR speckle reduction," in Proceedings SPIE conference Aerosense 2003, vol. 5095, Orlando, FL, April 2003.
8. A.M. Cormack, "Representation of a function by its line integrals, with some radiological applications," J. Appl. Phys., Vol. 35, pp. 195-207, 1964.
9. I. Daubechies, O. Runborg, and W. Sweldens, Normal Multiresolution Approximation of Curves, preprint, 2002.
10. P.J. Davis, Circulant Matrices, Pure and Applied Mathematics, Wiley: New York, 1979.
11. P. Dewaele, P. Wambacq, A. Oosterlinck, and J.L. Marchand, "Comparison of some speckle reduction techniques for SAR images," IGARSS, Vol. 10, pp. 2417-2422, 1990.
12. M.N. Do and M. Vetterli, "Orthonormal finite ridgelet transform for image compression," in Proceedings International Conference on Image Processing 2000, Vol. 2, pp. 367-370, 2000.
13. M.N. Do and M. Vetterli, "The finite ridgelet transform for image representation," Technical Report DSC/2001/019, Communication Systems Department, EPFL, 2001.
14. M.N. Do and M. Vetterli, "Contourlets," in Beyond Wavelets, G. V. Welland (Ed.), Academic Press: New York, 2003.
15. D. Donoho, "Wedgelets: Nearly-minimax estimation of edges," Annals of Statistics, Vol. 27, 1999.
16. D.L. Donoho and M.R. Duncan, Digital curvelet transform: Strategy, implementation and experiments, in Proc. Aerosense 2000, Wavelet Applications VII, SPIE, 4056, 2000.
17. S. Fukuda and H. Hirosawa, "Multiresolution analysis and processing of synthetic aperture radar images using wavelets," in Geoscience and Remote Sensing Symp., Proc. IGARSS 1997, IEEE Inter. Conf., Vol. 3, pp. 1187-1189, 1997.
18. J.W. Goodman, Some fundamental properties of speckle, J. Opt. Soc. Am., Vol. 66, pp. 1145-1150, 1976.
19. H. Guo, J.E. Odegard, M. Lang, R.A. Gopinath, I.W. Selesnick, and C.S. Burrus. "Wavelet based speckle reduction with application to SAR based ATD/R," in Image Processing, Proc. ICIP-94, IEEE Inter. Conf., Vol. 1, pp. 75-79, 1994.
20. T. Hsung, D.P.K. Lun, and W.C. Siu, "The discrete periodic Radon transform," Signal Processing, IEEE Transactions on, Vol. 44, 1996.
21. C.V. Jakowatz, D.E. Wahl, P.H. Eichel, D.C. Ghiglia, and P.A. Thompson, Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach, Kluwer Academic Publishers: Norwell, MA, 1996.
22. A.C. Kak and M. Slaney, Principles of Computerized Tomography Imaging, IEEE Press, 1987.
23. J.P.S. Kung, "Matchings and Radon transforms in lattices, ii. concordant sets," Math Proc. Camb. Phil. Soc., Vol. 101, pp. 221-231, 1987.
24. Y.H. Lu, Y.L. Loh, T.S. Yeo, and C.B. Zhang, "Speckle reduction by wavelet transform," in Microwave Conference, 1999 Asia Pacific, 1999, Vol. 2, pp. 542-545.
25. D.P.K. Lun, T.C. Hsung, and T.W. Shen, "Orthogonal discrete periodic Radon transform Part I: Theory and realization," in Signal Processing (EURASIP) (Elsevier Science, Amsterdam), Vol. 83, pp. 941-955, 2003.
26. D.P.K. Lun, T.C. Hsung, and T.W. Shen, "Orthogonal discrete periodic Radon transform Part II: Applications, Signal Processing (EURASIP), Elsevier Science, Amsterdam, Vol. 83, pp. 957-971, 2003.
27. A. Macovski and C. Meyer, "A noval fast scanning system," Works in Progress, Fifth Annual Meeting of the Society of Magnetic Resonance in Medicine, 1986, pp. 156-157.
28. S.Mallat, A Wavelet Tour of Signal Processing, Academic Press: New York, 1998.
29. F. Natterer, The Mathematics of Computerized Tomography, Wiley-Teubner, 1986.
30. C. Oliver and S. Quegan, Understanding Synthetic Aperture Radar Images, Artech House: Norwell, MA, 1998.
31. J.L. Stark, E.J. Candes, and D. Donoho, "The curvelet transform for image denoising," Image Processing, IEEE Transactions on, Vol. 11, 2002.
32. L. Sha, H. Guo, and A.W. Song, "An improved gridding method for spiral MRI using nonuniform fast Fourier transform," Journal of Magnetic Resonance, Vol. 162, pp. 250-258, 2003.
33. J.R. Sveinsson and J.A. Benediktsson, "Speckle reduction of SAR images using wavelet-domain hidden Markov models," in Geoscience and Remote Sensing Symp., Proc. IGARSS 2000, IEEE Inter. Conf., 2000, Vol. 4, pp. 1666-1668.
34. J.R. Sveinsson and J.A. Benediktsson, "Speckle reduction of SAR images in the complex wavelet-domain," in Geoscience and Remote Sensing Symp., Proc. IGARSS 2001, IEEE Inter. Conf., 2001, Vol. 5, pp. 2346-2348.
35. M.O. Ulfarsson, J.R. Sveinsson, and J.A. Benediktsson, "Speckle reduction of SAR images in the curvelet domain," in Geoscience and Remote Sensing Symp., Proc. IGARSS 2002, IEEE Inter. Conf., 2002, Vol. 1, pp. 315-317.