The shiftable complex directional pyramid - Part I: Theoretical aspects

IEEE Transactions on Signal Processing

Volumn 56, Issue 10 I, 2008, Pages 4651-4660

  Nguyen, Truong T ^a   Oraintara, Soontorm ^a  

^a University of Texas at Arlington   (United States)

Author keywords

Complex wavelet; Directional decomposition; Directional filter bank (DFB); Dual tree DWT; Multiresolution representation

Indexed keywords

IMAGE RETRIEVAL; TREES (MATHEMATICS); WAVE FILTERS;

COMPLEX WAVELET; DIRECTIONAL DECOMPOSITION; DIRECTIONAL FILTER BANK (DFB); DUAL-TREE DWT; MULTIRESOLUTION REPRESENTATION;

FILTER BANKS;

EID: 53149122505     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2007.912897     Document Type: Article

References (30)

1. G. Strang and T. Q. Nguyen, Wavelets and Filter Banks. Cambridge, U.K.: Wellesley Cambridge, 1996.
2. S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed. New York: Academic, 1999.
3. G. Strang, "Wavelets and dilation equations: A brief introduction," SIAM Rev., vol. 31, no. 4, pp. 614-627, Dec. 1989.
4. E. P. Simoncelli, W. T. Freeman, E. H. Adelson, and D. J. Heeger, "Shiftable multiscale transform," IEEE Trans. Inf. Theory, vol. 38, no. 2, pp. 587-607, Mar. 1992.
5. N. G. Kingsbury, "Complex wavelets for shift invariant analysis and filtering of signals," J. Appl. Computat. Harmonic Anal., vol. 10, no. 3, pp. 234-253, May 2001.
6. F. C. A. Fernandes, R. L. C. van Spaendonck, and C. S. Burros, "A new framework for complex wavelet transforms," IEEE Trans. Signal Process., vol. 51, no. 7, pp. 1825-1837, Jul. 2003.
7. T. T. Nguyen and S. Oraintara, "The shiftable complex directional pyramid-Part 2: Implementation and applications," IEEE Trans. Signal Process., vol. 56, no. 10, pt. 1, Oct. 2008.
8. I. W. Selesnick, "The double density dwt," in Wavelets in Signal and Image Analysis: From Theory to Practice, A. Petrosian and F. G. Meyer, Eds. Amsterdam, The Netherlands: Kluwer, 2001, ch. 2.
9. J.-L. Starck, E. J. Candès, and D. L. Donoho, "The curvelet transform for image denoising," IEEE Trans. Image Process., vol. 11, no. 6, pp. 670-684, Jun. 2002.
10. N. G. Kingsbury, "Image processing with complex wavelets," Phil. Trans. R. Soc. London A, vol. 357, no. 1760, pp. 2543-2560, Sep. 1999.
11. Y. P. Lin and P. P. Vaidyanathan, "Theory and design of two-dimensional filter banks: A review," Multidimens. Syst. Signal Process., vol. 7, pp. 263-330, 1996.
12. I. W. Selesnick, R. G. Baraniuk, and N. C. Kingsbury, "The dual-tree complex wavelet transform," IEEE Signal Process. Mag., vol. 22, no. 6, pp. 123-151, Nov. 2005.
13. C. Chaux, L. Duval, and J.-C. Pesquet, "Image analysis using a dual-tree m-band wavelet transform," IEEE Trans. Image Process., vol. 15, no. 8, pp. 2397-2412, May 2006.
14. F. G. Meyer and R. R. Coifman, "Brushlets: Steerable wavelet packets," in Beyond Wavelets, G. V. Welland, Ed. Amsterdam, The Netherlands: Academic, 2003, ch. 3, pp. 61-82.
15. R. A. Gopinath, "The phaselet transform-an integral redundancy nearly shift-invariant wavelet transform," IEEE Trans. Signal Process., vol. 51, no. 7, pp. 1792-1805, Jul. 2003.
16. I. W. Selesnick, "The double-density dual-tree dwt," IEEE Trans. Signal Process., vol. 52, no. 5, pp. 1304-1314, May 2004.
17. M. N. Do and M. Vetterli, "The contourlet transform: An efficient directional multiresolution image representation," IEEE Trans. Image Process., vol. 14, pp. 2107-2116, Dec. 2005.
18. P. Vaidyanathan, Multirate Systems and Filter Banks. Englewood Cliffs, NJ: Prentice-Hall, 1993.
19. R. H. Bamberger and M. J. T. Smith, "A filter bank for the directional decomposition of images: Theory and design," IEEE Trans. Signal Process., vol. 40, pp. 882-893, Apr. 1992.
20. T. T. Nguyen, "The Multiresolution Directional Filter Bank," Ph.D., Univ. Texas at Arlington, Arlington, 2006.
21. T. T. Nguyen and S. Oraintara, "A shift-invariant multiscale multidirection image decomposition," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP'06), France, May 2006, pp. 153-156.
22. I. W. Selesnick, "Hilbert transform pairs of wavelet bases," IEEE Signal Process. Lett., vol. 8, no. 6, pp. 170-173, Jun. 2001.
23. I. W. Selesnick, "The design of approximate hilbert transform pairs of wavelet bases," IEEE Trans. Signal Process., vol. 50, no. 5, pp. 1144-1152, May 2002.
24. S. I. Park, M. J. Smith, and R. M. Mersereau, "Improved structure of maximally decimated directional filter banks for spatial image analysis," IEEE Trans. Image Process., vol. 13, pp. 1424-1431, Nov. 2004.
25. M. N. Do and M. Vetterli, "Pyramidal directional filter banks and curvelets," in Proc. IEEE Int. Conf. Image Process. (ICIP), Thessaloniki, Greece, Oct. 2001.
26. J. Rosiles and M. J. Smith, "Texture classification with a biorthogonal directional filter bank," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., 2001, pp. 1549-1552.
27. M. N. Do and M. Vetterli, "Contourlets," in Beyond Wavelets, G. V. Welland, Ed. Amsterdam, The Netherlands: Academic, 2003, ch. 4, pp. 83-105.
28. A. L. Cunha, J. Zhou, and M. N. Do, "Nonsubsampled contourlet transform: Filter design and application in image denoising," in Proc. Int. Conf. Image Process. (ICIP 05), Genoa, Italy, Sep. 2005.
29. A. L. Cunha, J. Zhou, and M. N. Do, "The nonsubsampled contourlet transform: Theory, design, and applications," IEEE Trans. Image Process., vol. 15, pp. 3089-3101, 2006.
30. J. Zhou, A. L. Cunha, and M. N. Do, "Nonsubsampled contourlet transform: Construction and application in enhancement,"in Proc. Int. Conf. Image Process. (ICIP 05), Genoa, Italy, Sep. 2005.