Multidimensional, mapping-based complex wavelet transforms

IEEE Transactions on Image Processing

Volumn 14, Issue 1, 2005, Pages 110-124

  Fernandes, Felix C A ^a   van Spaendonck, Rutger L C ^b,c   Burrus, C Sidney ^b  

^a TEXAS INSTRUMENTS   (United States)

^b Rice University   (United States)

^c Shell E and P Europe   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; IMAGE CODING; ITERATIVE METHODS; OPTIMIZATION; WAVELET TRANSFORMS;

COMPLEX WAVELET TRANSFORM; DISCRETE WAVELET TRANSFORM; DOUBLE DENSITY WAVELET TRANSFORM; ITERATIVE OPTIMIZATION;

IMAGE PROCESSING;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; BIOLOGICAL MODEL; COMPARATIVE STUDY; COMPUTER ASSISTED DIAGNOSIS; COMPUTER GRAPHICS; COMPUTER SIMULATION; EVALUATION; IMAGE ENHANCEMENT; INFORMATION RETRIEVAL; MATHEMATICAL COMPUTING; METHODOLOGY; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING; STATISTICAL MODEL; VALIDATION STUDY;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; COMPUTER GRAPHICS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; INFORMATION STORAGE AND RETRIEVAL; MODELS, BIOLOGICAL; MODELS, STATISTICAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; PATTERN RECOGNITION, AUTOMATED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 11844304336     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2004.838701     Document Type: Article

References (39)

1. F. C. A. Fernandes, R. L. C. van Spaendonck, and C. S. Burrus, "A new framework for complex wavelet transforms," IEEE Trans. Signal Process., vol. 51, no. 7, pp. 1825-1837, Jul. 2003.
2. R. L. C. van Spaendonck, "Wavelet-based attributes for seismic interpretation," Ph.D. dissertation, Delft Univ. Technol., Delft, The Netherlands, 2001.
3. F. C. A. Fernandes, "Directional, shift-insensitive, complex wavelet transforms with controllable redundancy," Ph.D. dissertation, Rice Univ., Houston, TX, Jan. 2002.
4. R. L. C. van Spaendonck, F. C. A. Fernandes, and J. T. Fokkema, "Wavelet-based attributes for seismic interpretation, " Geophys. to be published.
5. 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, no. 4, pp. 882-893, Apr. 1992.
6. M. Do and M. Vetterli, "Pyramidal directional filter banks and curvelets," in IEEE Proc. Int. Conf. Image Processing, vol. 3, Oct. 2001, pp. 158-161.
7. E. P. Simoncelli, W. T. Freeman, E. H. Adelson, and D. J. Heeger, "Shiftable multiscale transforms," IEEE Trans. Inf. Theory, vol. 38, no. 2, pp. 587-607, Mar. 1992.
8. R. van Spaendonck and R. G. Baraniuk, "Directional scale analysis for seismic interpretation," in Ann. Meeting Abstracts, 1999, pp. 1844-1847.
9. D. L. Donoho, Wedgelets: Nearly-minimax estimation of edges, Tech. Rep., Stanford Univ., Stanford, CA, Aug. 1997.
10. R. L. Claypoole, Jr., "Adaptive wavelet transforms via lifting," Ph.D. dissertation, Rice Univ., Houston, TX, 1999.
11. F. G. Meyer and R. R. Coifman, "Brushlets: a tool for directional image analysis and image compression," Appl. Comput. Harmon. Anal., vol. 4, pp. 147-187, 1997.
12. E. J. Candés, "Ridgelets: Theory and applications," Ph.D. dissertation, Stanford Univ., Stanford, CA, 1998.
13. D. L. Donoho, Orthonormal ridgelets and linear singularities, Tech. Rep., Stanford Univ., Stanford, CA, 1998.
14. D. L. Donoho and M. R. Duncan, "Digital curvelet transform: strategy, implementation and experiments," Proc. SPIE, vol. 4056, 2000.
15. E. Candés and D. Donoho, Curvelets, Tech. Rep., Stanford Univ., Stanford, CA, 1999.
16. A. Watson and J. A. J. Ahumada, "Model of human visual-motion sensing," J. Opt. Soc. Amer., vol. 2, no. 2, pp. 322-342, 1985.
17. T. Burns, S. Rogers, D. Ruck, and M. Oxley, "Discrete, spatiotemporal, wavelet multiresolution analysis method for computing optical flow," Opt. Eng., vol. 33, no. 7, pp. 2236-2247, 1994.
18. J. Magarey and N. Kingsbury, "Motion estimation using a complex-valued wavelet transform," IEEE Trans. Signal Process., vol. 46, no. 4, pp. 1069-1084, Apr. 1998.
19. P. de Rivaz and N. Kingsbury, "Complex wavelet features for fast texture image retrieval," in IEEE Proc. Int. Conf. Image Processing vol. 1, Oct. 1999, pp. 109-113.
20. J. K. Romberg, H. Choi, R. G. Baraniuk, and N. G. Kingsbury, "Hidden Markov tree models for complex wavelet transforms," in Proc. IEEE Int. Conf Acoustics, Speech, Signal Processing, vol. 1, Jun. 2000, pp. 133-136.
21. I. Selesnick, "The design of approximate Hilbert transform pairs of wavelet bases," IEEE Trans. Signal Process., vol. 50, no. 5, pp. 1144-1152, May 2002.
22. I. W. Selesnick, "Hilbert transform pairs of wavelet bases," IEEE Signal Process. Lett., vol. 8, no. 6, pp. 170-173, Jun. 2001.
23. F. C. A. Fernandes, R. van Spaendonck, M. Coates, and C. S. Burrus, "Directional complex-wavelet processing," Proc. SPIE, vol. 4119, pp. 536-546, 2000.
24. I. W. Selesnick and L. Sendur, "Iterated oversampled filter banks and wavelet frames," Proc. SPIE, 2000.
25. F. C. A. Fernandes, I. W. Selesnick, R. L. C. van Spaendonck, and C. S. Burrus, "Complex wavelet transforms with allpass filters," Signal Process., vol. 83, no. 8, pp. 1689-1706, 2003.
26. R. van Spaendonck, T. Blu, R. Baraniuk, and M. Vetterli, "Orthogonal Hilbert transform filter banks and wavelets," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, vol. 6, Apr. 2003, pp. 505-508.
27. M. T. Orchard and H. Ates, "Equiripple Design of real and complex filter banks," Tech. Rep., Rice Univ., Houston, TX, 2003.
28. S. Mallat, "Zero-crossings of a wavelet transform," IEEE Trans. Inf. Theory, vol. 37, no. 4, pp. 1019-1033, Jul. 1991.
29. G. Beylkin, "On the representation of operators in bases of compactly supported wavelets," SIAM J. Numer. Anal., vol. 29, no. 6, pp. 1716-1740, 1992.
30. H. Guo, "Theory and applications of the shift-invariant, time-varying and undecimated wavelet transform," M.S. thesis, Rice Univ., Houston, TX, May 1995.
31. J. Liang and T. W. Parks, "A translation invariant wavelet representation algorithm with applications," IEEE Trans. Signal Process., vol. 44, no. 2, pp. 225-232, Feb. 1996.
32. S. A. Benno and J. M. F. Moura, "Scaling functions robust to translations," IEEE Trans. Signal Process., vol. 46, no. 12, pp. 3269-3281, Dec. 1998.
33. F. Bao and N. Erdol, "The optimal wavelet transform and translation invariance," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, vol. 3, Apr. 1994, pp. 13-16.
34. P. P. Vaidyanathan, Multirate Systems and Filter Banks. Englewood Cliffs, NJ: Prentice-Hall, 1992.
35. G. Strang and T. Nguyen, Wavelets and Filter Banks. Wellesley, MA: Wellesley-Cambridge, 1996.
36. 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. Norwell, MA: Kluwer, 2001.
37. T. H. Reeves and N. G. Kingsbury, "Prediction of coefficients from coarse to tine scales in the complex wavelet transform," in Proc. IEEE Int. Conf Acoust., Speech, Signal Processing, vol. 1, Jun. 2000, pp. 508-511.
38. J. Portilla and E. P. Simoncelli, "A parametric texture model based on joint statistics of complex wavelet coefficients," Int. J. Comput. Vis., 2000.
39. I. W. Selesnick, "Motion selective 3-D wavelet frames for video processing," in Proc. Int. Meeting Amer. Math. Soc., Orlando, FL, 2002.