Orthonormal shift-invariant wavelet packet decomposition and representation

Signal Processing

Volumn 57, Issue 3, 1997, Pages 251-270

  Cohen, Israel ^a   Raz, Shalom ^a   Malah, David ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Algorithm; Best basis; Shift invariant; Time frequency; Translation; Wavelet packets; Wavelets

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; DATA STRUCTURES; INVARIANCE; WAVELET TRANSFORMS;

FINITE DEPTH SUBTREES; SEARCH ALGORITHM; SHIFT INVARIANT WAVELET PACKET DECOMPOSITION;

PACKET SWITCHING;

EID: 0031097511     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-1684(97)00007-8     Document Type: Article

References (49)

1. F. Bao, N. Erdol, The optimal wavelet transform and translation invariance, in: Proc. 19th IEEE Internat. Conf. Acoust. Speech Signal Process. Adelaide, 19-22 April 1994, pp. III.13-III.16.
2. S.A. Benno, J.M.F. Moura, Nearly shiftable scaling functions, in: Proc. 20th IEEE Internat. Conf. Acoust. Speech Signal Process. Detroit, MS, 8-12 May 1995, pp. 1097-1100.
3. Z. Berman, J.S. Baras, Properties of the multiscale maxima and zero-crossings representations, IEEE Trans. Signal Process. 41 (12) (December 1993) 3216-3231.
4. G. Beylkin, On the representation of operators in bases of compactly supported wavelets, SIAM J. Numer. Anal 6 (6) (December 1992) 1716-1740.
5. P.J. Burt, Fast filter transforms for image processing, Comput. Graph. Image Process. 16 (1981) 20-51.
6. T. Chang, C.J. Kuo, Texture analysis and classification with tree-structured wavelet transform, IEEE Trans. Image Process. 2 (October 1993) 429-441.
7. L. Cohen, Time-frequency distributions - a review, Proc. IEEE 77 (7) (July 1989) 941-981.
8. I. Cohen, S. Raz, D. Malah, Shift invariant wavelet packet bases, in: Proc. 20th IEEE Internat. Conf. Acoustics, Speech Signal Process., Detroit, Michigan, 8-12 May 1995, pp. 1081-1084.
9. I. Cohen, S. Raz, D. Malah, Shift-invariant adaptive local trigonometric decomposition, in: Proc. 4th European Conf. Speech Commun. Technology, Madrid, Spain, 18-21 September 1995, pp. 247-250.
10. I. Cohen, S. Raz, D. Malah, Shift-invariant adaptive representations in libraries of bases, Technical Report, Technion - Israel Institute of Technology, Haifa, Israel, December 1995.
11. R.R. Coifman, D.L. Donoho, Translation-invariant denoising, in: A. Antoniadis and G. Oppenheim (Ed.), Wavelet and Statistics, Lecture Notes in Statistics, Springer, Berlin, 1995, pp. 125-150.
12. R.R. Coifman, Y. Meyer, Orthonormal wave packet bases, Yale University, August 1989 (in: ftp pascal.math.yale. edu/pub/wavelets/wavepkt.tcx).
13. R.R. Coifman, Y. Meyer, S. Quake, M.V. Wickerhauser, Signal processing and compression with wave packets, in: Proc. Conf. Wavelets, Marseilles, Spring 1989.
14. R.R. Coifman, Y. Meyer, V. Wickerhauser, Size properties of wavelet packets, in: M.B. Ruskai et al. (Eds.), Wavelets and Their Applications, Jones and Bartlett, Boston, 1992, pp. 453-470.
15. R.R. Coifman, M.V. Wickerhauser, Entropy-based algorithms for best basis selection, IEEE Trans. Inform. Theory 38 (March 1992) 713-718.
16. R.R. Coifman, M.V. Wickerhauser, Adapted waveform analysis as a tool for modeling, feature extraction, and denoising, Optical Engineering 33 (7) (July 1994) 2170-2174.
17. I. Daubechies, Orthonormal bases of compactly supported wavelets, Commun. Pure Appl. Math. 41 (1988) 909-996.
18. I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF Regional Conf. Ser. Appl. Math., SIAM, Philadelphia, Pennsylvania, 1992.
19. I. Daubechies, Orthonormal bases of compactly supported wavelets, II. Variations on a theme, SIAM J. Math. Anal. 24 (1993) 499-519.
20. G. Davis, S. Mallat, Z. Zhang, Adaptive time-frequency decompositions, Opt. Eng. 33 (7) (July 1994) 2183-2191.
21. S. Del Marco, P. Heller, J. Weiss, An M-band 2-dimensional translation-invariant wavelet transform and applications, in: Proc. 20th IEEE Internat. Conf. Acoust. Speech Signal Process., Detroit, Michigan, 8-12 May 1995, pp. 1077-1080.
22. S.P. Del Marco, J. Weiss, K. Jagler, Wavepacket-based transient signal detector using a translation invariant wavelet transform, Proc. SPIE 2242 (1994) 792-802.
23. C. Herley, J. Kovačević, K. Ramchandran, M. Vetterli, Tilings of the time-frequency plane: Construction of arbitrary orthogonal bases and fast tiling algorithms, IEEE Trans. Signal Process 41 (December 1993) 3341-3359.
24. C. Herley, Z. Xiong, K. Ramchandran, M.T. Orchard, An efficient algorithm to find a jointly optimal time-frequency segmentation using time-varying filter banks, in: Proc. 20th IEEE Internat. Conf. Acoust. Speech Signal Process., Detroit, MI, 8-12 May 1995, pp. 1516-1519.
25. R. Hummel, R. Moniot, Reconstructions from zero crossings in scale space. IEEE Trans. Acoust. Speech Signal Process. 37 (December 1989) 2111-2130.
26. B. Jawerth, Y. Liu, W. Sweldens, Signal compression with smooth local trigonometric bases, Optical Eng. 33 (7) (July 1994) 2125-2135.
27. R. Kronland-Martinet, J. Morlet, A. Grossman, Analysis of sound patterns through wavelet transforms, Internat J. Pattern Rec. Art. Intell. 1 (1987) 273-301.
28. A. Laine, J. Fan, Texture classification by wavelet packet signatures, IEEE Trans. Pattern Anal. Mechine Intell. 15 (11) (November 1993) 1186-1191.
29. J. Liang, T.W. Parks, A two-dimensional translation invariant wavelet representation and its application, in: Proc. Internat. Conf. Image Process., Austin, TX, 13-16 November 1994, pp. 66-70.
30. J. Liang, T.W. Parks, A translation invariant wavelet representation algorithm with applications, IEEE Trans. Signal Process. 44 (2) (February 1996) 225-232.
31. S.G. Mallat, A theory for multiresolution signal decomposition: The wavelet decomposition, IEEE Trans. Pattern Anal. Machine Intell. 11 (July 1989) 674-693.
32. S. Mallat, Zero crossings of a wavelet transform, IEEE Trans. Inform. Theory 37 (July 1991) 1019-1033.
33. S. Mallat, W.L. Hwang, Singularity detection and processing with wavelets, IEEE Trans. Inform. Theory 38 (2) (March 1992) 617-643.
34. S. Mallat, S. Zhong, Characterization of signals from multiscale edges, IEEE Trans. Pattern Anal. Machine Intell. 14 (July 1992) 710-732.
35. S. Mallat, Z. Zhang, Matching pursuit with time-frequency dictionaries, IEEE Trans. Signal Process. 41 (December 1993) 3397-3415.
36. G.P. Nason, B.W. Silverman, The stationary wavelet transform and some statistical applications, in: A. Antoniadis and G. Oppenheim (Eds), Wavelet and Statistics, Lecture Notes in Statistics, Springer, Berlin, 1995, pp. 281-300.
37. J.-C. Pesquet, H. Krim, H. Carfantan, J.G. Proakis, Estimation of noisy signals using time-invariant wavelet packets, in: Proc. Asilomar Conf., Monterey, CA, USA, Vol. 1, November 1993, pp. 31-34.
38. K. Ramchandran, M. Vetterli, Best wavelet packet bases in a rate-distortion sense, IEEE Trans. Image Process. 2 (April 1993) 160-175.
39. O. Rioul, P. Duhamel, Fast algorithms for discrete and continuous wavelet transforms, IEEE Trans. Inform Theory 38 (March 1992) 569-586.
40. O. Rioul, M. Vetterli, Wavelets and signal processing, IEEE Signal Process. Mag. 8 (October 1991) 14-38.
41. N. Saito, Local feature extraction and its applications using a library of bases, Ph.D. Dissertation, Yale Univ., New Haven, December 1994.
42. N. Saito, G. Beylkin, Multiresolution representation using the auto-correlation functions of compactly supported wavelets, IEEE Trans. Signal Process. 41 (December 1993) 3584-3590.
43. E.P. Simoncelli, W.T. Freeman, E.H. Adelson, D.J. Heeger, Shiftable multiscale transforms, IEEE Trans. Inform. Theory, 38 (2) (March 1992) 587-607.
44. M. Vetterli, Wavelet and filter banks for discrete-time signal processing, in: M.B. Ruskai et al. (Eds.), Wavelets and Their Applications, Jones and Bartlett, Boston, 1992, pp. 17-52.
45. M. Vetterli, C. Herley, Wavelets and filter banks: Theory and design, IEEE Trans. Signal Process. 40 (September 1992) 2207-2232.
46. G.G. Walter, Wavelets and Other Orthogonal Systems With Applications, CRC Press, Boca Raton, FL, 1994.
47. E. Wesfreid, M.V. Wickerhauser, Adapted local trigonometric transforms and speech processing, IEEE Trans. Signal Process. 41 (12) (December 1993) 3596-3600.
48. M.V. Wickerhauser, Acoustic signal compression with wavelet packets, in: C.K. Chui (Ed.), Wavelets - A Tutorial in Theory and Applications, Academic Press, Boston, 1992, pp. 679-700.
49. M.V. Wickerhauser, Adapted Wavelet Analysis from Theory to Software, AK Peters, Wellesley, MA, 1994.