Image processing with complex daubechies wavelets

Journal of Mathematical Imaging and Vision

Volumn 7, Issue 3, 1997, Pages 211-223

  Lina, Jean Marc ^a,b,c  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b Atlantic Nuclear Services Ltd Canada   (Canada)

^c Atlantic Nuclear Technologies Ltd   (Canada)

Author keywords

Complex signals; Daubechies wavelets; Image processing; Restoration

Indexed keywords

IMAGE ENHANCEMENT; IMAGE PROCESSING; IMAGE RECONSTRUCTION; SIGNAL THEORY;

COMPLEX SIGNALS; ITERATIVE ALGORITHMS; SYMMETRIC DAUBECHIES WAVELETS;

WAVELET TRANSFORMS;

EID: 0031166725     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008274210946     Document Type: Article

References (29)

1. D. Marr, Vision, W.H. Freeman: San Francisco, 1982.
2. D. Marr and E. Hildreth, "Theory of edge detection," Proc. Royal So. London, Vol. 207, pp. 187-217, 1980.
3. J. Canny, "A computational approach to edge detection," IEEE Trans. Pattern Anal. Machine Intell., Vol. 8, pp. 679-698, 1986;
4. I.D.G. Macleod, "On finding structures in picture," in Picture Language Machines, S. Kaneff (Ed.), Academic Press: New York, p. 231, 1970.
5. S. Mallat, "Zero-crossings of a wavelet transform," IEEE Trans. Info. Theory, Vol. 37, pp. 1019-1033, 1991.
6. S. Mallat and S. Zhong, "Characterization of signals from multiscale edges," IEEE Trans. Patt. Anal. Machine Intell., Vol. 14, pp. 710-732, 1992.
7. W. Lawton, "Applications of complex valued wavelet transforms to subband decomposition," IEEE Trans, on Signal Proc., Vol. 41, pp. 3566-3568, 1993.
8. J.M. Lina and M. Mayrand, "Complex Daubechies Wavelets," App. Comp. Harmonic Anal., Vol. 2, pp. 219-229, 1995.
9. L. Gagnon and J.M. Lina, "Symmetric daubechies wavelet and numerical solution of NLS equations," Jour. Phys. A, Vol. 27, pp. 8207-8230, 1994.
10. B. Beizer, J.M. Lina, and J. Villasenor, "Complex linear phase filters for efficient image coding," to be published in IEEE Trans, on Signal Proc., 1995;
11. L. Gagnon, J.M. Lina, and B. Goulard, "Sharpening enhancement of digitalized mammograms with complex symmetric daubechies wavelets," 17th IEEE and EMBS Conf., Montreal, Sept. 1995.
12. J.-M. Lina, "From Daubechies to Marr," ANS-PhysNum Report 20, Univ. of Montreal, March 1995.
13. A.V Oppenheim and J.S. Li, "The importance of phase in signals," Proc. IEEE, Vol. 69, pp. 529-541, 1981.
14. M. Hayes, "The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform," IEEE Trans. ASSP, Vol. 30, pp. 140-154, 1982.
15. A. Levi and H. Stark, "Signal restoration from phase by projections onto convex sets," J. Opt. Soc. Am., Vol. 73, pp. 810-822, 1983.
16. R. De Vore and B.J. Lucier, "Fast wavelet techniques for near-optimal image processing," P roc. 1992 IEEE Military Commun. Conf., IEEE Communications Soc., NY, 1992.
17. D. Donoho and I. Johnstone, "Adapting to unknown smoothness via wavelet shrinkage," to be published in J. Amer. Statist. Assoc., 1995 (and reference therein).
18. I. Daubechies, "Orthonormal bases of compactly supported wavelets," Comm. Pure Appl. Math., Vol. 41, pp. 909-996, 1988.
19. I. Daubechies, Ten Lectures on Wavelets, SIAM, CBMS Series, 1992, seep. 253.
20. I (2, F[z, 1/z]) for F a subfield of C," Comm. Purre Appl. Math., Vol. 45, p. 485, 1990.
21. A.F. Laine, S. Schuler, J. Fan, and W. Huda, "Mammographie feature enhancement by multiscale analysis," IEEE Transactions on Medical Imaging, Vol. 13, pp. 725-740, 1994.
22. J. Lu, D.M. Healy, Jr., and J.B. Weaver, "Contrast enhancement of medical images using multiscale edge representation," SPIE Wavelet Applications, Vol. 2242, pp. 711-719, 1994.
23. D.C. Youla and H. Webb, "Image restoration by the method of convex projections," IEEE Trans, on Medical Imaging, Vol. 1, No. 2, pp. 81-94, 1982.
24. G.P. Nason, "Wavelet regression by cross-validation," Tech. Report 447. Dept. of Statistic, Stanford (April 1994), and references therein.
25. J. Daugman, "Uncertainty relation for resolution in space, spacial frequency, and orientation optimized by two-dimentional visual cortical filters," J. Opt. Soc. Am. A, Vol. 2, No. 7, p. 1160, 1985.
26. S. Mallat, "Multifrequency channel decomposition of images and wavelet models," IEEE Trans. ASSP., Vol. 37, No. 12, p. 2091, 1989.
27. D.A. Pollen and S. Ronner, "Phase relationships between adjacent simple cells in the visual cortex," in Science, Vol. 212, p. 1409, 1981.
28. A. Burgess and H. Ghandeharian, "Visual signal detection. I. Ability to use phase information," J. Opt. Soc. Am., Vol. 1, pp. 900-905, 1984.
29. M.C. Morrone and D.C. Burr, "Feature detection in human vision: A phase-dependent energy model," Proc. R. Soc. Land. Vol. B235, p. 221, 1988.