An introduction to wavelet theory and application for the radiological physicist

Medical Physics

Volumn 25, Issue 10, 1998, Pages 1985-1993

  Harpen, Michael D ^a  

^a UNIVERSITY OF SOUTH ALABAMA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIOMEDICAL SIGNAL PROCESSING; COMPUTER AIDED DIAGNOSIS; DIAGNOSTIC RADIOGRAPHY; EXTRACTION; FEATURE EXTRACTION; IMAGE COMPRESSION;

COMPUTER AIDED; DIAGNOSTIC RADIOLOGY; MATHEMATICAL TREATMENTS; NOISE SUPPRESSION; TELERADIOLOGY; WAVELET THEORY;

WAVELET TRANSFORMS;

ARTICLE; IMAGE PROCESSING; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; NOISE; PRIORITY JOURNAL; RADIATION PHYSICS;

EID: 0031789514     PISSN: 00942405     EISSN: None     Source Type: Journal    
DOI: 10.1118/1.598387     Document Type: Article

References (30)

1. D. Gabor, "Theory of communication," J. Inst. Elec. Eng. 93, 429-457 (1946).
2. G. M Davis, "Wavelet-based analysis of fractal image compress," IEEE Trans. Image Process. 7, 141-154 (1998).
3. V. Anh, F. Gras, and H. T. Tsui, "Fractal segmentation using multiresolution B-spline wavelets," ISSPA 2, 589-592 (1996).
4. J. Morlet, G. Arens, I. Fourgeau, and D. Giard, "Wave propagation and sampling theory," Geophysics 47, 203-236 (1982)
5. A. Grossmann and J. Morlet, "Decomposition of hardy functions into square integrable wavelets of constant shape," SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 15, 723-736 (1984).
6. A. Grossmann, J. Morlet, and T. Paul, "Transformations associated to square integrable group representations," J. Math. Phys. 26, 2473-2479 (1985).
7. S. Mallat, "Multiresolution approximation and wavelets," Trans. Am. Math. Soc. 315, 69-88 (1989).
8. S. Mallat, "A theory for multiresolution signal decomposition: The wavelet representation," IEEE Trans. Pattern. Anal. Mach. Intell. 31, 674-693 (1989).
9. S. Mallat, "Multifrequency channel decompositions of images and wavelet models," IEEE Trans. Acoust., Speech. Signal Process. 37, 2091-2110 (1987).
10. I. Daubechies, "Orthonormal bases of compactly supported wavelets," Commun. Pure Appl. Math. 41, 909-996 (1988).
11. G. Strang, "Wavelet transforms versus Fourier transforms," Bull. Am. Math. Soc. 28, 288-305 (1993).
12. M Unser, "A practical guide to the implementation of the wavelet transform," in Wavelets in Medicine and Biology, edited by A. Aldroubi and M. Unser (CRC Press, New York, 1996).
13. O. Rioul and M. Vetterli, "Wavelets and signal processing," IEEE Signal Process. Mag. 8, 11-38 (1991)
14. I. Daubechies, Ten Lectures on Wavelets (SIAM Philadelphia, 1992).
15. A. Cohen, I. Daubechies, and J. C. Fauveau, "Biorthogonal bases of compactly supported wavelets," Commun. Pure Appl. Math. 45, 485-560 (1992).
16. C. K. Chui, An Introduction to Wavelets (Academic, New York, 1992).
17. R. DeVore, B. Jaeverth, and B. J Lucier, "Image compression through wavelet transform coding," IEEE Trans. Inf. Theory 38, 719-746 (1992).
18. D Donoho and I Johnstone, "Ideal spatial adaptation via wavelet shrinkage," Biometrika 81, 425-455 (1994).
19. E. Kolaczyk, "An application of wavelet shrinkage to tomagraphy," in Wavelets in Medicine and Biology, edited by A Aldroubi and M. Unser (CRC Press, New York, 1996)
20. F. R. Farrokh, K. J. R. Liu, and C. A. Berenstein, "Local tomography in fan-beam geometry using wavelets," IEEE International Conference on Image Processing 2, 709-712 (1996).
21. A. H. Delany and Y. Bresler, "Multiresolution tomographic reconstruction using wavelets," IEEE International Conference on Image Processing 1, 830-834 (1994).
22. T. Olson and J. DeStefano, "Wavelet localization of the Radon transform," IEEE Trans. Signal Process. 42, 2055-2067 (1994).
23. B. Sahiner and A. E. Yagle, "Limited angle tography using wavelets," IEEE Nuclear Science Symposium and Medical Imaging Conference 3, 1912-1916 (1994).
24. C. Kappeler and S. P. Mueller, "Wavelet compression of noisy tomographic images," SPIE 2569, 644-652 (1995).
25. R. Devore, B Lucier, and Z. Yank, "Feature extraction in digital mammography," in Wavelets in Medicine and Biology, edited by A. Aldroubi and M. Unser (CRC Press, New York, 1996).
26. D. Healy and J. Weaver, "Two applications of wavelet transforms in MR imaging," IEEE Trans. Inf. Theory 38, 840-860 (1992).
27. L. Auslander and I. Gertner, "Wide-band ambiguity function and a.x + b group," Ln Signal Processing. Part I: Signal Processing Theory, edited by L. Auslander, T. Kailath, and S. Mitter (Springer-Verlag, New York, 1990).
28. W. Schempp, "Wavelets in high-resolution radar imaging and clinical magnetic Resonance tomography," Cybernetics and Systems 28, 1-23 (1997).
29. G Battle and P. Federbush, "Ondelettes and phase cell cluster expansions: a vindication," Commun. Math Phys. 110, 601-615 (1987).
30. C. Heneghan, S. B. Lowen, and M. C. Teich, "Two-dimensional fractional Browman Motion: Wavelet analysis and synthesis," Proceedings of the IEEE Southwest Symposium On Image Analysis and Interpretation, pp. 213-217 (1996).