Two Applications of Wavelet Transforms in Magnetic Resonance Imaging

IEEE Transactions on Information Theory

Volumn 38, Issue 2, 1992, Pages 840-860

  Healy, Dennis M ^a   Weaver, John B ^a  

^a DARTMOUTH COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

IMAGE PROCESSING - IMAGE CODING; MATHEMATICAL TECHNIQUES - PHASE SPACE METHODS; MATHEMATICAL TRANSFORMATIONS; RELAXATION PROCESSES;

COMBINATORIAL SCHEDULING; IMAGE ACQUISITION; INSTANT IMAGING; NUCLEAR MAGNETIC SPIN; TIME-FREQUENCY TRANSFORMS; WAVELET ENCODING;

MAGNETIC RESONANCE IMAGING;

EID: 0026759942     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.119740     Document Type: Article

References (52)

1. D. J. Atkinson and R. R. Edelman, “Ultrafast MR imaging of the heart,” Radio., vol. 169, no. 37, 1988.
2. W. P. Aue, S. Miller, T. A. Cross, and X. Seelig, “Volume selective excitation: A novel approach to topical NMR,” J. Mag. Res., vol. 56, pp,350–354. 1984.
3. F. Bloch, “Nuclear induction,” Phys. Rev., vol. 70, p. 460, 1946.
4. R. A. Brooks, G. DiChiro, and M. R. Keller, “Explanation of cerebral white-gray contrast in computed tomography,” J. Comput. Assist. Tomog., vol. 4, pp. 489–491, 1980.
5. C-N Chen and D. I. Hoult, Biomedical Magnetic Resonance Technology, New York: Hilger, 1989.
6. Z. H. Cho, O. Nacioglu, and H. W. Park, “Methods and algorithms for Fourier-transform nuclear magnetic resonance tomography,” J. Opt. Soc. Amer., vol, 4, 1987.
7. I. Daubechies, “The wavelet transform, time-frequency localization, and signal analysis, IEEE Trans Inform. Theory, vol. 36, no. 5, pp. 961–1005, 1990.
8. I. Daubechies, “Orthonormal bases of compactly supported supported wavelets,” Comm. Pure Appl. Math., vol. 41, pp. 909–996, 1988.
9. I. Daubechies, A. Grossmann, and Y. Meyer, “Painless non-orthogonal expansions,” J. Math. Phys., vol. 27, 1271–1283, 1986.
10. J. Driscoll, D. M. Healy, and G. Isaak, “Scheduling dyadic intervals,” Dartmouth College 1991.
11. R. T. Droege, S. N. Wiencer, M. S. Rzeszotarski, G. N. Holland, and I. R. Young, “Nuclear magnetic resonance: A gray scale model for head images,” Radiol., vol. 148, pp. 763–771, 1983.
12. W. T. Dixon, L. N. Du, D. D. Faul, M. Gado, and S. Rossnick, “Projection angiograms of blood labeled by adiabatic fast passage,” Magnet. Res. Med., vol. 3, pp. 454–462, 1986.
13. R. R. Edelman et al., “Intercerebral arteriovenous malformations: Evaluation with selective MR angiography and venography,” Radio., vol. 173, pp. 831–837, 1989.
14. W. A. Edelstein, J. M. S. Hutchinson, G. Johnson, and T. Redpath, “Spin warp NMR imaging and applications to human whole-body imaging,” Phys. Med. Biol., vol. 25, pp. 751–756, 1980.
15. R. R. Ernst, “Methodology of magnetic resonance imaging,” Quart. Rev. Biophys., vol. 19, pp. 183–220, 1987.
16. F. Farzameh, S. J. Riederer, and N. J. Pelc, “Analysis of T2 limitations and off-resonance effects on spatial resolution and artifacts in echo-planar imaging,” Magnet. Res. Med., vol. 14, p. 125, 1990.
17. J. M. Fulmer and S. E. Harms, “The temporomandibular joint,” Magnet. Res. Imag., vol. 1, pp. 75–84, 1989.
18. D. Gabor, “Theory of communication,” J. Inst. Electr. Eng., vol. 93, pp. 429–457, 1946.
19. A. Grossmann and J. Morlet, “Decomposition of Hardy functions into square integrable wavelets of constant shape,” SIAM J. Math. Anal., vol. 15, pp. 723–736, 1984.
20. F. A. Grunbaum, “Soliton mathematics in signal processing,” in Signal Processing. New York: Springer-Verlag, 1990.
21. A. Haase et al., “FLASH imaging: Rapid NMR imaging using low flip angle pulses,” J. Magnet. Res., vol. 67, 258–266, 1986.
22. D. Healy and J. B. Weaver, “Wavelet transforms for MR imaging,” submitted for publication.
23. C. B. Higgins, W. Holt, P. Pflugfelder, and V. Sechtem, “Functional evaluation of the heart with magnetic resonance imaging,” Magnet. Res. Med., vol. 6, pp. 121–139, 1988.
24. M. Holschneider, “Inverse radon transforms through inverse wavelet transforms,” submitted for publication.
25. D. I. Hoult and P. C. Lauterbur, “The sensitivity of the Zeugmatographic experiment involving human samples,” J. Magnet. Res., vol. 34, pp. 425–433, 1979.
26. P. M. Joseph, L. Axel, and D. O’Donnell, “Potential problems with selective pulses in NMR imaging systems,” Med. Phys., vol. 11, pp. 772–777, 1984.
27. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging. New York: IEEE Press, 1988.
28. K. F. King and P. R. Moran, “A unified description of NMR imaging, data-collection strategies, and reconstruction,” Med. Phys., vol. 11, 1984.
29. A. Kumar, D. Welt, and R. R. Ernst, “NMR Fourier Zeugmatography,” J. Magnet. Res., vol. 18, pp. 69–83, 1975.
30. P. C. Lauterbur, “Image formation by induced local interactions: Examples employing nuclear magnetic resonance,” Nature, vol. 242, p. 190, 1973.
31. D. LeBihan, J. Delannoy, and R. L. Levin, “Temperature mapping with MR imaging of molecular diffusion: Application to hyperthermia,” Radiol., vol. 171. pp. 853–858, 1989.
32. J. M. Liberman et al., “Gated magnetic resonance imaging of the normal and diseased heart,” Radiol., vol. 152, pp. 465–470, 1984.
33. A. Macovski, “Selection projection imaging: Applications to radiology and NMR,” IEEE Trans. Med. Imaging, vol. 1, pp. 42–47, 1982.
34. A. Macovski, “Volumetric NMR imaging with time-varying gradients,” Magnet. Res. Med., vol. 2, pp. 29–40, 1985.
35. S. Mallat, “A theory for multiresolution signal decomposition: The wavelet representation,” IEEE Trans. Pattern Anal. Machine Intell., vol. 31, pp. 674–693, 1989.
36. S. Mallat, “Multiresolution approximation and wavelets,” Trans. AMS, vol. 135, pp. 69–88, 1989.
37. P. Mansfield, “Multi-planar image formation using NMR Spin echoes,” J. Phys. C: Solid State Phys., vol. 10, pp. L550-L58, 1977.
38. P. Mansfield, A. A. Maudsley, and T. Baines, “Fast scan proton density by NMR,” J. Phys., vol. E9, pp. 271–278, 1976.
39. P. Mansfield and P. G. Morris, NMR Imaging in Biomedicine. New York: Academic, 1982.
40. P. Mansfield and I. L. Pykett, “Biological and medical imaging by NMR,” J. Mag. Res., vol. 29, pp. 355–373, 1978.
41. Y. Meyer, “Principe d'incertitude, bases hilbertiennes, et algebres d'operateurs,” Seminaire Bourbaki, vol. 662, pp. 1985–1986.
42. P. R. Moran, “A flow velocity zeugmatographic interlace for NMR imaging in humans,” Mag. Res. Imaging, vol. 1, pp. 197–202, 1982.
43. 2weighted MRI and spectroscopy,” Mag. Res. Med., vol. 14, pp. 330–346, 1990.
44. I. L. Pykett and R. R. Rzedzian, “Instant imaging of the body by magnetic resonance,” Mag. Res. Med., vol. 5, pp. 563–571, 1987.
45. R. R. Rzedzian and I. L. Pykett, “Instant images of the human heart using new, whole-body MR imaging systems,” Amer. J. Roentgenology, vol. 149, pp. 245–250, 1987.
46. F. G. Shellock, J. H. Mink, and J. M. Fox, “Patellofemoral joint: Kinematic MR imaging to assess tracking abnormalities,” Radiol., vol. 168, pp. 551–553, 1988.
47. D. Slepian, “On bandwidth,” Proc. IEEE, vol. 64, pp. 292–300, 1976.
48. C. P. Slichter, Principles of Magnetic Resonance. New York: Springer-Verlag, 1980, p. 34.
49. D. D. Stark et al., “Forty-millisecond MR imaging of the abdomen at 2.0T,” Radiol., vol. 173, pp. 111–116, 1989.
50. M. K. Stehling et al., “Whole-body echo-planar MR imaging at 0.5T,” Radiol., vol. 170, pp. 257–263, 1989.
51. E. O. Stejskal and J. E. Tanner, “Spin diffusion measurements: Spin-echoes in the presence of a time-dependent field gradient,” J. Chem. Phys., vol. 42, pp. 288–292, 1965.
52. J. B. Weaver, Y. Xu, D. M. Healy, Jr., and J. Driscoll, “Wavelet encoded MR imaging,” accepted for publication in Mag. Res. Med.