Convolution backprojection formulas for 3-D vector tomography with application to MRI

IEEE Transactions on Image Processing

Volumn 5, Issue 10, 1996, Pages 1462-1472

  Prince, Jerry L ^a,b  

^a IEEE

^b Johns Hopkins University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC IMAGING; COMPUTER SIMULATION; COMPUTERIZED TOMOGRAPHY; IMAGE RECONSTRUCTION; PHASE SHIFT; POLARIZATION; THEOREM PROVING; THREE DIMENSIONAL;

ACOUSTIC FLOW; CONVOLUTION BACKPROJECTION; MAGNETIC RESONANCE SCANNER; PROBE TRANSFORM; TIME OF FLIGHT MEASUREMENT; VECTOR TOMOGRAPHY;

MAGNETIC RESONANCE IMAGING;

EID: 0030269648     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/83.536894     Document Type: Article

References (25)

1. S. A. Johnson, J. F. Greenleaf, M. Tanaka, and G. Flandro, "Reconstructing three-dimensional fluid velocity vector fields from acoustic transmission measurements," in Acoustical Holography, vol. 7, L. Kessler, Ed. New York: Plenum, 1977, pp. 307-326.
2. S. Takuso et al., "Introduction of mass conservations law to improve the tomographic estimation of flow velocity distribution from differential time-of-flight data," J. Acoust. Soc. Amer., vol. 77, no. 6, pp. 2104-2106, 1985.
3. G. Paris et al., "Three-dimensional beam-deflection optical tomography of a supersonic jet," Appl. Opt., vol. 27, no. 24, pp. 5202-5212, 1988.
4. W. Munk and C. Wunsch, "Ocean acoustic tomography: a scheme for large-scale monitoring," Deep-Sea Research, vol. 26A, pp. 123-161, 1979.
5. B. M. Howe, P. F. Worchester, and W. Munk, "Ocean acoustic tomography: Mesoscale velocity," J. Geophys. Research, vol. 92, pp. 3785-3805, 1987.
6. S. J. Norton, "Tomographic reconstruction of 2-D vector fields: application for flow imaging," Geophys. J., vol. 97, pp. 161-168, 1988.
7. H. Braun and A. Hauck, "Tomographic reconstruction of vector fields," IEEE Trans. Signal Processing, vol. 39, no. 2, pp. 464-471, 1991.
8. D. Rouseff and K. B. Winters, "Two-dimensional vector flow inversion by diffraction tomography," Inverse Problems, vol. 10, pp. 687-697, 1994.
9. S. J. Norton, "Unique tomographic reconstruction of vector fields using boundary data," IEEE Trans. Image Processing, vol. 1, no. 3, pp. 406-412, July 1992.
10. P. Juhlin, "Principles of doppler tomography," Lund Inst. Technol., Dept. Math., Lund, Sweden, Tech. Rep. LUTFD2/(TFMA-92)/7002+17P, Aug. 1992.
11. J. L. Prince, "A 3-D projection theorem for vector tomography with application to MRI," in Proc. 8th Workshop Image Multidimen. Signal Processing, 1993, pp. 100-101.
12. M. Zahn, "Transform relationship between Kerr-effect optical phase shift and nonuniform electric field distributions," IEEE Trans. Dielectr. Electr. Insulat., vol. 1, no. 2, pp. 235-246, 1994.
13. V. A. Sharafutdinov, Integral Geometry of Tensor Fields. VSP: 1994.
14. J. L. Prince, "Tomographic reconstruction of 3-D vector fields using inner product probes," IEEE Trans. Image Processing, vol. 3, no. 2, pp. 216-219, Mar. 1994.
15. L. Desbat and A. Wernsdorfer, "Direct algebraic reconstruction and optimal sampling in vector field tomography," IEEE Trans. Signal Processing, vol. 43, no. 8, pp. 1798-1808, Aug. 1995.
16. S. R. Deans, The Radon Transform and Some of Its Applications. New York: Wiley, 1983.
17. P. M. Morse and H. Feshbach, Methods of Theoretical Physics. New York: McGraw-Hill, 1953.
18. K. B. Winters and D. Rouseff, "A filtered backprojection method for the tomographic reconstruction of fluid vorticity," Inverse Problems, vol. 6, pp. L33-L38, 1990.
19. H. Barrett, "The Radon transform and its applications," in Progress in Optics XXI. E. Wolf, Ed. New York: Elsevier, 1984, pp. 217-286.
20. F. Natterer, The Mathematics of Computerized Tomography. New York: Wiley, 1986.
21. L. A. Shepp, "Computerized tomography and nuclear magnetic resonance," J. Comput. Assist. Tomog., vol. 4, no. 1, pp. 94-107, 1980.
22. N. J. Pelc, R. J. Herfkens, A. Shimakawa, and D. R. Enzmann, "Phase contrast cine magnetic resonance imaging," Magn. Resonance Quar., vol. 7, no. 4, pp. 229-254, 1991.
23. S. Ljunggren, "A simple graphical representation of Fourier-based imaging methods," J. Magn. Resonance, vol. 54, pp. 338-343, 1983.
24. P. R. Moran, "A flow velocity zeugmatographic interlace for NMR imaging in humans," Magn. Resonance Imaging, vol. 1, pp. 197-201, 1982.
25. P. Sprawls and M. J. Bronskill, Eds, in Proc. Physics MRI '92 AAPM Summer Sch.., Amer. Assoc. Physicists in Med., Amer. Inst. Physics, 1993.