Abstract

A system for reconstruction of computed tomography (CT) images in a video frame time (1/30 sec) is described. The system implements the filtered backprojection algorithm using an electrooptic filtering technique, an optical backprojection, and a video detector. When coupled to a real-time system for acquiring projection data, the combined system realizes what we term CT videography.

© 1985 Optical Society of America

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References

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  1. D. P. Boyd, M. J. Lipton, “Cardiac Computed Tomography,” Proc. IEEE 71, 298 (1983).
    [CrossRef]
  2. H. H. Barrett, W. Swindell, “Analog Reconstruction Methods for Transaxial Tomography,” Proc. IEEE 65, 89 (1977).
    [CrossRef]
  3. A. F. Gmitro, J. E. Grievenkamp, W. Swindell, H. H. Barrett, M. Y. Chiu, S. K. Gordon, “Optical Computers for Reconstructing Objects from Their X-Ray Projections,” Opt. Eng. 19, 260 (1980).
    [CrossRef]
  4. H. H. Barrett, “Optical Processing in Radon Space,” Opt. Lett. 7, 248 (1982).
    [CrossRef] [PubMed]
  5. A. F. Gmitro, G. R. Gindi, H. H. Barrett, R. L. Easton, “Two-Dimensional Image Processing by One-Dimensional Filtering of Projection Data,” Proc. Soc. Photo. Opt. Instrum. Eng. 388, 132 (1983).
  6. W. T. Rhodes, “Acousto-Optic Signal Processing: Convolution and Correlation,” Proc. IEEE 69, 65 (1981).
    [CrossRef]
  7. N. J. Berg, J. N. Lee, Acoust-Optic Signal Processing: Theory and Practice (Marcel Dekkar, New York, 1983).
  8. H. H. Barrett, W. Swindell, Radiological Imaging, Vols. 1, 2 (Academic, New York, 1981).
  9. D. L. Hecht, “Multifrequency Acousto-optic Diffraction,” IEEE Trans. Sonics Ultrason. SU-24, 7 (1977).
    [CrossRef]
  10. R. L. Easton, A. J. Ticknor, H. H. Barrett, “Two-Dimensional Complex Fourier Transform Via the Radon Transform,” Appl. Opt. 24, 3817 (1985).
    [CrossRef] [PubMed]

1985

1983

A. F. Gmitro, G. R. Gindi, H. H. Barrett, R. L. Easton, “Two-Dimensional Image Processing by One-Dimensional Filtering of Projection Data,” Proc. Soc. Photo. Opt. Instrum. Eng. 388, 132 (1983).

D. P. Boyd, M. J. Lipton, “Cardiac Computed Tomography,” Proc. IEEE 71, 298 (1983).
[CrossRef]

1982

1981

W. T. Rhodes, “Acousto-Optic Signal Processing: Convolution and Correlation,” Proc. IEEE 69, 65 (1981).
[CrossRef]

1980

A. F. Gmitro, J. E. Grievenkamp, W. Swindell, H. H. Barrett, M. Y. Chiu, S. K. Gordon, “Optical Computers for Reconstructing Objects from Their X-Ray Projections,” Opt. Eng. 19, 260 (1980).
[CrossRef]

1977

H. H. Barrett, W. Swindell, “Analog Reconstruction Methods for Transaxial Tomography,” Proc. IEEE 65, 89 (1977).
[CrossRef]

D. L. Hecht, “Multifrequency Acousto-optic Diffraction,” IEEE Trans. Sonics Ultrason. SU-24, 7 (1977).
[CrossRef]

Barrett, H. H.

R. L. Easton, A. J. Ticknor, H. H. Barrett, “Two-Dimensional Complex Fourier Transform Via the Radon Transform,” Appl. Opt. 24, 3817 (1985).
[CrossRef] [PubMed]

A. F. Gmitro, G. R. Gindi, H. H. Barrett, R. L. Easton, “Two-Dimensional Image Processing by One-Dimensional Filtering of Projection Data,” Proc. Soc. Photo. Opt. Instrum. Eng. 388, 132 (1983).

H. H. Barrett, “Optical Processing in Radon Space,” Opt. Lett. 7, 248 (1982).
[CrossRef] [PubMed]

A. F. Gmitro, J. E. Grievenkamp, W. Swindell, H. H. Barrett, M. Y. Chiu, S. K. Gordon, “Optical Computers for Reconstructing Objects from Their X-Ray Projections,” Opt. Eng. 19, 260 (1980).
[CrossRef]

H. H. Barrett, W. Swindell, “Analog Reconstruction Methods for Transaxial Tomography,” Proc. IEEE 65, 89 (1977).
[CrossRef]

H. H. Barrett, W. Swindell, Radiological Imaging, Vols. 1, 2 (Academic, New York, 1981).

Berg, N. J.

N. J. Berg, J. N. Lee, Acoust-Optic Signal Processing: Theory and Practice (Marcel Dekkar, New York, 1983).

Boyd, D. P.

D. P. Boyd, M. J. Lipton, “Cardiac Computed Tomography,” Proc. IEEE 71, 298 (1983).
[CrossRef]

Chiu, M. Y.

A. F. Gmitro, J. E. Grievenkamp, W. Swindell, H. H. Barrett, M. Y. Chiu, S. K. Gordon, “Optical Computers for Reconstructing Objects from Their X-Ray Projections,” Opt. Eng. 19, 260 (1980).
[CrossRef]

Easton, R. L.

R. L. Easton, A. J. Ticknor, H. H. Barrett, “Two-Dimensional Complex Fourier Transform Via the Radon Transform,” Appl. Opt. 24, 3817 (1985).
[CrossRef] [PubMed]

A. F. Gmitro, G. R. Gindi, H. H. Barrett, R. L. Easton, “Two-Dimensional Image Processing by One-Dimensional Filtering of Projection Data,” Proc. Soc. Photo. Opt. Instrum. Eng. 388, 132 (1983).

Gindi, G. R.

A. F. Gmitro, G. R. Gindi, H. H. Barrett, R. L. Easton, “Two-Dimensional Image Processing by One-Dimensional Filtering of Projection Data,” Proc. Soc. Photo. Opt. Instrum. Eng. 388, 132 (1983).

Gmitro, A. F.

A. F. Gmitro, G. R. Gindi, H. H. Barrett, R. L. Easton, “Two-Dimensional Image Processing by One-Dimensional Filtering of Projection Data,” Proc. Soc. Photo. Opt. Instrum. Eng. 388, 132 (1983).

A. F. Gmitro, J. E. Grievenkamp, W. Swindell, H. H. Barrett, M. Y. Chiu, S. K. Gordon, “Optical Computers for Reconstructing Objects from Their X-Ray Projections,” Opt. Eng. 19, 260 (1980).
[CrossRef]

Gordon, S. K.

A. F. Gmitro, J. E. Grievenkamp, W. Swindell, H. H. Barrett, M. Y. Chiu, S. K. Gordon, “Optical Computers for Reconstructing Objects from Their X-Ray Projections,” Opt. Eng. 19, 260 (1980).
[CrossRef]

Grievenkamp, J. E.

A. F. Gmitro, J. E. Grievenkamp, W. Swindell, H. H. Barrett, M. Y. Chiu, S. K. Gordon, “Optical Computers for Reconstructing Objects from Their X-Ray Projections,” Opt. Eng. 19, 260 (1980).
[CrossRef]

Hecht, D. L.

D. L. Hecht, “Multifrequency Acousto-optic Diffraction,” IEEE Trans. Sonics Ultrason. SU-24, 7 (1977).
[CrossRef]

Lee, J. N.

N. J. Berg, J. N. Lee, Acoust-Optic Signal Processing: Theory and Practice (Marcel Dekkar, New York, 1983).

Lipton, M. J.

D. P. Boyd, M. J. Lipton, “Cardiac Computed Tomography,” Proc. IEEE 71, 298 (1983).
[CrossRef]

Rhodes, W. T.

W. T. Rhodes, “Acousto-Optic Signal Processing: Convolution and Correlation,” Proc. IEEE 69, 65 (1981).
[CrossRef]

Swindell, W.

A. F. Gmitro, J. E. Grievenkamp, W. Swindell, H. H. Barrett, M. Y. Chiu, S. K. Gordon, “Optical Computers for Reconstructing Objects from Their X-Ray Projections,” Opt. Eng. 19, 260 (1980).
[CrossRef]

H. H. Barrett, W. Swindell, “Analog Reconstruction Methods for Transaxial Tomography,” Proc. IEEE 65, 89 (1977).
[CrossRef]

H. H. Barrett, W. Swindell, Radiological Imaging, Vols. 1, 2 (Academic, New York, 1981).

Ticknor, A. J.

Appl. Opt.

IEEE Trans. Sonics Ultrason.

D. L. Hecht, “Multifrequency Acousto-optic Diffraction,” IEEE Trans. Sonics Ultrason. SU-24, 7 (1977).
[CrossRef]

Opt. Eng.

A. F. Gmitro, J. E. Grievenkamp, W. Swindell, H. H. Barrett, M. Y. Chiu, S. K. Gordon, “Optical Computers for Reconstructing Objects from Their X-Ray Projections,” Opt. Eng. 19, 260 (1980).
[CrossRef]

Opt. Lett.

Proc. IEEE

D. P. Boyd, M. J. Lipton, “Cardiac Computed Tomography,” Proc. IEEE 71, 298 (1983).
[CrossRef]

H. H. Barrett, W. Swindell, “Analog Reconstruction Methods for Transaxial Tomography,” Proc. IEEE 65, 89 (1977).
[CrossRef]

W. T. Rhodes, “Acousto-Optic Signal Processing: Convolution and Correlation,” Proc. IEEE 69, 65 (1981).
[CrossRef]

Proc. Soc. Photo. Opt. Instrum. Eng.

A. F. Gmitro, G. R. Gindi, H. H. Barrett, R. L. Easton, “Two-Dimensional Image Processing by One-Dimensional Filtering of Projection Data,” Proc. Soc. Photo. Opt. Instrum. Eng. 388, 132 (1983).

Other

N. J. Berg, J. N. Lee, Acoust-Optic Signal Processing: Theory and Practice (Marcel Dekkar, New York, 1983).

H. H. Barrett, W. Swindell, Radiological Imaging, Vols. 1, 2 (Academic, New York, 1981).

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Figures (6)

Fig. 1
Fig. 1

Geometry of the projection operation.

Fig. 2
Fig. 2

Convolution of projection data with processing kernel h(x′) to obtain a filtered projection.

Fig. 3
Fig. 3

Backprojection of filtered data back into the image coordinates.

Fig. 4
Fig. 4

Electrooptical convolver using an acoustooptic cell.

Fig. 5
Fig. 5

Binary transmission mask used to encode the function h.

Fig. 6
Fig. 6

Block diagram to the overall system for real-time CT reconstruction.

Equations (10)

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λ ( x , ϕ ) = f ( r ) δ ( x r · n ˆ ) d 2 r ,
f ( r ) = 1 2 π 2 0 π d ϕ [ λ ϕ ( x ) * h ( x ) ] x = r · n ˆ .
h ( x ) = d d x [ P ( 1 x ) ] ,
V ( t ) = C λ ϕ ( t ) cos ( 2 π ν 0 t ) ,
Δ n ( x , t ) = C λ ϕ ( t x υ ) cos [ 2 π ν 0 ( t x υ ) ] ,
T ( x , t ) = C { 1 + i 2 λ ϕ ( t x υ ) exp [ i 2 π ν 0 ( t x υ ) ] + i 2 λ ϕ ( t x υ ) exp [ i 2 π ν 0 ( t x υ ) ] } .
U ( x , t ) = C { 1 + i 2 λ ϕ ( t x υ ) exp [ i 2 π ν 0 ( t x υ ) ] } .
T m ( x ) = C [ 1 + h ( x υ ) cos ( 2 π ν 0 x υ ) ] = C [ 1 + 1 2 h ( x υ ) exp ( i 2 π ν 0 x υ ) + 1 2 h ( x υ ) exp ( i 2 π ν 0 x υ ) ,
U 1 ( x , t ) = C [ i λ ϕ ( t x υ ) exp [ i 2 π ν 0 ( t x υ ) ] + h ( x u ) exp ( i 2 π ν 0 x υ ) ]
S ( t ) = C | U 1 | 2 d x = C | λ ϕ ( t x υ ) | 2 d x + C | h ( x υ ) | 2 d x + 2 C sin ( 2 π ν 0 t ) λ ϕ ( t x υ ) h ( x υ ) d x ,

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