Abstract

In many applications of computed tomography, we cannot acquire the projection data at all angles evenly spaced over 360°. In such cases, the computed tomography images reconstructed using a limited number of projections, measured over a narrow angle range, are characterized by approximately elliptical distortion along the view angles used and poor contrast at angles not used (anisotropic resolution). This systematic geometric distortion is caused by the 2-D point spread function of the reconstruction process. In this paper, we show that such geometric distortion and other artifacts introduced in the reconstruction process can be reduced substantially by deconvolution performed via Wiener filtering using a priori knowledge derived from the given projections. The 2-D system transfer function used in the deconvolution is obtained from the reconstruction of a test image by the same reconstruction algorithm which has been used for reconstructing the unknown object.

© 1985 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. P. Medoff, W. R. Brody, M. Nassi, A. Macovski, “Iterative Convolution Backprojection Algorithms for Image Reconstruction from Limited Data,” J. Opt. Soc. Am. 73, 1493 (1983).
    [CrossRef]
  2. M. Nassi, W. R. Brody, B. P. Medoff, A. Macovski, “Iterative Reconstruction-Reprojection: An Algorithm for Limited Data Cardiac Computed Tomography,” IEEE Trans. Biomed. Eng. BME-29, 333 (1982).
    [CrossRef]
  3. T. Sato, S. J. Norton, M. Linzer, O. Ikeda, M. Hirama, “Tomographic Image Reconstruction from Limited Projections Using Interactive Revision in Image and Transform Spaces,” Appl. Opt. 20, 395 (1981).
    [CrossRef] [PubMed]
  4. P. B. Heffernan, R. A. Robb, “Image Reconstruction from Incomplete Projection Data: Iterative Reconstruction-Projection Technique,” IEEE Trans. Biomed. Eng. BME-30, 838 (1983).
    [CrossRef]
  5. T. J. Hall, A. M. Darling, M. A. Fiddy, “Image Reconstruction and Restoration Incorporating Prior Knowledge,” Opt. Lett. 7, 467 (1982).
    [CrossRef] [PubMed]
  6. T. Inouye, “Image Reconstruction with Limited Angle Projection Data,” IEEE Trans. Nucl. Sci. NS-26, 2666 (1979).
  7. R. W. Gerchberg, “Super-resolution Through Error Energy Reduction,” Opt. Acta 21, 709 (1974).
    [CrossRef]
  8. A. Papoulis, “A New Algorithm in Spectral Analysis and Band-Limited Extrapolation,” IEEE Trans. Circuits Syst. CAS-22, 735 (1975).
    [CrossRef]
  9. K. C. Tam, V. Perez-Mendez, “Limited-angle Three Dimensional Reconstruction Using Fourier Transform Iterations and Radon Transform Iterations,” Opt. Eng. 20, 586 (1981).
    [CrossRef]
  10. K. C. Tam, V. Perez-Mendez, “Tomographic Imaging with Limited-Angle Input,” J. Opt. Soc. Am. 71, 582 (1981).
    [CrossRef]
  11. A. Peres, “Tomographic Reconstruction from Limited Angular Data,” J. Comput. Assist. Tomogr. 3, 800 (1979).
    [PubMed]
  12. T. Sato, S. J. Norton, M. Linzer, O. Ikeda, M. Hirama, “Tomographic Image Reconstruction from Limited Projections Using Iterative Revisions in Image and Transform Spaces,” Appl. Opt. 20, 395 (1981).
    [CrossRef] [PubMed]
  13. C. Byrne, R. Fitzgerald, “Reconstruction from Partial Information with Application to Tomography,” SIAM J. Appl. Math. 42, 933 (1982).
    [CrossRef]
  14. G. Minerbo, “MENT: A Maximum Entropy Algorithm for Reconstructing a Source from Projection Data,” Comput. Graphics Image Process. 10, 48 (1979).
    [CrossRef]
  15. M. C. Kemp, “Maximum Entropy Reconstruction in Emission Tomography,” Med. Radionuclide Imaging 1, 313 (1980).
  16. S. F. Burch, S. F. Gull, J. Skilling, “Image Restoration by a Powerful Maximum Entropy Method,” Comput. Vision Graphics Image Process. 23, 113 (1983).
    [CrossRef]
  17. S. F. Gull, G. J. Daniell, “Image Reconstruction from Incomplete and Noisy Data,” Nature London 272, 686 (1978).
    [CrossRef]
  18. K. M. Hanson, G. W. Wecksung, “Bayesian Approach to Limited-Angle Reconstruction in Computed Tomography,” J. Opt. Soc. Am. 73, 1501 (1983).
    [CrossRef]
  19. R. M. Rangayyan, A. P. Dhawan, R. Gordon, “Algorithms for Limited-View Computed Tomography: An Annotated Bibliography and A Challenge,” Appl. Opt. 24, 4022 (1985).
    [CrossRef]
  20. R. Gordon, R. M. Rangayyan, “Geometric Deconvolution: A Meta-Algorithm for Limited View Computed Tomography,” IEEE Trans. Biomed. Eng. BME-30, 806 (1983).
    [CrossRef]
  21. R. Gordon, “Artifacts in Reconstructions Made from a Few Projections,” in Proceedings, First International Joint Conference on Pattern Recognition, 30 Oct.–1 Nov., Washington, D.C. (IEEE Computer Society, Northridge, Calif., 1973), pp. 275–285.
  22. R. Gordon, “A Proposal for Deconvolution of Reconstructions,” Workshop on Information Treatment in Electron Microscopy, Basel (1972), 2 pp.
  23. A. Klug, R. A. Crowther, “Three-Dimensional Image Reconstruction from the Viewpoint of Information Theory,” Nature London 238, 435 (1972).
    [CrossRef]
  24. M. A. King, R. B. Schwinger, P. W. Doherty, “Fast Wiener Digital Post-Processing of SPECT Images,” J. Nucl. Med. 24, 81 (1983).
  25. R. Gordon, “A Tutorial on ART (Algebraic Reconstruction Techniques),” IEEE Trans. Nucl. Sci. NS-21, 78, 95 (1974).
  26. R. Gordon, G. T. Herman, “Three Dimensional Reconstruction from Projections: A Review of Algorithms, Int. Rev. Cytol. 38, 111 (1974).
    [CrossRef] [PubMed]
  27. H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).
  28. R. C. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, Reading, Mass., 1977).
  29. P. H. Lutz, “Fourier Image Reconstruction Incorporating Three Simple Interpolation Techniques,” Department of Computer Science Technical Report 104, State University of New York at Buffalo (1975).

1985 (1)

R. M. Rangayyan, A. P. Dhawan, R. Gordon, “Algorithms for Limited-View Computed Tomography: An Annotated Bibliography and A Challenge,” Appl. Opt. 24, 4022 (1985).
[CrossRef]

1983 (6)

R. Gordon, R. M. Rangayyan, “Geometric Deconvolution: A Meta-Algorithm for Limited View Computed Tomography,” IEEE Trans. Biomed. Eng. BME-30, 806 (1983).
[CrossRef]

M. A. King, R. B. Schwinger, P. W. Doherty, “Fast Wiener Digital Post-Processing of SPECT Images,” J. Nucl. Med. 24, 81 (1983).

P. B. Heffernan, R. A. Robb, “Image Reconstruction from Incomplete Projection Data: Iterative Reconstruction-Projection Technique,” IEEE Trans. Biomed. Eng. BME-30, 838 (1983).
[CrossRef]

B. P. Medoff, W. R. Brody, M. Nassi, A. Macovski, “Iterative Convolution Backprojection Algorithms for Image Reconstruction from Limited Data,” J. Opt. Soc. Am. 73, 1493 (1983).
[CrossRef]

S. F. Burch, S. F. Gull, J. Skilling, “Image Restoration by a Powerful Maximum Entropy Method,” Comput. Vision Graphics Image Process. 23, 113 (1983).
[CrossRef]

K. M. Hanson, G. W. Wecksung, “Bayesian Approach to Limited-Angle Reconstruction in Computed Tomography,” J. Opt. Soc. Am. 73, 1501 (1983).
[CrossRef]

1982 (3)

C. Byrne, R. Fitzgerald, “Reconstruction from Partial Information with Application to Tomography,” SIAM J. Appl. Math. 42, 933 (1982).
[CrossRef]

M. Nassi, W. R. Brody, B. P. Medoff, A. Macovski, “Iterative Reconstruction-Reprojection: An Algorithm for Limited Data Cardiac Computed Tomography,” IEEE Trans. Biomed. Eng. BME-29, 333 (1982).
[CrossRef]

T. J. Hall, A. M. Darling, M. A. Fiddy, “Image Reconstruction and Restoration Incorporating Prior Knowledge,” Opt. Lett. 7, 467 (1982).
[CrossRef] [PubMed]

1981 (4)

1980 (1)

M. C. Kemp, “Maximum Entropy Reconstruction in Emission Tomography,” Med. Radionuclide Imaging 1, 313 (1980).

1979 (3)

G. Minerbo, “MENT: A Maximum Entropy Algorithm for Reconstructing a Source from Projection Data,” Comput. Graphics Image Process. 10, 48 (1979).
[CrossRef]

A. Peres, “Tomographic Reconstruction from Limited Angular Data,” J. Comput. Assist. Tomogr. 3, 800 (1979).
[PubMed]

T. Inouye, “Image Reconstruction with Limited Angle Projection Data,” IEEE Trans. Nucl. Sci. NS-26, 2666 (1979).

1978 (1)

S. F. Gull, G. J. Daniell, “Image Reconstruction from Incomplete and Noisy Data,” Nature London 272, 686 (1978).
[CrossRef]

1975 (1)

A. Papoulis, “A New Algorithm in Spectral Analysis and Band-Limited Extrapolation,” IEEE Trans. Circuits Syst. CAS-22, 735 (1975).
[CrossRef]

1974 (3)

R. W. Gerchberg, “Super-resolution Through Error Energy Reduction,” Opt. Acta 21, 709 (1974).
[CrossRef]

R. Gordon, “A Tutorial on ART (Algebraic Reconstruction Techniques),” IEEE Trans. Nucl. Sci. NS-21, 78, 95 (1974).

R. Gordon, G. T. Herman, “Three Dimensional Reconstruction from Projections: A Review of Algorithms, Int. Rev. Cytol. 38, 111 (1974).
[CrossRef] [PubMed]

1972 (1)

A. Klug, R. A. Crowther, “Three-Dimensional Image Reconstruction from the Viewpoint of Information Theory,” Nature London 238, 435 (1972).
[CrossRef]

Andrews, H. C.

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).

Brody, W. R.

B. P. Medoff, W. R. Brody, M. Nassi, A. Macovski, “Iterative Convolution Backprojection Algorithms for Image Reconstruction from Limited Data,” J. Opt. Soc. Am. 73, 1493 (1983).
[CrossRef]

M. Nassi, W. R. Brody, B. P. Medoff, A. Macovski, “Iterative Reconstruction-Reprojection: An Algorithm for Limited Data Cardiac Computed Tomography,” IEEE Trans. Biomed. Eng. BME-29, 333 (1982).
[CrossRef]

Burch, S. F.

S. F. Burch, S. F. Gull, J. Skilling, “Image Restoration by a Powerful Maximum Entropy Method,” Comput. Vision Graphics Image Process. 23, 113 (1983).
[CrossRef]

Byrne, C.

C. Byrne, R. Fitzgerald, “Reconstruction from Partial Information with Application to Tomography,” SIAM J. Appl. Math. 42, 933 (1982).
[CrossRef]

Crowther, R. A.

A. Klug, R. A. Crowther, “Three-Dimensional Image Reconstruction from the Viewpoint of Information Theory,” Nature London 238, 435 (1972).
[CrossRef]

Daniell, G. J.

S. F. Gull, G. J. Daniell, “Image Reconstruction from Incomplete and Noisy Data,” Nature London 272, 686 (1978).
[CrossRef]

Darling, A. M.

Dhawan, A. P.

R. M. Rangayyan, A. P. Dhawan, R. Gordon, “Algorithms for Limited-View Computed Tomography: An Annotated Bibliography and A Challenge,” Appl. Opt. 24, 4022 (1985).
[CrossRef]

Doherty, P. W.

M. A. King, R. B. Schwinger, P. W. Doherty, “Fast Wiener Digital Post-Processing of SPECT Images,” J. Nucl. Med. 24, 81 (1983).

Fiddy, M. A.

Fitzgerald, R.

C. Byrne, R. Fitzgerald, “Reconstruction from Partial Information with Application to Tomography,” SIAM J. Appl. Math. 42, 933 (1982).
[CrossRef]

Gerchberg, R. W.

R. W. Gerchberg, “Super-resolution Through Error Energy Reduction,” Opt. Acta 21, 709 (1974).
[CrossRef]

Gonzalez, R. C.

R. C. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, Reading, Mass., 1977).

Gordon, R.

R. M. Rangayyan, A. P. Dhawan, R. Gordon, “Algorithms for Limited-View Computed Tomography: An Annotated Bibliography and A Challenge,” Appl. Opt. 24, 4022 (1985).
[CrossRef]

R. Gordon, R. M. Rangayyan, “Geometric Deconvolution: A Meta-Algorithm for Limited View Computed Tomography,” IEEE Trans. Biomed. Eng. BME-30, 806 (1983).
[CrossRef]

R. Gordon, “A Tutorial on ART (Algebraic Reconstruction Techniques),” IEEE Trans. Nucl. Sci. NS-21, 78, 95 (1974).

R. Gordon, G. T. Herman, “Three Dimensional Reconstruction from Projections: A Review of Algorithms, Int. Rev. Cytol. 38, 111 (1974).
[CrossRef] [PubMed]

R. Gordon, “Artifacts in Reconstructions Made from a Few Projections,” in Proceedings, First International Joint Conference on Pattern Recognition, 30 Oct.–1 Nov., Washington, D.C. (IEEE Computer Society, Northridge, Calif., 1973), pp. 275–285.

R. Gordon, “A Proposal for Deconvolution of Reconstructions,” Workshop on Information Treatment in Electron Microscopy, Basel (1972), 2 pp.

Gull, S. F.

S. F. Burch, S. F. Gull, J. Skilling, “Image Restoration by a Powerful Maximum Entropy Method,” Comput. Vision Graphics Image Process. 23, 113 (1983).
[CrossRef]

S. F. Gull, G. J. Daniell, “Image Reconstruction from Incomplete and Noisy Data,” Nature London 272, 686 (1978).
[CrossRef]

Hall, T. J.

Hanson, K. M.

Heffernan, P. B.

P. B. Heffernan, R. A. Robb, “Image Reconstruction from Incomplete Projection Data: Iterative Reconstruction-Projection Technique,” IEEE Trans. Biomed. Eng. BME-30, 838 (1983).
[CrossRef]

Herman, G. T.

R. Gordon, G. T. Herman, “Three Dimensional Reconstruction from Projections: A Review of Algorithms, Int. Rev. Cytol. 38, 111 (1974).
[CrossRef] [PubMed]

Hirama, M.

Hunt, B. R.

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).

Ikeda, O.

Inouye, T.

T. Inouye, “Image Reconstruction with Limited Angle Projection Data,” IEEE Trans. Nucl. Sci. NS-26, 2666 (1979).

Kemp, M. C.

M. C. Kemp, “Maximum Entropy Reconstruction in Emission Tomography,” Med. Radionuclide Imaging 1, 313 (1980).

King, M. A.

M. A. King, R. B. Schwinger, P. W. Doherty, “Fast Wiener Digital Post-Processing of SPECT Images,” J. Nucl. Med. 24, 81 (1983).

Klug, A.

A. Klug, R. A. Crowther, “Three-Dimensional Image Reconstruction from the Viewpoint of Information Theory,” Nature London 238, 435 (1972).
[CrossRef]

Linzer, M.

Lutz, P. H.

P. H. Lutz, “Fourier Image Reconstruction Incorporating Three Simple Interpolation Techniques,” Department of Computer Science Technical Report 104, State University of New York at Buffalo (1975).

Macovski, A.

B. P. Medoff, W. R. Brody, M. Nassi, A. Macovski, “Iterative Convolution Backprojection Algorithms for Image Reconstruction from Limited Data,” J. Opt. Soc. Am. 73, 1493 (1983).
[CrossRef]

M. Nassi, W. R. Brody, B. P. Medoff, A. Macovski, “Iterative Reconstruction-Reprojection: An Algorithm for Limited Data Cardiac Computed Tomography,” IEEE Trans. Biomed. Eng. BME-29, 333 (1982).
[CrossRef]

Medoff, B. P.

B. P. Medoff, W. R. Brody, M. Nassi, A. Macovski, “Iterative Convolution Backprojection Algorithms for Image Reconstruction from Limited Data,” J. Opt. Soc. Am. 73, 1493 (1983).
[CrossRef]

M. Nassi, W. R. Brody, B. P. Medoff, A. Macovski, “Iterative Reconstruction-Reprojection: An Algorithm for Limited Data Cardiac Computed Tomography,” IEEE Trans. Biomed. Eng. BME-29, 333 (1982).
[CrossRef]

Minerbo, G.

G. Minerbo, “MENT: A Maximum Entropy Algorithm for Reconstructing a Source from Projection Data,” Comput. Graphics Image Process. 10, 48 (1979).
[CrossRef]

Nassi, M.

B. P. Medoff, W. R. Brody, M. Nassi, A. Macovski, “Iterative Convolution Backprojection Algorithms for Image Reconstruction from Limited Data,” J. Opt. Soc. Am. 73, 1493 (1983).
[CrossRef]

M. Nassi, W. R. Brody, B. P. Medoff, A. Macovski, “Iterative Reconstruction-Reprojection: An Algorithm for Limited Data Cardiac Computed Tomography,” IEEE Trans. Biomed. Eng. BME-29, 333 (1982).
[CrossRef]

Norton, S. J.

Papoulis, A.

A. Papoulis, “A New Algorithm in Spectral Analysis and Band-Limited Extrapolation,” IEEE Trans. Circuits Syst. CAS-22, 735 (1975).
[CrossRef]

Peres, A.

A. Peres, “Tomographic Reconstruction from Limited Angular Data,” J. Comput. Assist. Tomogr. 3, 800 (1979).
[PubMed]

Perez-Mendez, V.

K. C. Tam, V. Perez-Mendez, “Limited-angle Three Dimensional Reconstruction Using Fourier Transform Iterations and Radon Transform Iterations,” Opt. Eng. 20, 586 (1981).
[CrossRef]

K. C. Tam, V. Perez-Mendez, “Tomographic Imaging with Limited-Angle Input,” J. Opt. Soc. Am. 71, 582 (1981).
[CrossRef]

Rangayyan, R. M.

R. M. Rangayyan, A. P. Dhawan, R. Gordon, “Algorithms for Limited-View Computed Tomography: An Annotated Bibliography and A Challenge,” Appl. Opt. 24, 4022 (1985).
[CrossRef]

R. Gordon, R. M. Rangayyan, “Geometric Deconvolution: A Meta-Algorithm for Limited View Computed Tomography,” IEEE Trans. Biomed. Eng. BME-30, 806 (1983).
[CrossRef]

Robb, R. A.

P. B. Heffernan, R. A. Robb, “Image Reconstruction from Incomplete Projection Data: Iterative Reconstruction-Projection Technique,” IEEE Trans. Biomed. Eng. BME-30, 838 (1983).
[CrossRef]

Sato, T.

Schwinger, R. B.

M. A. King, R. B. Schwinger, P. W. Doherty, “Fast Wiener Digital Post-Processing of SPECT Images,” J. Nucl. Med. 24, 81 (1983).

Skilling, J.

S. F. Burch, S. F. Gull, J. Skilling, “Image Restoration by a Powerful Maximum Entropy Method,” Comput. Vision Graphics Image Process. 23, 113 (1983).
[CrossRef]

Tam, K. C.

K. C. Tam, V. Perez-Mendez, “Limited-angle Three Dimensional Reconstruction Using Fourier Transform Iterations and Radon Transform Iterations,” Opt. Eng. 20, 586 (1981).
[CrossRef]

K. C. Tam, V. Perez-Mendez, “Tomographic Imaging with Limited-Angle Input,” J. Opt. Soc. Am. 71, 582 (1981).
[CrossRef]

Wecksung, G. W.

Wintz, P.

R. C. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, Reading, Mass., 1977).

Appl. Opt. (3)

Comput. Graphics Image Process. (1)

G. Minerbo, “MENT: A Maximum Entropy Algorithm for Reconstructing a Source from Projection Data,” Comput. Graphics Image Process. 10, 48 (1979).
[CrossRef]

Comput. Vision Graphics Image Process. (1)

S. F. Burch, S. F. Gull, J. Skilling, “Image Restoration by a Powerful Maximum Entropy Method,” Comput. Vision Graphics Image Process. 23, 113 (1983).
[CrossRef]

IEEE Trans. Biomed. Eng. (3)

P. B. Heffernan, R. A. Robb, “Image Reconstruction from Incomplete Projection Data: Iterative Reconstruction-Projection Technique,” IEEE Trans. Biomed. Eng. BME-30, 838 (1983).
[CrossRef]

M. Nassi, W. R. Brody, B. P. Medoff, A. Macovski, “Iterative Reconstruction-Reprojection: An Algorithm for Limited Data Cardiac Computed Tomography,” IEEE Trans. Biomed. Eng. BME-29, 333 (1982).
[CrossRef]

R. Gordon, R. M. Rangayyan, “Geometric Deconvolution: A Meta-Algorithm for Limited View Computed Tomography,” IEEE Trans. Biomed. Eng. BME-30, 806 (1983).
[CrossRef]

IEEE Trans. Circuits Syst. (1)

A. Papoulis, “A New Algorithm in Spectral Analysis and Band-Limited Extrapolation,” IEEE Trans. Circuits Syst. CAS-22, 735 (1975).
[CrossRef]

IEEE Trans. Nucl. Sci. (2)

T. Inouye, “Image Reconstruction with Limited Angle Projection Data,” IEEE Trans. Nucl. Sci. NS-26, 2666 (1979).

R. Gordon, “A Tutorial on ART (Algebraic Reconstruction Techniques),” IEEE Trans. Nucl. Sci. NS-21, 78, 95 (1974).

Int. Rev. Cytol. (1)

R. Gordon, G. T. Herman, “Three Dimensional Reconstruction from Projections: A Review of Algorithms, Int. Rev. Cytol. 38, 111 (1974).
[CrossRef] [PubMed]

J. Comput. Assist. Tomogr. (1)

A. Peres, “Tomographic Reconstruction from Limited Angular Data,” J. Comput. Assist. Tomogr. 3, 800 (1979).
[PubMed]

J. Nucl. Med. (1)

M. A. King, R. B. Schwinger, P. W. Doherty, “Fast Wiener Digital Post-Processing of SPECT Images,” J. Nucl. Med. 24, 81 (1983).

J. Opt. Soc. Am. (3)

Med. Radionuclide Imaging (1)

M. C. Kemp, “Maximum Entropy Reconstruction in Emission Tomography,” Med. Radionuclide Imaging 1, 313 (1980).

Nature London (2)

S. F. Gull, G. J. Daniell, “Image Reconstruction from Incomplete and Noisy Data,” Nature London 272, 686 (1978).
[CrossRef]

A. Klug, R. A. Crowther, “Three-Dimensional Image Reconstruction from the Viewpoint of Information Theory,” Nature London 238, 435 (1972).
[CrossRef]

Opt. Acta (1)

R. W. Gerchberg, “Super-resolution Through Error Energy Reduction,” Opt. Acta 21, 709 (1974).
[CrossRef]

Opt. Eng. (1)

K. C. Tam, V. Perez-Mendez, “Limited-angle Three Dimensional Reconstruction Using Fourier Transform Iterations and Radon Transform Iterations,” Opt. Eng. 20, 586 (1981).
[CrossRef]

Opt. Lett. (1)

SIAM J. Appl. Math. (1)

C. Byrne, R. Fitzgerald, “Reconstruction from Partial Information with Application to Tomography,” SIAM J. Appl. Math. 42, 933 (1982).
[CrossRef]

Other (5)

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).

R. C. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, Reading, Mass., 1977).

P. H. Lutz, “Fourier Image Reconstruction Incorporating Three Simple Interpolation Techniques,” Department of Computer Science Technical Report 104, State University of New York at Buffalo (1975).

R. Gordon, “Artifacts in Reconstructions Made from a Few Projections,” in Proceedings, First International Joint Conference on Pattern Recognition, 30 Oct.–1 Nov., Washington, D.C. (IEEE Computer Society, Northridge, Calif., 1973), pp. 275–285.

R. Gordon, “A Proposal for Deconvolution of Reconstructions,” Workshop on Information Treatment in Electron Microscopy, Basel (1972), 2 pp.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (18)

Fig. 1
Fig. 1

(a) Fourier spectrum of a point image, (b) Fourier spectrum of the reconstruction of the point image using multiplicative ART using eight views at 55, 65, …, 125°. (c) Amplitude spectrum of the system transfer function.

Fig. 2
Fig. 2

Test image.

Fig. 3
Fig. 3

Limited-view reconstruction of the test image by multiplicative ART using eight views at 55, 65, 75, …, 125°.

Fig. 4
Fig. 4

Fourier spectrum of the test image.

Fig. 5
Fig. 5

Fourier spectrum of the reconstructed image shown in Fig. 3.

Fig. 6
Fig. 6

(a) Interpolated spectrum of Fig. 3 which is used to obtain the 2-D noise-to-signal ratio function and also used as a clipping function, (b) The 2-D noise-to-signal ratio function.

Fig. 7
Fig. 7

Deconvolved spectrum obtained after Wiener deconvolution. The system transfer function H(u,υ) was obtained from the 2-D point spread function.

Fig. 8
Fig. 8

Deconvolved spectrum after clipping.

Fig. 9
Fig. 9

Restored image obtained by taking the inverse FFT of the spectrum shown in Fig. 8.

Fig. 10
Fig. 10

Restored image when a disk image was used as a basis function to obtain the system transfer function H(u,υ).

Fig. 11
Fig. 11

Second test image taken from a Sony video camera.

Fig. 12
Fig. 12

Limited-view reconstruction of the test image shown in Fig. 11 using multiplicative ART and the same eight views used for Fig. 3.

Fig. 13
Fig. 13

Basis image used to obtain the system transfer function.

Fig. 14
Fig. 14

Restored image from the reconstruction shown in Fig. 12

Fig. 15
Fig. 15

Image of a face having well distributed grey levels.

Fig. 16
Fig. 16

Limited-view reconstruction of the face image by multiplicative ART using only five views at 45, 67.5, 90, 112.5, and 135.°

Fig. 17
Fig. 17

The restored image of face reconstruction.

Fig. 18
Fig. 18

Schematic flow diagram of Wiener deconvolution algorithm.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

g ( x , y ) = h ( x , y ) * f ( x , y ) + n ( x , y ) ,
F ˆ ( u , υ ) = { | H ( u , υ ) | 2 / [ | H ( u , υ ) | 2 + W ( u , υ ) ] } G ( u , υ ) / H ( u , υ ) ,
H ( u , υ ) = K ( u , υ ) / J ( u , υ ) ,
W ( u , υ ) = | N ( u , υ ) | 2 / | S ( u , υ ) | 2 .
H ( u , υ ) = D ( u , υ ) / B ( u , υ ) ,

Metrics