Abstract

Positron emission tomography (PET) and single-photon emission computed tomography have revolutionized the field of medicine and biology. Penalized iterative algorithms based on maximum a posteriori (MAP) estimation eliminate noisy artifacts by utilizing available prior information in the reconstruction process but often result in a blurring effect. MAP-based algorithms fail to determine the density class in the reconstructed image and hence penalize the pixels irrespective of the density class. Reconstruction with better edge information is often difficult because prior knowledge is not taken into account. The recently introduced median-root-prior (MRP)-based algorithm preserves the edges, but a steplike streaking effect is observed in the reconstructed image, which is undesirable. A fuzzy approach is proposed for modeling the nature of interpixel interaction in order to build an artifact-free edge-preserving reconstruction. The proposed algorithm consists of two elementary steps: (1) edge detection, in which fuzzy-rule-based derivatives are used for the detection of edges in the nearest neighborhood window (which is equivalent to recognizing nearby density classes), and (2) fuzzy smoothing, in which penalization is performed only for those pixels for which no edge is detected in the nearest neighborhood. Both of these operations are carried out iteratively until the image converges. Analysis shows that the proposed fuzzy-rule-based reconstruction algorithm is capable of producing qualitatively better reconstructed images than those reconstructed by MAP and MRP algorithms. The reconstructed images are sharper, with small features being better resolved owing to the nature of the fuzzy potential function.

© 2005 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Vardi, L. A. Shepp, L. Kaufmann, “A statistical model for position emission tomography,” J. Am. Stat. Assoc. 80, 8–37 (1985).
    [CrossRef]
  2. L. A. Shepp, Y. Vardi, “Maximum likelihood estimation for emission tomography,” IEEE Trans. Med. Imaging 1, 113–121 (1982).
    [CrossRef]
  3. C. M. Chen, S. Y. Lee, “Parallelization of the EM algorithm for 3-D PET image reconstruction,” IEEE Trans. Med. Imaging 10, 513–522 (1991).
    [CrossRef] [PubMed]
  4. K. Rajan, L. M. Patnaik, J. Ramakrishna, “High speed computation of the EM algorithm for PET image reconstruction,” IEEE Trans. Nucl. Sci. 41, 1–5 (1994).
    [CrossRef]
  5. T. Hebert, R. Leahy, “A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors,” IEEE Trans. Med. Imaging 8, 194–202 (1989).
    [CrossRef] [PubMed]
  6. E. Levitan, G. T. Herman, “A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography,” IEEE Trans. Med. Imaging 6, 185–192 (1987).
    [CrossRef] [PubMed]
  7. P. J. Green, “Bayesian reconstruction from emission tomography data using a modified EM algorithm,” IEEE Trans. Med. Imaging 9, 84–93 (1990).
    [CrossRef]
  8. Z. Zhou, R. M. Leahy, J. Qi, “Approximate maximum likelihood hyperparameter estimation for Gibbs prior,” IEEE Trans. Image Process. 6, 844–861 (1997).
    [CrossRef]
  9. T. Herbert, R. Leahy, “Statistic based MAP image reconstruction from Poisson data using Gibbs priors,” IEEE Trans. Signal Process. 40, 2290–2303 (1992).
    [CrossRef]
  10. J. Nuyts, D. Bequ, P. Dupont, L. Mortelmans, “A concave prior penalizing relative differences for maximum-a-posteriori reconstruction in emission tomography,” IEEE Trans. Nucl. Sci. 49, 56–60 (2002).
    [CrossRef]
  11. S. Alenius, U. Ruotsalainen, “Using local median as the location of prior distribution in iterative emission tomography reconstruction,” IEEE Trans. Nucl. Sci. 45, 3097–3104 (1998).
    [CrossRef]
  12. S. Alenius, U. Ruotsalainen, “Generalization of median root prior reconstruction,” IEEE Trans. Med. Imaging 21, 1413–1420 (2002).
    [CrossRef]
  13. L. A. Shepp, B. F. Logan, “The Fourier reconstruction of a head section,” IEEE Trans. Nucl. Sci. 21, 21–43 (1974).
    [CrossRef]
  14. J. A. Fessler, “Penalized weighted least-squares image reconstruction for positron emission tomography,” IEEE Trans. Med. Imaging 13, 290–300 (1994).
    [CrossRef] [PubMed]
  15. D. Van De Ville, M. Nachtegael, D. V. Weken, E. E. Kerre, W. Philips, I. Lemahieu, “Noise reduction by fuzzy image filtering,” IEEE Trans. Fuzzy Syst. 11, 429–436 (2003).
    [CrossRef]
  16. D. Van De Ville, W. Philips, I. Lemahieu, “Fuzzy-based motion detection and its application to de-interlacing,” in Fuzzy Techniques in Image Processing, E. E. Kerre and M. Nachtegael, eds., Vol. 52 of Studies in Fuzziness and Soft Computing (Springer-Verlag, 2002), pp. 337–369.
  17. M. Nachtegael, E. E. Kerre, “Decomposing and constructing fuzzy morphological operations over α-cuts: continuous and discrete case,” IEEE Trans. Fuzzy Syst. 8, 615626 (2000).
    [CrossRef]
  18. S. Bothorel, B. Bouchon, S. Muller, “A fuzzy logic-based approach for semiological analysis of microcalcification in mammographic images,” Int. J. Intell. Syst. 12, 819843 (1997).
  19. E. Veclerov, J. Llacer, “Stopping rule for MLE algorithm based on statistical hypothesis testing,” IEEE Trans. Med. Imaging 6, 313–319 (1987).
    [CrossRef]
  20. X. Ouyang, W. H. Wong, V. E. Johnson, X. Hu, C. T. Chen, “Incorporation of correlated structural images in PET image reconstruction,” IEEE Trans. Med. Imaging 13, 627–640 (1994).
    [CrossRef] [PubMed]
  21. S. J. Lee, A. Rangarajan, G. Gindi, “Bayesian image reconstruction in SPECT using higher order mechanical models as priors,” IEEE Trans. Med. Imaging 14, 669680 (1995).
  22. S. J. Lee, “Accelerated deterministic annealing algorithms for transmission CT re-construction using ordered subsets,” IEEE Trans. Nucl. Sci. 49, 2373–2380 (2002).
    [CrossRef]
  23. J. Besag, “Spatial interaction and the statistical analysis of lattice systems,” J. R. Stat. Soc. Ser. B. Methodol. 36, 192–236 (1974).
  24. P. P. Mondal, K. Rajan, “Iterative image reconstruction for emission tomography using fuzzy potential,” in IEEE International Nuclear Science Symposium and Medical Imaging Conference (IEEE, 2004), paper M9–283.
  25. P. P. Mondal, K. Rajan, “Fuzzy rule based image reconstruction for PET,” in IEEE International Conference on Systems, Man and Cybernetics (IEEE, 2004), pp. 3028–3032.
  26. P. P. Mondal, Rajan Kanhirodan, “Image reconstruction for PET using fuzzy potential,” in International Workshop on Machine Learning for Signal Processing (MLSP) (IEEE, 2004).
  27. L. A. Zadeh, “Fuzzy Logic,” IEEE Computer, April, 1988, pp. 83–93.
  28. N. Rajeevan, K. Rajgopal, G. Krishna, “Vector-extrapolated fast maximum likelihood estimation algorithms for emission tomography,” IEEE Trans. Med. Imaging 11, 9–20 (1992).
    [CrossRef] [PubMed]
  29. L. Kaufmann, “Implementing and accelerating the EM-algorithm for positron emission tomography,” IEEE Trans. Med. Imaging 6, 37–51 (1987).
    [CrossRef]

2003 (1)

D. Van De Ville, M. Nachtegael, D. V. Weken, E. E. Kerre, W. Philips, I. Lemahieu, “Noise reduction by fuzzy image filtering,” IEEE Trans. Fuzzy Syst. 11, 429–436 (2003).
[CrossRef]

2002 (3)

J. Nuyts, D. Bequ, P. Dupont, L. Mortelmans, “A concave prior penalizing relative differences for maximum-a-posteriori reconstruction in emission tomography,” IEEE Trans. Nucl. Sci. 49, 56–60 (2002).
[CrossRef]

S. Alenius, U. Ruotsalainen, “Generalization of median root prior reconstruction,” IEEE Trans. Med. Imaging 21, 1413–1420 (2002).
[CrossRef]

S. J. Lee, “Accelerated deterministic annealing algorithms for transmission CT re-construction using ordered subsets,” IEEE Trans. Nucl. Sci. 49, 2373–2380 (2002).
[CrossRef]

2000 (1)

M. Nachtegael, E. E. Kerre, “Decomposing and constructing fuzzy morphological operations over α-cuts: continuous and discrete case,” IEEE Trans. Fuzzy Syst. 8, 615626 (2000).
[CrossRef]

1998 (1)

S. Alenius, U. Ruotsalainen, “Using local median as the location of prior distribution in iterative emission tomography reconstruction,” IEEE Trans. Nucl. Sci. 45, 3097–3104 (1998).
[CrossRef]

1997 (1)

Z. Zhou, R. M. Leahy, J. Qi, “Approximate maximum likelihood hyperparameter estimation for Gibbs prior,” IEEE Trans. Image Process. 6, 844–861 (1997).
[CrossRef]

1995 (1)

S. J. Lee, A. Rangarajan, G. Gindi, “Bayesian image reconstruction in SPECT using higher order mechanical models as priors,” IEEE Trans. Med. Imaging 14, 669680 (1995).

1994 (3)

K. Rajan, L. M. Patnaik, J. Ramakrishna, “High speed computation of the EM algorithm for PET image reconstruction,” IEEE Trans. Nucl. Sci. 41, 1–5 (1994).
[CrossRef]

J. A. Fessler, “Penalized weighted least-squares image reconstruction for positron emission tomography,” IEEE Trans. Med. Imaging 13, 290–300 (1994).
[CrossRef] [PubMed]

X. Ouyang, W. H. Wong, V. E. Johnson, X. Hu, C. T. Chen, “Incorporation of correlated structural images in PET image reconstruction,” IEEE Trans. Med. Imaging 13, 627–640 (1994).
[CrossRef] [PubMed]

1992 (2)

T. Herbert, R. Leahy, “Statistic based MAP image reconstruction from Poisson data using Gibbs priors,” IEEE Trans. Signal Process. 40, 2290–2303 (1992).
[CrossRef]

N. Rajeevan, K. Rajgopal, G. Krishna, “Vector-extrapolated fast maximum likelihood estimation algorithms for emission tomography,” IEEE Trans. Med. Imaging 11, 9–20 (1992).
[CrossRef] [PubMed]

1991 (1)

C. M. Chen, S. Y. Lee, “Parallelization of the EM algorithm for 3-D PET image reconstruction,” IEEE Trans. Med. Imaging 10, 513–522 (1991).
[CrossRef] [PubMed]

1990 (1)

P. J. Green, “Bayesian reconstruction from emission tomography data using a modified EM algorithm,” IEEE Trans. Med. Imaging 9, 84–93 (1990).
[CrossRef]

1989 (1)

T. Hebert, R. Leahy, “A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors,” IEEE Trans. Med. Imaging 8, 194–202 (1989).
[CrossRef] [PubMed]

1987 (3)

E. Levitan, G. T. Herman, “A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography,” IEEE Trans. Med. Imaging 6, 185–192 (1987).
[CrossRef] [PubMed]

E. Veclerov, J. Llacer, “Stopping rule for MLE algorithm based on statistical hypothesis testing,” IEEE Trans. Med. Imaging 6, 313–319 (1987).
[CrossRef]

L. Kaufmann, “Implementing and accelerating the EM-algorithm for positron emission tomography,” IEEE Trans. Med. Imaging 6, 37–51 (1987).
[CrossRef]

1985 (1)

Y. Vardi, L. A. Shepp, L. Kaufmann, “A statistical model for position emission tomography,” J. Am. Stat. Assoc. 80, 8–37 (1985).
[CrossRef]

1982 (1)

L. A. Shepp, Y. Vardi, “Maximum likelihood estimation for emission tomography,” IEEE Trans. Med. Imaging 1, 113–121 (1982).
[CrossRef]

1974 (2)

L. A. Shepp, B. F. Logan, “The Fourier reconstruction of a head section,” IEEE Trans. Nucl. Sci. 21, 21–43 (1974).
[CrossRef]

J. Besag, “Spatial interaction and the statistical analysis of lattice systems,” J. R. Stat. Soc. Ser. B. Methodol. 36, 192–236 (1974).

Alenius, S.

S. Alenius, U. Ruotsalainen, “Generalization of median root prior reconstruction,” IEEE Trans. Med. Imaging 21, 1413–1420 (2002).
[CrossRef]

S. Alenius, U. Ruotsalainen, “Using local median as the location of prior distribution in iterative emission tomography reconstruction,” IEEE Trans. Nucl. Sci. 45, 3097–3104 (1998).
[CrossRef]

Bequ, D.

J. Nuyts, D. Bequ, P. Dupont, L. Mortelmans, “A concave prior penalizing relative differences for maximum-a-posteriori reconstruction in emission tomography,” IEEE Trans. Nucl. Sci. 49, 56–60 (2002).
[CrossRef]

Besag, J.

J. Besag, “Spatial interaction and the statistical analysis of lattice systems,” J. R. Stat. Soc. Ser. B. Methodol. 36, 192–236 (1974).

Bothorel, S.

S. Bothorel, B. Bouchon, S. Muller, “A fuzzy logic-based approach for semiological analysis of microcalcification in mammographic images,” Int. J. Intell. Syst. 12, 819843 (1997).

Bouchon, B.

S. Bothorel, B. Bouchon, S. Muller, “A fuzzy logic-based approach for semiological analysis of microcalcification in mammographic images,” Int. J. Intell. Syst. 12, 819843 (1997).

Chen, C. M.

C. M. Chen, S. Y. Lee, “Parallelization of the EM algorithm for 3-D PET image reconstruction,” IEEE Trans. Med. Imaging 10, 513–522 (1991).
[CrossRef] [PubMed]

Chen, C. T.

X. Ouyang, W. H. Wong, V. E. Johnson, X. Hu, C. T. Chen, “Incorporation of correlated structural images in PET image reconstruction,” IEEE Trans. Med. Imaging 13, 627–640 (1994).
[CrossRef] [PubMed]

Dupont, P.

J. Nuyts, D. Bequ, P. Dupont, L. Mortelmans, “A concave prior penalizing relative differences for maximum-a-posteriori reconstruction in emission tomography,” IEEE Trans. Nucl. Sci. 49, 56–60 (2002).
[CrossRef]

Fessler, J. A.

J. A. Fessler, “Penalized weighted least-squares image reconstruction for positron emission tomography,” IEEE Trans. Med. Imaging 13, 290–300 (1994).
[CrossRef] [PubMed]

Gindi, G.

S. J. Lee, A. Rangarajan, G. Gindi, “Bayesian image reconstruction in SPECT using higher order mechanical models as priors,” IEEE Trans. Med. Imaging 14, 669680 (1995).

Green, P. J.

P. J. Green, “Bayesian reconstruction from emission tomography data using a modified EM algorithm,” IEEE Trans. Med. Imaging 9, 84–93 (1990).
[CrossRef]

Hebert, T.

T. Hebert, R. Leahy, “A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors,” IEEE Trans. Med. Imaging 8, 194–202 (1989).
[CrossRef] [PubMed]

Herbert, T.

T. Herbert, R. Leahy, “Statistic based MAP image reconstruction from Poisson data using Gibbs priors,” IEEE Trans. Signal Process. 40, 2290–2303 (1992).
[CrossRef]

Herman, G. T.

E. Levitan, G. T. Herman, “A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography,” IEEE Trans. Med. Imaging 6, 185–192 (1987).
[CrossRef] [PubMed]

Hu, X.

X. Ouyang, W. H. Wong, V. E. Johnson, X. Hu, C. T. Chen, “Incorporation of correlated structural images in PET image reconstruction,” IEEE Trans. Med. Imaging 13, 627–640 (1994).
[CrossRef] [PubMed]

Johnson, V. E.

X. Ouyang, W. H. Wong, V. E. Johnson, X. Hu, C. T. Chen, “Incorporation of correlated structural images in PET image reconstruction,” IEEE Trans. Med. Imaging 13, 627–640 (1994).
[CrossRef] [PubMed]

Kanhirodan, Rajan

P. P. Mondal, Rajan Kanhirodan, “Image reconstruction for PET using fuzzy potential,” in International Workshop on Machine Learning for Signal Processing (MLSP) (IEEE, 2004).

Kaufmann, L.

L. Kaufmann, “Implementing and accelerating the EM-algorithm for positron emission tomography,” IEEE Trans. Med. Imaging 6, 37–51 (1987).
[CrossRef]

Y. Vardi, L. A. Shepp, L. Kaufmann, “A statistical model for position emission tomography,” J. Am. Stat. Assoc. 80, 8–37 (1985).
[CrossRef]

Kerre, E. E.

D. Van De Ville, M. Nachtegael, D. V. Weken, E. E. Kerre, W. Philips, I. Lemahieu, “Noise reduction by fuzzy image filtering,” IEEE Trans. Fuzzy Syst. 11, 429–436 (2003).
[CrossRef]

M. Nachtegael, E. E. Kerre, “Decomposing and constructing fuzzy morphological operations over α-cuts: continuous and discrete case,” IEEE Trans. Fuzzy Syst. 8, 615626 (2000).
[CrossRef]

Krishna, G.

N. Rajeevan, K. Rajgopal, G. Krishna, “Vector-extrapolated fast maximum likelihood estimation algorithms for emission tomography,” IEEE Trans. Med. Imaging 11, 9–20 (1992).
[CrossRef] [PubMed]

Leahy, R.

T. Herbert, R. Leahy, “Statistic based MAP image reconstruction from Poisson data using Gibbs priors,” IEEE Trans. Signal Process. 40, 2290–2303 (1992).
[CrossRef]

T. Hebert, R. Leahy, “A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors,” IEEE Trans. Med. Imaging 8, 194–202 (1989).
[CrossRef] [PubMed]

Leahy, R. M.

Z. Zhou, R. M. Leahy, J. Qi, “Approximate maximum likelihood hyperparameter estimation for Gibbs prior,” IEEE Trans. Image Process. 6, 844–861 (1997).
[CrossRef]

Lee, S. J.

S. J. Lee, “Accelerated deterministic annealing algorithms for transmission CT re-construction using ordered subsets,” IEEE Trans. Nucl. Sci. 49, 2373–2380 (2002).
[CrossRef]

S. J. Lee, A. Rangarajan, G. Gindi, “Bayesian image reconstruction in SPECT using higher order mechanical models as priors,” IEEE Trans. Med. Imaging 14, 669680 (1995).

Lee, S. Y.

C. M. Chen, S. Y. Lee, “Parallelization of the EM algorithm for 3-D PET image reconstruction,” IEEE Trans. Med. Imaging 10, 513–522 (1991).
[CrossRef] [PubMed]

Lemahieu, I.

D. Van De Ville, M. Nachtegael, D. V. Weken, E. E. Kerre, W. Philips, I. Lemahieu, “Noise reduction by fuzzy image filtering,” IEEE Trans. Fuzzy Syst. 11, 429–436 (2003).
[CrossRef]

D. Van De Ville, W. Philips, I. Lemahieu, “Fuzzy-based motion detection and its application to de-interlacing,” in Fuzzy Techniques in Image Processing, E. E. Kerre and M. Nachtegael, eds., Vol. 52 of Studies in Fuzziness and Soft Computing (Springer-Verlag, 2002), pp. 337–369.

Levitan, E.

E. Levitan, G. T. Herman, “A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography,” IEEE Trans. Med. Imaging 6, 185–192 (1987).
[CrossRef] [PubMed]

Llacer, J.

E. Veclerov, J. Llacer, “Stopping rule for MLE algorithm based on statistical hypothesis testing,” IEEE Trans. Med. Imaging 6, 313–319 (1987).
[CrossRef]

Logan, B. F.

L. A. Shepp, B. F. Logan, “The Fourier reconstruction of a head section,” IEEE Trans. Nucl. Sci. 21, 21–43 (1974).
[CrossRef]

Mondal, P. P.

P. P. Mondal, Rajan Kanhirodan, “Image reconstruction for PET using fuzzy potential,” in International Workshop on Machine Learning for Signal Processing (MLSP) (IEEE, 2004).

P. P. Mondal, K. Rajan, “Iterative image reconstruction for emission tomography using fuzzy potential,” in IEEE International Nuclear Science Symposium and Medical Imaging Conference (IEEE, 2004), paper M9–283.

P. P. Mondal, K. Rajan, “Fuzzy rule based image reconstruction for PET,” in IEEE International Conference on Systems, Man and Cybernetics (IEEE, 2004), pp. 3028–3032.

Mortelmans, L.

J. Nuyts, D. Bequ, P. Dupont, L. Mortelmans, “A concave prior penalizing relative differences for maximum-a-posteriori reconstruction in emission tomography,” IEEE Trans. Nucl. Sci. 49, 56–60 (2002).
[CrossRef]

Muller, S.

S. Bothorel, B. Bouchon, S. Muller, “A fuzzy logic-based approach for semiological analysis of microcalcification in mammographic images,” Int. J. Intell. Syst. 12, 819843 (1997).

Nachtegael, M.

D. Van De Ville, M. Nachtegael, D. V. Weken, E. E. Kerre, W. Philips, I. Lemahieu, “Noise reduction by fuzzy image filtering,” IEEE Trans. Fuzzy Syst. 11, 429–436 (2003).
[CrossRef]

M. Nachtegael, E. E. Kerre, “Decomposing and constructing fuzzy morphological operations over α-cuts: continuous and discrete case,” IEEE Trans. Fuzzy Syst. 8, 615626 (2000).
[CrossRef]

Nuyts, J.

J. Nuyts, D. Bequ, P. Dupont, L. Mortelmans, “A concave prior penalizing relative differences for maximum-a-posteriori reconstruction in emission tomography,” IEEE Trans. Nucl. Sci. 49, 56–60 (2002).
[CrossRef]

Ouyang, X.

X. Ouyang, W. H. Wong, V. E. Johnson, X. Hu, C. T. Chen, “Incorporation of correlated structural images in PET image reconstruction,” IEEE Trans. Med. Imaging 13, 627–640 (1994).
[CrossRef] [PubMed]

Patnaik, L. M.

K. Rajan, L. M. Patnaik, J. Ramakrishna, “High speed computation of the EM algorithm for PET image reconstruction,” IEEE Trans. Nucl. Sci. 41, 1–5 (1994).
[CrossRef]

Philips, W.

D. Van De Ville, M. Nachtegael, D. V. Weken, E. E. Kerre, W. Philips, I. Lemahieu, “Noise reduction by fuzzy image filtering,” IEEE Trans. Fuzzy Syst. 11, 429–436 (2003).
[CrossRef]

D. Van De Ville, W. Philips, I. Lemahieu, “Fuzzy-based motion detection and its application to de-interlacing,” in Fuzzy Techniques in Image Processing, E. E. Kerre and M. Nachtegael, eds., Vol. 52 of Studies in Fuzziness and Soft Computing (Springer-Verlag, 2002), pp. 337–369.

Qi, J.

Z. Zhou, R. M. Leahy, J. Qi, “Approximate maximum likelihood hyperparameter estimation for Gibbs prior,” IEEE Trans. Image Process. 6, 844–861 (1997).
[CrossRef]

Rajan, K.

K. Rajan, L. M. Patnaik, J. Ramakrishna, “High speed computation of the EM algorithm for PET image reconstruction,” IEEE Trans. Nucl. Sci. 41, 1–5 (1994).
[CrossRef]

P. P. Mondal, K. Rajan, “Fuzzy rule based image reconstruction for PET,” in IEEE International Conference on Systems, Man and Cybernetics (IEEE, 2004), pp. 3028–3032.

P. P. Mondal, K. Rajan, “Iterative image reconstruction for emission tomography using fuzzy potential,” in IEEE International Nuclear Science Symposium and Medical Imaging Conference (IEEE, 2004), paper M9–283.

Rajeevan, N.

N. Rajeevan, K. Rajgopal, G. Krishna, “Vector-extrapolated fast maximum likelihood estimation algorithms for emission tomography,” IEEE Trans. Med. Imaging 11, 9–20 (1992).
[CrossRef] [PubMed]

Rajgopal, K.

N. Rajeevan, K. Rajgopal, G. Krishna, “Vector-extrapolated fast maximum likelihood estimation algorithms for emission tomography,” IEEE Trans. Med. Imaging 11, 9–20 (1992).
[CrossRef] [PubMed]

Ramakrishna, J.

K. Rajan, L. M. Patnaik, J. Ramakrishna, “High speed computation of the EM algorithm for PET image reconstruction,” IEEE Trans. Nucl. Sci. 41, 1–5 (1994).
[CrossRef]

Rangarajan, A.

S. J. Lee, A. Rangarajan, G. Gindi, “Bayesian image reconstruction in SPECT using higher order mechanical models as priors,” IEEE Trans. Med. Imaging 14, 669680 (1995).

Ruotsalainen, U.

S. Alenius, U. Ruotsalainen, “Generalization of median root prior reconstruction,” IEEE Trans. Med. Imaging 21, 1413–1420 (2002).
[CrossRef]

S. Alenius, U. Ruotsalainen, “Using local median as the location of prior distribution in iterative emission tomography reconstruction,” IEEE Trans. Nucl. Sci. 45, 3097–3104 (1998).
[CrossRef]

Shepp, L. A.

Y. Vardi, L. A. Shepp, L. Kaufmann, “A statistical model for position emission tomography,” J. Am. Stat. Assoc. 80, 8–37 (1985).
[CrossRef]

L. A. Shepp, Y. Vardi, “Maximum likelihood estimation for emission tomography,” IEEE Trans. Med. Imaging 1, 113–121 (1982).
[CrossRef]

L. A. Shepp, B. F. Logan, “The Fourier reconstruction of a head section,” IEEE Trans. Nucl. Sci. 21, 21–43 (1974).
[CrossRef]

Van De Ville, D.

D. Van De Ville, M. Nachtegael, D. V. Weken, E. E. Kerre, W. Philips, I. Lemahieu, “Noise reduction by fuzzy image filtering,” IEEE Trans. Fuzzy Syst. 11, 429–436 (2003).
[CrossRef]

D. Van De Ville, W. Philips, I. Lemahieu, “Fuzzy-based motion detection and its application to de-interlacing,” in Fuzzy Techniques in Image Processing, E. E. Kerre and M. Nachtegael, eds., Vol. 52 of Studies in Fuzziness and Soft Computing (Springer-Verlag, 2002), pp. 337–369.

Vardi, Y.

Y. Vardi, L. A. Shepp, L. Kaufmann, “A statistical model for position emission tomography,” J. Am. Stat. Assoc. 80, 8–37 (1985).
[CrossRef]

L. A. Shepp, Y. Vardi, “Maximum likelihood estimation for emission tomography,” IEEE Trans. Med. Imaging 1, 113–121 (1982).
[CrossRef]

Veclerov, E.

E. Veclerov, J. Llacer, “Stopping rule for MLE algorithm based on statistical hypothesis testing,” IEEE Trans. Med. Imaging 6, 313–319 (1987).
[CrossRef]

Weken, D. V.

D. Van De Ville, M. Nachtegael, D. V. Weken, E. E. Kerre, W. Philips, I. Lemahieu, “Noise reduction by fuzzy image filtering,” IEEE Trans. Fuzzy Syst. 11, 429–436 (2003).
[CrossRef]

Wong, W. H.

X. Ouyang, W. H. Wong, V. E. Johnson, X. Hu, C. T. Chen, “Incorporation of correlated structural images in PET image reconstruction,” IEEE Trans. Med. Imaging 13, 627–640 (1994).
[CrossRef] [PubMed]

Zadeh, L. A.

L. A. Zadeh, “Fuzzy Logic,” IEEE Computer, April, 1988, pp. 83–93.

Zhou, Z.

Z. Zhou, R. M. Leahy, J. Qi, “Approximate maximum likelihood hyperparameter estimation for Gibbs prior,” IEEE Trans. Image Process. 6, 844–861 (1997).
[CrossRef]

IEEE Trans. Fuzzy Syst. (2)

D. Van De Ville, M. Nachtegael, D. V. Weken, E. E. Kerre, W. Philips, I. Lemahieu, “Noise reduction by fuzzy image filtering,” IEEE Trans. Fuzzy Syst. 11, 429–436 (2003).
[CrossRef]

M. Nachtegael, E. E. Kerre, “Decomposing and constructing fuzzy morphological operations over α-cuts: continuous and discrete case,” IEEE Trans. Fuzzy Syst. 8, 615626 (2000).
[CrossRef]

IEEE Trans. Image Process. (1)

Z. Zhou, R. M. Leahy, J. Qi, “Approximate maximum likelihood hyperparameter estimation for Gibbs prior,” IEEE Trans. Image Process. 6, 844–861 (1997).
[CrossRef]

IEEE Trans. Med. Imaging (12)

L. A. Shepp, Y. Vardi, “Maximum likelihood estimation for emission tomography,” IEEE Trans. Med. Imaging 1, 113–121 (1982).
[CrossRef]

C. M. Chen, S. Y. Lee, “Parallelization of the EM algorithm for 3-D PET image reconstruction,” IEEE Trans. Med. Imaging 10, 513–522 (1991).
[CrossRef] [PubMed]

T. Hebert, R. Leahy, “A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors,” IEEE Trans. Med. Imaging 8, 194–202 (1989).
[CrossRef] [PubMed]

E. Levitan, G. T. Herman, “A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography,” IEEE Trans. Med. Imaging 6, 185–192 (1987).
[CrossRef] [PubMed]

P. J. Green, “Bayesian reconstruction from emission tomography data using a modified EM algorithm,” IEEE Trans. Med. Imaging 9, 84–93 (1990).
[CrossRef]

S. Alenius, U. Ruotsalainen, “Generalization of median root prior reconstruction,” IEEE Trans. Med. Imaging 21, 1413–1420 (2002).
[CrossRef]

J. A. Fessler, “Penalized weighted least-squares image reconstruction for positron emission tomography,” IEEE Trans. Med. Imaging 13, 290–300 (1994).
[CrossRef] [PubMed]

E. Veclerov, J. Llacer, “Stopping rule for MLE algorithm based on statistical hypothesis testing,” IEEE Trans. Med. Imaging 6, 313–319 (1987).
[CrossRef]

X. Ouyang, W. H. Wong, V. E. Johnson, X. Hu, C. T. Chen, “Incorporation of correlated structural images in PET image reconstruction,” IEEE Trans. Med. Imaging 13, 627–640 (1994).
[CrossRef] [PubMed]

S. J. Lee, A. Rangarajan, G. Gindi, “Bayesian image reconstruction in SPECT using higher order mechanical models as priors,” IEEE Trans. Med. Imaging 14, 669680 (1995).

N. Rajeevan, K. Rajgopal, G. Krishna, “Vector-extrapolated fast maximum likelihood estimation algorithms for emission tomography,” IEEE Trans. Med. Imaging 11, 9–20 (1992).
[CrossRef] [PubMed]

L. Kaufmann, “Implementing and accelerating the EM-algorithm for positron emission tomography,” IEEE Trans. Med. Imaging 6, 37–51 (1987).
[CrossRef]

IEEE Trans. Nucl. Sci. (5)

S. J. Lee, “Accelerated deterministic annealing algorithms for transmission CT re-construction using ordered subsets,” IEEE Trans. Nucl. Sci. 49, 2373–2380 (2002).
[CrossRef]

L. A. Shepp, B. F. Logan, “The Fourier reconstruction of a head section,” IEEE Trans. Nucl. Sci. 21, 21–43 (1974).
[CrossRef]

K. Rajan, L. M. Patnaik, J. Ramakrishna, “High speed computation of the EM algorithm for PET image reconstruction,” IEEE Trans. Nucl. Sci. 41, 1–5 (1994).
[CrossRef]

J. Nuyts, D. Bequ, P. Dupont, L. Mortelmans, “A concave prior penalizing relative differences for maximum-a-posteriori reconstruction in emission tomography,” IEEE Trans. Nucl. Sci. 49, 56–60 (2002).
[CrossRef]

S. Alenius, U. Ruotsalainen, “Using local median as the location of prior distribution in iterative emission tomography reconstruction,” IEEE Trans. Nucl. Sci. 45, 3097–3104 (1998).
[CrossRef]

IEEE Trans. Signal Process. (1)

T. Herbert, R. Leahy, “Statistic based MAP image reconstruction from Poisson data using Gibbs priors,” IEEE Trans. Signal Process. 40, 2290–2303 (1992).
[CrossRef]

J. Am. Stat. Assoc. (1)

Y. Vardi, L. A. Shepp, L. Kaufmann, “A statistical model for position emission tomography,” J. Am. Stat. Assoc. 80, 8–37 (1985).
[CrossRef]

J. R. Stat. Soc. Ser. B. Methodol. (1)

J. Besag, “Spatial interaction and the statistical analysis of lattice systems,” J. R. Stat. Soc. Ser. B. Methodol. 36, 192–236 (1974).

Other (6)

P. P. Mondal, K. Rajan, “Iterative image reconstruction for emission tomography using fuzzy potential,” in IEEE International Nuclear Science Symposium and Medical Imaging Conference (IEEE, 2004), paper M9–283.

P. P. Mondal, K. Rajan, “Fuzzy rule based image reconstruction for PET,” in IEEE International Conference on Systems, Man and Cybernetics (IEEE, 2004), pp. 3028–3032.

P. P. Mondal, Rajan Kanhirodan, “Image reconstruction for PET using fuzzy potential,” in International Workshop on Machine Learning for Signal Processing (MLSP) (IEEE, 2004).

L. A. Zadeh, “Fuzzy Logic,” IEEE Computer, April, 1988, pp. 83–93.

S. Bothorel, B. Bouchon, S. Muller, “A fuzzy logic-based approach for semiological analysis of microcalcification in mammographic images,” Int. J. Intell. Syst. 12, 819843 (1997).

D. Van De Ville, W. Philips, I. Lemahieu, “Fuzzy-based motion detection and its application to de-interlacing,” in Fuzzy Techniques in Image Processing, E. E. Kerre and M. Nachtegael, eds., Vol. 52 of Studies in Fuzziness and Soft Computing (Springer-Verlag, 2002), pp. 337–369.

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.


Metrics