## Fuzzy-rule-based image reconstruction for positron emission tomography

JOSA A, Vol. 22, Issue 9, pp. 1763-1771 (2005)

http://dx.doi.org/10.1364/JOSAA.22.001763

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### 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

**OCIS Codes**

(100.3010) Image processing : Image reconstruction techniques

(110.6960) Imaging systems : Tomography

(170.3880) Medical optics and biotechnology : Medical and biological imaging

(170.6960) Medical optics and biotechnology : Tomography

**Citation**

Partha P. Mondal and K. Rajan, "Fuzzy-rule-based image reconstruction for positron emission tomography," J. Opt. Soc. Am. A **22**, 1763-1771 (2005)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-9-1763

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### References

- Y. Vardi, L. A. Shepp, and L. Kaufmann, "A statistical model for position emission tomography," J. Am. Stat. Assoc. 80, 8-37 (1985).
- L. A. Shepp and Y. Vardi, "Maximum likelihood estimation for emission tomography," IEEE Trans. Med. Imaging 1, 113-121 (1982).
- C. M. Chen and S. Y. Lee, "Parallelization of the EM algorithm for 3-D PET image reconstruction," IEEE Trans. Med. Imaging 10, 513-522 (1991).
- K. Rajan, L. M. Patnaik, and J. Ramakrishna, "High speed computation of the EM algorithm for PET image reconstruction," IEEE Trans. Nucl. Sci. 41, 1-5 (1994).
- T. Hebert and 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).
- E. Levitan and 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).
- P. J. Green, "Bayesian reconstruction from emission tomography data using a modified EM algorithm," IEEE Trans. Med. Imaging 9, 84-93 (1990).
- Z. Zhou, R. M. Leahy, and J. Qi, "Approximate maximum likelihood hyperparameter estimation for Gibbs prior," IEEE Trans. Image Process. 6, 844-861 (1997).
- T. Herbert and R. Leahy, "Statistic based MAP image reconstruction from Poisson data using Gibbs priors," IEEE Trans. Signal Process. 40, 2290-2303 (1992).
- J. Nuyts, D. Bequ, P. Dupont, and L. Mortelmans, "A concave prior penalizing relative differences for maximum-a-posteriori reconstruction in emission tomography," IEEE Trans. Nucl. Sci. 49, 56-60 (2002).
- S. Alenius and U. Ruotsalainen, "Using local median as the location of prior distribution in iterative emission tomography reconstruction," IEEE Trans. Nucl. Sci. 45, 3097-3104 (1998).
- S. Alenius and U. Ruotsalainen, "Generalization of median root prior reconstruction," IEEE Trans. Med. Imaging 21, 1413-1420 (2002).
- L. A. Shepp and B. F. Logan, "The Fourier reconstruction of a head section," IEEE Trans. Nucl. Sci. 21, 21-43 (1974).
- J. A. Fessler, "Penalized weighted least-squares image reconstruction for positron emission tomography," IEEE Trans. Med. Imaging 13, 290-300 (1994).
- D. Van De Ville, M. Nachtegael, D. V. Weken, E. E. Kerre, W. Philips, and I. Lemahieu, "Noise reduction by fuzzy image filtering," IEEE Trans. Fuzzy Syst. 11, 429-436 (2003).
- D. Van De Ville, W. Philips, and 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.
- M. Nachtegael and E. E. Kerre, "Decomposing and constructing fuzzy morphological operations over alpha-cuts: continuous and discrete case," IEEE Trans. Fuzzy Syst. 8, 615626 (2000).
- S. Bothorel, B. Bouchon, and S. Muller, "A fuzzy logic-based approach for semiological analysis of microcalcification in mammographic images," Int. J. Intell. Syst.12, 819843 (1997).
- E. Veclerov and J. Llacer, "Stopping rule for MLE algorithm based on statistical hypothesis testing," IEEE Trans. Med. Imaging 6, 313-319 (1987).
- X. Ouyang, W. H. Wong, V. E. Johnson, X. Hu, and C. T. Chen, "Incorporation of correlated structural images in PET image reconstruction," IEEE Trans. Med. Imaging 13, 627-640 (1994).
- S. J. Lee, A. Rangarajan, and G. Gindi, "Bayesian image reconstruction in SPECT using higher order mechanical models as priors," IEEE Trans. Med. Imaging 14, 669680 (1995).
- S. J. Lee, "Accelerated deterministic annealing algorithms for transmission CT re-construction using ordered subsets," IEEE Trans. Nucl. Sci. 49, 2373-2380 (2002).
- J. Besag, "Spatial interaction and the statistical analysis of lattice systems," J. R. Stat. Soc. Ser. B. Methodol. 36, 192-236 (1974).
- P. P. Mondal and 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 and 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 and 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.
- N. Rajeevan, K. Rajgopal, and G. Krishna, "Vector-extrapolated fast maximum likelihood estimation algorithms for emission tomography," IEEE Trans. Med. Imaging 11, 9-20 (1992).
- L. Kaufmann, "Implementing and accelerating the EM-algorithm for positron emission tomography," IEEE Trans. Med. Imaging 6, 37-51 (1987).

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