Convergent Bayesian Reconstruction for PET Using New MRF Quadratic Membrane-Plate Hybrid Multi-order Prior

  • Yang Chen
  • Wufan Chen
  • Yanqiu Feng
  • Qianjin Feng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4091)


The effectiveness of Bayesian reconstruction, or maximum a posteriori (MAP) method, has been proved in positron emission tomography. In this article, a novel convex MRF (Markov random fields) Membrane-Plate hybrid prior for Bayesian reconstruction, which combines quadratic smoothness prior of different orders, is proposed. The design of the new prior is based on the intrinsic properties of the two smoothness prior of different orders and aims to make an adaptive use of the two smoothness priors. The convexity of the new prior energy functional is ensured. Simulation experiments of their application in PET (Positron Emission Tomography) reconstruction are illustrated. Visional and quantitative comparisons showed the new hybrid prior’ good performance in lowering noise effect and preserving edges.


Bayesian reconstruction MRF (Markov random fields) PET (Positron Emission Tomography) Membrane-Plate hybrid prior 


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  1. 1.
    Lange, K.: Convergence of EM image reconstruction algorithms with Gibbs smoothness. IEEE Trans. Med. Imag. 9, 439–446 (1990)CrossRefGoogle Scholar
  2. 2.
    Bouman, C.A., Sauer, K.: A generalized Gaussian image model for edge-preserving MAP estimation. IEEE Trans. Image Processing 2, 296–310 (1993)CrossRefGoogle Scholar
  3. 3.
    Johnson, V., Wong, W.H., Hu, X., Chen, C.T.: Image restoration using Gibbs prior: Boundary modeling, treatment of blurring, and selection of hyperparameter. IEEE Trans. Pattern Anal Machine Intell. 13, 413–425 (1991)CrossRefGoogle Scholar
  4. 4.
    Johnson, V.: A framework for incorporating structural prior information into the estimation of medical image. In: Barrett, H.H., Gmitro, A.F. (eds.) Information processing in Medical Imaging, pp. 307–321. Springer, Berlin (1993)CrossRefGoogle Scholar
  5. 5.
    Bowsher, J.E., Johnson, V.E., Turkington, T.G., Jaszczak, R.J., Floyd, C.E., Coleman, R.E.: Bayesian reconstruction and use of anatomical a priori information for emission tomography. IEEE Tran. Med. Imag. 15, 673–686 (1996)CrossRefGoogle Scholar
  6. 6.
    Yu, D.F., Fessler, J.A.: Edge-Preserving Tomographic Reconstruction with Nonlocal Regularization. IEEE Trans. Med. Imag. 21, 159–173 (2002)CrossRefGoogle Scholar
  7. 7.
    Lee, S.J., Rangarajan, A., Gindi, G.: Bayesian Image Reconstruction in SPECT Using Higher Order Mechanical Models as Prior. IEEE Trans. on Medical Imaging MI-14(4), 669–680 (1995)Google Scholar
  8. 8.
    Li, S.Z.: Markov Random Field Modeling in image Analysis, pp. 1–40. Springer, Tokyo (2001)zbMATHGoogle Scholar
  9. 9.
    Fessler, J.A., Erdoğan, H.: A paraboloidal surrogates algorithm for convergent penalized-likelihood emission reconstruction. In: Proc. IEEE Nuc. Sci. Symp. Med. Im. Conf., vol. 2, pp. 1132–1135 (1998)Google Scholar
  10. 10.
    Erdoğan, H., Fessler, J.A.: Monotonic algorithms for transmission tomography. IEEE Tr. Med. Im. 18, 801–814 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yang Chen
    • 1
  • Wufan Chen
    • 1
  • Yanqiu Feng
    • 1
  • Qianjin Feng
    • 1
  1. 1.Institute of Medical Information&Technology, School of Biomedical EngineeringSouthern Medical UniversityGuangzhouChina

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