Skip to main content

Joint Bayesian PET Reconstruction Algorithm Using a Quadratic Hybrid Multi-order Prior

  • Conference paper
  • 1795 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4418))

Abstract

To overcome the ill-posed problem of image reconstruction with noisy detected data in PET reconstruction, Bayesian reconstruction or maximum a posteriori (MAP) method has its superiority over others with regard to image quality and convergence. Based on Markov Random Fields (MRF) and Bayesian reconstruction theory, quadratic membrane (QM) prior and quadratic plate (QP) prior function differently for different objective surfaces with different properties. It is reasonable to believe that a hybrid prior which combines the two quadratic prior can work better than just using one prior alone. In this paper, a MRF quadratic hybrid prior multi-order model is proposed. A threshold estimation method based on statistical classification is devised to facilitate a selectively utilization of QM prior, QP prior in the quadratic hybrid multi-order (QHM) prior. Application of the proposed QHM prior in PET reconstruction with joint estimation algorithm is also given. Visional and quantitative comparisons of the results of experiments prove the new hybrid prior’s good performance in lowering noise effect and preserving edges for PET reconstruction.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Budinger, T.F., Gullberg, G.T., Huesman, R.H.: Emission computed tomography. In: Herman, G.T. (ed.) Image Reconstruction from Projections: Implementation and applications, pp. 147–246. Springer, Berlin (1979)

    Google Scholar 

  2. Levitan, E., Herman, G.T.: A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography. IEEE Trans. Med. Imag. 6, 185–192 (1987)

    Article  Google Scholar 

  3. Green, P.J.: Bayesian reconstruction from emission tomography data using a modified EM algorithm. IEEE Trans. Med. Imag. 9, 84–93 (1990)

    Article  Google Scholar 

  4. Lange, K.: Convergence of EM image reconstruction algorithms with Gibbs smoothness. IEEE Trans. Med. Imag. 9, 439–446 (1990)

    Article  Google Scholar 

  5. Johnson, V., et al.: Image restoration using Gibbs prior: Boundary modeling, treatment of blurring, and selection of hyperparameter. IEEE Trans. Pattern Anal. Machine Intell. 13, 413–425 (1991)

    Article  Google Scholar 

  6. Gindi, G., et al.: Bayesian Reconstruction for Emission Tomography via Deterministic Annealing. In: Barrett, H., Gmitro, A. (eds.) Information Processing in Medical Imaging, pp. 322–338. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  7. Li, S.Z.: Markov Random Field Modeling in image Analysis, pp. 1–40. Springer, Tokyo (2001)

    MATH  Google Scholar 

  8. Lee, S.J., Choi, Y., Gindi, G.R.: Validation of new Gibbs priors for Bayesian tomographic reconstruction using numerical studies and physically acquired data. IEEE Trans. Nucl. Sci. 46, 2154–2161 (1999)

    Article  Google Scholar 

  9. Hensick, P.V., Chelberg, D.M.: Automatic gradient threshold determination for edge detection. IEEE Trans. Imag. Processing 5, 784–787 (1996)

    Article  Google Scholar 

  10. McLachlan, G.J., Basford, K.E.: Mixture Models. Marcel Dekker, New York (1987)

    Google Scholar 

  11. Hsiao, I.-T., Rangarajan, A., Gindi, G.: Joint-MAP Reconstruction/Segmentation for Transmission Tomography Using Mixture-Models as Priors. In: Proc. IEEE Nuclear Science Symposium and Medical Imaging Conference, II, pp. 1689–1693. IEEE Computer Society Press, Los Alamitos (1998)

    Chapter  Google Scholar 

  12. 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. IEEE Computer Society Press, Los Alamitos (1998)

    Google Scholar 

  13. Fessler, J.A.: Aspire 3.0 user’s guide: A sparse reconstruction library. Communication & Signal Processing Laboratory Technical Report No. 293, Department of Electrical and Computer Engineering, University of Michigan, Ann Arbor (1998)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

André Gagalowicz Wilfried Philips

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer Berlin Heidelberg

About this paper

Cite this paper

Chen, Y. et al. (2007). Joint Bayesian PET Reconstruction Algorithm Using a Quadratic Hybrid Multi-order Prior. In: Gagalowicz, A., Philips, W. (eds) Computer Vision/Computer Graphics Collaboration Techniques. MIRAGE 2007. Lecture Notes in Computer Science, vol 4418. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71457-6_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-71457-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71456-9

  • Online ISBN: 978-3-540-71457-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics