Medical and Biological Engineering and Computing

, Volume 44, Issue 11, pp 983–997 | Cite as

Image reconstruction for positron emission tomography using fuzzy nonlinear anisotropic diffusion penalty

  • Hongqing Zhu
  • Huazhong Shu
  • Jian Zhou
  • Christine Toumoulin
  • Limin Luo
Original Article


Iterative algorithms such as maximum likelihood-expectation maximization (ML-EM) become the standard for the reconstruction in emission computed tomography. However, such algorithms are sensitive to noise artifacts so that the reconstruction begins to degrade when the number of iterations reaches a certain value. In this paper, we have investigated a new iterative algorithm for penalized-likelihood image reconstruction that uses the fuzzy nonlinear anisotropic diffusion (AD) as a penalty function. The proposed algorithm does not suffer from the same problem as that of ML-EM algorithm, and it converges to a low noisy solution even if the iteration number is high. The fuzzy reasoning instead of a nonnegative monotonically decreasing function was used to calculate the diffusion coefficients which control the whole diffusion. Thus, the diffusion strength is controlled by fuzzy rules expressed in a linguistic form. The proposed method makes use of the advantages of fuzzy set theory in dealing with uncertain problems and nonlinear AD techniques in removing the noise as well as preserving the edges. Quantitative analysis shows that the proposed reconstruction algorithm is suitable to produce better reconstructed images when compared with ML-EM, ordered subsets EM (OS-EM), Gaussian-MAP, MRP, TV-EM reconstructed images.


Fuzzy Nonlinear anisotropic diffusion Positron emission tomography (PET) Image reconstruction Maximum likelihood-expectation maximization (ML-EM) 



This work was supported by National Basic Research Program of China under grant No. 2003CB716102 and Program for New Century Excellent Talents in University under grant No. NCET-04-0477. It has been carried out in the frame of the CRIBs, a joint international laboratory associating Southeast University, the University of Rennes 1 and INSERM, with a grant provided by the French Consulate in Shanghai. We thank the anonymous referees for their careful review and valuable comments to improve the quality of the paper.


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Copyright information

© International Federation for Medical and Biological Engineering 2006

Authors and Affiliations

  • Hongqing Zhu
    • 1
    • 4
  • Huazhong Shu
    • 1
    • 3
  • Jian Zhou
    • 1
    • 3
  • Christine Toumoulin
    • 2
    • 3
  • Limin Luo
    • 1
    • 3
  1. 1.Laboratory of Image Science and Technology, Department of Computer Science and EngineeringSoutheast UniversityNanjingPeople’s Republic of China
  2. 2.Laboratoire Traitement du Signal et de l’ImageUniversité de Rennes I – INSERM U642RennesFrance
  3. 3.Centre de Recherche en Information Biomédicale Sino-français (CRIBs)Rennes CedexFrance
  4. 4.ShanghaiPeople’s Republic of China

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