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Tomographic reconstruction from a small number of projections by an efficient sum-product reasoning method

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Abstract

Tomographic reconstruction from a small number of projections is still a challenging problem. In the paper, we formulate this problem as a statistical graphical model by the smooth assumption that the image has a structure where neighbor pixels have a larger probability to take a closer value. This Markov random filed framework allows easily integrating other prior information. Reasoning in the model can be solved using belief propagation algorithm. However, one projection line involves multiple pixels. This leads to high order cliques and exponential computation in the message passing procedure. A variable-change strategy is used to largely reduce the computation and forms an efficient sum-product reasoning algorithm. Numerical simulation examples show that the proposed method greatly surpasses traditional methods, such as FBP, EM and ART. Our method is suitable not only for the case of a very small amount of projection, but also for the multi-pixel-value case.

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Acknowledgments

This research is supported in part by the National Natural Science Foundation of China under Contracts No. 61027014 and No. 61203184. The authors would also like to thank the anonymous reviewers.

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Authors and Affiliations

  1. Shenzhen Key Laboratory of Micro-Nano Photonic Information Technology, Shenzhen University, 3688, Nanhai Ave, Shenzhen, 518060, China

    Wenwen Zeng, Jingzhen Li & Yupeng Fan

  2. Shenzhen Key Laboratory of Electromagnetic Control, Shenzhen University, 3688 Nanhai Ave, Shenzhen, 518060, China

    Xiaopin Zhong

  3. College of Optoelectronic Engineering, Shenzhen University, 3688 Nanhai Ave, Shenzhen, 518060, China

    Wenwen Zeng & Yupeng Fan

Authors
  1. Wenwen Zeng
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  2. Xiaopin Zhong
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  3. Jingzhen Li
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  4. Yupeng Fan
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Corresponding author

Correspondence to Xiaopin Zhong.

Additional information

Communicated by Cristina Turner.

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Zeng, W., Zhong, X., Li, J. et al. Tomographic reconstruction from a small number of projections by an efficient sum-product reasoning method. Comp. Appl. Math. 36, 1559–1575 (2017). https://doi.org/10.1007/s40314-016-0313-0

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  • DOI: https://doi.org/10.1007/s40314-016-0313-0

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