中国物理B ›› 2015, Vol. 24 ›› Issue (10): 104204-104204.doi: 10.1088/1674-1056/24/10/104204

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇    下一篇

An iterative virtual projection method to improve the reconstruction performance for ill-posed emission tomographic problems

柳华蔚, 郑树, 周怀春   

  1. Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China
  • 收稿日期:2015-01-11 修回日期:2015-05-13 出版日期:2015-10-05 发布日期:2015-10-05
  • 基金资助:
    Project supported by the China National Funds for Distinguished Young Scientists of National Natural Science Foundation of China (Grant No. 51025622), the National Natural Science Foundation of China (Grant No. 51406095), and the 100 Top Talents Program of Tsinghua University, Beijing, China (2011).

An iterative virtual projection method to improve the reconstruction performance for ill-posed emission tomographic problems

Liu Hua-Wei (柳华蔚), Zheng Shu (郑树), Zhou Huai-Chun (周怀春)   

  1. Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China
  • Received:2015-01-11 Revised:2015-05-13 Online:2015-10-05 Published:2015-10-05
  • Contact: Zhou Huai-Chun E-mail:hczh@mail.tsinghua.edu.cn
  • Supported by:
    Project supported by the China National Funds for Distinguished Young Scientists of National Natural Science Foundation of China (Grant No. 51025622), the National Natural Science Foundation of China (Grant No. 51406095), and the 100 Top Talents Program of Tsinghua University, Beijing, China (2011).

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摘要： In order to improve the reconstruction performance for ill-posed emission tomographic problems with limited projections, a generalized interpolation method is proposed in this paper, in which the virtual lines of projection are fabricated from, but not linearly dependent on, the measured projections. The method is called the virtual projection (VP) method. Also, an iterative correction method for the integral lengths is proposed to reduce the error brought about by the virtual lines of projection. The combination of the two methods is called the iterative virtual projection (IVP) method. Based on a scheme of equilateral triangle plane meshes and a six asymmetrically arranged detection system, numerical simulations and experimental verification are conducted. Simulation results obtained by using a non-negative linear least squares method, without any other constraints or regularization, demonstrate that the VP method can gradually reduce the reconstruction error and converges to the desired one by fabricating additional effective projections. When the mean square deviation of normal error superimposed on the simulated measured projections is smaller than 0.03, i.e., the signal-to-noise ratio (SNR) for the measured projections is higher than 30.4, the IVP method can further reduce the reconstruction error reached by the VP method apparently. In addition, as the regularization matrix in the Tikhonov regularization method is updated by an iterative correction process similar to the IVP method presented in this paper, or the Tikhonov regularization method is used in the IVP method, good improvement is achieved.

关键词: ill-posed problem, emission tomography, limited projections, Tikhonov regularization

Abstract: In order to improve the reconstruction performance for ill-posed emission tomographic problems with limited projections, a generalized interpolation method is proposed in this paper, in which the virtual lines of projection are fabricated from, but not linearly dependent on, the measured projections. The method is called the virtual projection (VP) method. Also, an iterative correction method for the integral lengths is proposed to reduce the error brought about by the virtual lines of projection. The combination of the two methods is called the iterative virtual projection (IVP) method. Based on a scheme of equilateral triangle plane meshes and a six asymmetrically arranged detection system, numerical simulations and experimental verification are conducted. Simulation results obtained by using a non-negative linear least squares method, without any other constraints or regularization, demonstrate that the VP method can gradually reduce the reconstruction error and converges to the desired one by fabricating additional effective projections. When the mean square deviation of normal error superimposed on the simulated measured projections is smaller than 0.03, i.e., the signal-to-noise ratio (SNR) for the measured projections is higher than 30.4, the IVP method can further reduce the reconstruction error reached by the VP method apparently. In addition, as the regularization matrix in the Tikhonov regularization method is updated by an iterative correction process similar to the IVP method presented in this paper, or the Tikhonov regularization method is used in the IVP method, good improvement is achieved.

Key words: ill-posed problem, emission tomography, limited projections, Tikhonov regularization

中图分类号:  (Image reconstruction; tomography)

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