An adaptive regularization parameter choice strategy for multispectral bioluminescence tomography

Authors

  • Feng Jinchao,

    1. The College of Electronic Information and Control Engineering, Beijing University of Technology, Beijing 100124, China
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    • c)

      Jinchao Feng and Chenghu Qin contributed equally to this paper.

  • Qin Chenghu,

    1. Medical Image Processing Group, Institute of Automation, Chinese Academy of Sciences, P. O. Box 2728, Beijing 100190, China
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    • c)

      Jinchao Feng and Chenghu Qin contributed equally to this paper.

  • Jia Kebin,

    1. The College of Electronic Information and Control Engineering, Beijing University of Technology, Beijing 100124, China
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  • Han Dong,

    1. Medical Image Processing Group, Institute of Automation, Chinese Academy of Sciences, P. O. Box 2728, Beijing 100190, China
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  • Liu Kai,

    1. Medical Image Processing Group, Institute of Automation, Chinese Academy of Sciences, P. O. Box 2728, Beijing 100190, China
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  • Zhu Shouping,

    1. Medical Image Processing Group, Institute of Automation, Chinese Academy of Sciences, P. O. Box 2728, Beijing 100190, China
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  • Yang Xin,

    1. Medical Image Processing Group, Institute of Automation, Chinese Academy of Sciences, P. O. Box 2728, Beijing 100190, China
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  • Tian Jie

    1. Medical Image Processing Group, Institute of Automation, Chinese Academy of Sciences, P. O. Box 2728, Beijing 100190, China and School of Life Sciences and Technology, Xidian University, Xi'an 710071, China
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    • Author to whom correspondence should be addressed. Electronic mail: tian@ieee.org


Abstract

Purpose:

Bioluminescence tomography (BLT) provides an effective tool for monitoring physiological and pathological activitiesin vivo. However, the measured data in bioluminescence imaging are corrupted by noise. Therefore, regularization methods are commonly used to find a regularized solution. Nevertheless, for the quality of the reconstructed bioluminescent source obtained by regularization methods, the choice of the regularization parameters is crucial. To date, the selection of regularization parameters remains challenging. With regards to the above problems, the authors proposed a BLT reconstruction algorithm with an adaptive parameter choice rule.

Methods:

The proposed reconstruction algorithm uses a diffusion equation for modeling the bioluminescent photon transport. The diffusion equation is solved with a finite element method. Computed tomography (CT) images provide anatomical information regarding the geometry of the small animal and its internal organs. To reduce the ill-posedness of BLT, spectral information and the optimal permissible source region are employed. Then, the relationship between the unknown source distribution and multiview and multispectral boundary measurements is established based on the finite element method and the optimal permissible source region. Since the measured data are noisy, the BLT reconstruction is formulated asl2 data fidelity and a general regularization term. When choosing the regularization parameters for BLT, an efficient model function approach is proposed, which does not require knowledge of the noise level. This approach only requests the computation of the residual and regularized solution norm. With this knowledge, we construct the model function to approximate the objective function, and the regularization parameter is updated iteratively.

Results:

First, the micro-CT based mouse phantom was used for simulation verification. Simulation experiments were used to illustrate why multispectral data were used rather than monochromatic data. Furthermore, the study conducted using an adaptive regularization parameter demonstrated our ability to accurately localize the bioluminescent source. With the adaptively estimated regularization parameter, the reconstructed center position of the source was (20.37, 31.05, 12.95) mm, and the distance to the real source was 0.63 mm. The results of the dual-source experiments further showed that our algorithm could localize the bioluminescent sources accurately. The authors then presented experimental evidence that the proposed algorithm exhibited its calculated efficiency over the heuristic method. The effectiveness of the new algorithm was also confirmed by comparing it with the L-curve method. Furthermore, various initial speculations regarding the regularization parameter were used to illustrate the convergence of our algorithm. Finally,in vivo mouse experiment further illustrates the effectiveness of the proposed algorithm.

Conclusions:

Utilizing numerical, physical phantom andin vivo examples, we demonstrated that the bioluminescent sources could be reconstructed accurately with automatic regularization parameters. The proposed algorithm exhibited superior performance than both the heuristic regularization parameter choice method and L-curve method based on the computational speed and localization error.

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