Molecular Imaging and Biology

, Volume 20, Issue 1, pp 37–46 | Cite as

Sparse Reconstruction of Fluorescence Molecular Tomography Using Variable Splitting and Alternating Direction Scheme

  • Jinzuo Ye
  • Yang Du
  • Yu An
  • Yamin Mao
  • Shixin Jiang
  • Wenting Shang
  • Kunshan He
  • Xin Yang
  • Kun WangEmail author
  • Chongwei ChiEmail author
  • Jie TianEmail author
Research Article



Fluorescence molecular tomography (FMT) is a novel imaging modality for three-dimensional preclinical research and has many potential applications for drug therapy evaluation and tumor diagnosis. However, FMT presents an ill-conditioned and ill-posed inverse problem, which is a challenge for its tomography reconstruction. Due to the importance of FMT reconstruction, it is valuable and necessary to develop further practical reconstruction methods for FMT.


In this study, an efficient method using variable splitting strategy as well as alternating direction strategy (VSAD) was proposed for FMT reconstruction. In this method, the variable splitting strategy and the augmented Lagrangian function were first introduced to obtain an equivalent optimization formulation of the original problem. Then, the alternating direction scheme was used to solve the optimization problem and to accelerate its convergence. To examine the property of the VSAD method, three numerical simulation experiments (accuracy assessment experiment, robustness assessment experiment, and reconstruction speed assessment experiment) were performed and analyzed.


The results indicated that the reconstruction accuracy, the reconstruction robustness, and the reconstruction speed of FMT were satisfactory by using the proposed VSAD method. Two in vivo studies, which were conducted by using two nude mouse models, further confirmed the advantages of the proposed method.


The results indicated that the proposed VSAD algorithm is effective for FMT reconstruction. It was accurate, robust, and efficient for FMT imaging and was feasibly applied for in vivo FMT applications.

Key words

Fluorescence molecular tomography Reconstruction Variable splitting Alternating direction scheme In vivo imaging 



This paper is supported by the National Basic Research Program of China (973 Program) under Grant No. 2015CB755500, the National Natural Science Foundation of China under Grant Nos. 81227901, 81527805, 61231004, 81470083, 61671449, 61501462, and 81501594, and the Scientific Research and Equipment Development Project of Chinese Academy of Sciences under Grant No. YZ201457.

Compliance with Ethical Standards

Conflict of Interest

The authors declare no conflict of interests.

Supplementary material

11307_2017_1088_MOESM1_ESM.pdf (705 kb)
ESM 1 (PDF 704 kb).


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Copyright information

© World Molecular Imaging Society 2017

Authors and Affiliations

  1. 1.CAS Key Laboratory of Molecular Imaging, Institute of AutomationChinese Academy of SciencesBeijingChina
  2. 2.The State Key Laboratory of Management and Control for Complex System, Institute of AutomationChinese Academy of SciencesBeijingChina
  3. 3.The Department of Biomedical Engineering, School of Computer and Information TechnologyBeijing Jiaotong UniversityBeijingChina

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