title: An adaptive regularization parameter choice strategy for multispectral bioluminescence tomography.
abstract: OBJECTIVE
  Bioluminescence tomography (BLT) provides an effective tool for monitoring physiological and pathological activities in 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 as l(2) 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 and in 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.
authors: The College of Electronic Information and Control Engineering, Beijing University of Technology, Beijing, China.
authors: Jinchao
authors: J
authors: Feng
authors: Chenghu
authors: C
authors: Qin
authors: Kebin
authors: K
authors: Jia
authors: Dong
authors: D
authors: Han
authors: Kai
authors: K
authors: Liu
authors: Shouping
authors: S
authors: Zhu
authors: Xin
authors: X
authors: Yang
authors: Jie
authors: J
authors: Tian
mesh_terms: D000465:Algorithms; D000818:Animals; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional; D008163:Luminescent Measurements / Q000379:methods*; D051379:Mice; D019047:Phantoms, Imaging; D014054:Tomography / Q000379:methods*; D014057:Tomography, X-Ray Computed