Image reconstruction of fluorescent molecular tomography based on the tree structured Schur complement decomposition.
BACKGROUND
The inverse problem of fluorescent molecular tomography (FMT) often involves complex large-scale matrix operations, which may lead to unacceptable computational errors and complexity. In this research, a tree structured Schur complement decomposition strategy is proposed to accelerate the reconstruction process and reduce the computational complexity. Additionally, an adaptive regularization scheme is developed to improve the ill-posedness of the inverse problem.


METHODS
The global system is decomposed level by level with the Schur complement system along two paths in the tree structure. The resultant subsystems are solved in combination with the biconjugate gradient method. The mesh for the inverse problem is generated incorporating the prior information. During the reconstruction, the regularization parameters are adaptive not only to the spatial variations but also to the variations of the objective function to tackle the ill-posed nature of the inverse problem.


RESULTS
Simulation results demonstrate that the strategy of the tree structured Schur complement decomposition obviously outperforms the previous methods, such as the conventional Conjugate-Gradient (CG) and the Schur CG methods, in both reconstruction accuracy and speed. As compared with the Tikhonov regularization method, the adaptive regularization scheme can significantly improve ill-posedness of the inverse problem.


CONCLUSIONS
The methods proposed in this paper can significantly improve the reconstructed image quality of FMT and accelerate the reconstruction process.
Zou
Wei
W
School of Electronics and Information Engineering, Soochow University, Suzhou 215021, China.
Wang
Jiajun
J
Feng
David Dagan
DD
D000042:Absorption; D000465:Algorithms; D020342:Finite Element Analysis; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D019047:Phantoms, Imaging; D012542:Scattering, Radiation; D014054:Tomography / Q000379:methods*