Image reconstruction of fluorescent molecular tomography based on the tree structured Schur complement decomposition

Abstract

BackgroundThe 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.MethodsThe 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.ResultsSimulation 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.ConclusionsThe methods proposed in this paper can significantly improve the reconstructed image quality of FMT and accelerate the reconstruction process.

Adaptive monotone fast iterative shrinkage thresholding algorithm for fluorescence molecular tomography

“…Different ways can be used to obtain solutions to (1), among which the FEM is a representative one with flexibilities to deal with irregular boundaries [14]. In the framework of FEM, the domain Ω is divided into P elements and joined at N vertex nodes.…”