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.
Highlights
The inverse problem of fluorescent molecular tomography (FMT) often involves complex large-scale matrix operations, which may lead to unacceptable computational errors and complexity
There has been increasing interest in the molecularly-based medical imaging method, such as fluorescent molecular tomography (FMT) [2,3,4], in which the injected fluorophore may accumulate in diseased tissue
The subspace created from the right singular vectors of the singular value decomposition (SVD) is optimal
Summary
Images of μaxf for two objects phantom using the different algorithms, from which it can be seen that the proposed method can reconstruct the images more accurately than the other two methods even after the first iteration. From this table, it can be seen that the time needed for our algorithm after 30 iterations is less than that of the Schur CG method. To further validate the proposed algorithm for 3D reconstruction, a phantom as illustrated in Figure 11 is used for simulations. Above two methods for a quantitative comparison From this table, we can conclude that our proposed algorithm can speed up the reconstruction process and achieve high accuracy for the 3D case
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