RGMLN:Residual Graph Model Learning Network for Bioluminescence Tomography

For bioluminescence tomography reconstruction, regularization algorithms and deep learning frameworks have been widely studied and achieved impressive results. However, the parameter selection of the regularization algorithm and the poor interpretability of deep learning methods have become the key factors that affect the reconstruction results and hinder its applicability. To mitigate the effects of this problem, in this paper, we proposed a novel residual graph model learning network (RGMLN) for bioluminescence tomography reconstruction by combining the advantages of regularization method and deep learning. RGMLN is based on the inference process of the thresholding iterative shrinkage algorithm. The difference is that the penalty term of the regularization method was replaced by a learnable nonlinear mapping between the residual and source distributions to ensure the interpretability of network. Meanwhile, considering the non-Euclidean property of the finite element mesh, a graph convolution operation based on Laplacian graph theory was conducted to aggregate features of mesh nodes using the topological information of the tetrahedral mesh. Lastly, based on residual learning and auto-encoder strategies, gradient descent and prox mapping modules were designed to structure the model-driven RGMLN method to take advantage of both the interpretability of iterative techniques and the flexibility of learning methods. Both numerical and in vivo experiments confirmed that the proposed network has excellent positioning accuracy and can be applied to different meshes and wavelengths.