Diffuse optical tomography (DOT) employs near-infrared light to reveal the optical parameters of biological tissues. Due to the strong scattering of photons in tissues and the limited surface measurements, DOT reconstruction is severely ill-posed. The Levenberg-Marquardt (LM) is a popular iteration method for DOT, however, it is computationally expensive and its reconstruction accuracy needs improvement. In this study, we propose a neural model based iteration algorithm which combines the graph neural network with Levenberg-Marquardt (GNNLM), which utilizes a graph data structure to represent the finite element mesh. In order to verify the performance of the graph neural network, two GNN variants, namely graph convolutional neural network (GCN) and graph attention neural network (GAT) were employed in the experiments. The results showed that GCNLM performs best in the simulation experiments within the training data distribution. However, GATLM exhibits superior performance in the simulation experiments outside the training data distribution and real experiments with breast-like phantoms. It demonstrated that the GATLM trained with simulation data can generalize well to situations outside the training data distribution without transfer training. This offers the possibility to provide more accurate absorption coefficient distributions in clinical practice.
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