Model-based graph convolutional network for diffuse optical tomography

Diffuse optical tomography (DOT) is a promising non-invasive optical imaging technology that can provide functional information of biological tissues. Since the diffused light undergoes multiple scattering in biological tissues, and the boundary measurements are limited, the inverse problem of DOT is ill-posed and ill-conditioned. To overcome these limitations, inverse problems in DOT are often mitigated using regularization techniques, which use data fitting and regularization terms to suppress the effects of measurement noise and modeling errors. Tikhonov regularization, utilizing the L2 norm as its regularization term, often leads to images that are excessively smooth. In recent years, with the continuous development of deep learning algorithms, many researchers have used Model-based deep learning methods for reconstruction. However, the reconstruction of DOT is solved on mesh, arising from a finite element method for inverse problems, it is difficult to use it directly for convolutional network. Therefore, we propose a model-based graph convolutional network (Model-GCN). Overall, Model-GCN achieves better image reconstruction results compared to Tikhonov, with lower absolute bias error (ABE). Specifically, for total hemoglobin (HbT) and water, the average reduction in ABE is 68.3% and 77.3%, respectively. Additionally, the peak signal-to-noise (PSNR) values are on average increased by 6.4dB and 7.0dB.