Model-Based Convolution Neural Network for 3D Near-Infrared Spectral Tomography.

Near-infrared spectral tomography (NIRST) is a non-invasive imaging technique that provides functional information about biological tissues. Due to diffuse light propagation in tissue and limited boundary measurements, NIRST image reconstruction presents an ill-posed and ill-conditioned computational problem that is difficult to solve. To address this challenge, we developed a reconstruction algorithm (Model-CNN) that integrates a diffusion equation model with a convolutional neural network (CNN). The CNN learns a regularization prior to restrict solutions to the space of desirable chromophore concentration images. Efficacy of Model-CNN was evaluated by training on numerical simulation data, and then applying the network to physical phantom and clinical patient NIRST data. Results demonstrated the superiority of Model-CNN over the conventional Tikhonov regularization approach and a deep learning algorithm (FC-CNN) in terms of absolute bias error (ABE) and peak signal-to-noise ratio (PSNR). Specifically, in comparison to Tikhonov regularization, Model-CNN reduced average ABE by 55% for total hemoglobin (HbT) and 70% water (H $_{\mathbf {{2}}}$ O) concentration, while improved PSNR by an average of 5.3 dB both for HbT and H $_{\mathbf {{2}}}$ O images. Meanwhile, image processing time was reduced by 82%, relative to the Tikhonov regularization. As compared to FC-CNN, the Model-CNN achieved a 91% reduction in ABE for HbT and 75% for H $_{\mathbf {{2}}}$ O images, with increases in PSNR by 7.3 dB and 4.7 dB, respectively. Notably, this Model-CNN approach was not trained on patient data; but instead, was trained on simulated phantom data with simpler geometrical shapes and optical source-detector configurations; yet, achieved superior image recovery when faced with real-world data.