A Novel Loss Function Incorporating Imaging Acquisition Physics for PET Attenuation Map Generation Using Deep Learning

In PET/CT imaging, CT is used for PET attenuation correction (AC). Mismatch between CT and PET due to patient body motion results in AC artifacts. In addition, artifact caused by metal, beam-hardening and count-starving in CT itself also introduces inaccurate AC for PET. Maximum likelihood reconstruction of activity and attenuation (MLAA) was proposed to solve those issues by simultaneously reconstructing tracer activity (lambda-MLAA) and attenuation map (mu-MLAA) based on the PET raw data only. However, mu-MLAA suffers from high noise and lambda-MLAA suffers from large bias as compared to the reconstruction using the CT-based attenuation map (mu-CT). Recently, a convolutional neural network (CNN) was applied to predict the CT attenuation map (mu-CNN) from lambda-MLAA and mu-MLAA, in which an image-domain loss (IM-loss) function between the mu-CNN and the ground truth mu-CT was used. However, IM-loss does not directly measure the AC errors according to the PET attenuation physics, where the line-integral projection of the attenuation map (mu) along the path of the two annihilation events, instead of the l itself, is used for AC. Therefore, a network trained with the IM-loss may yield suboptimal performance in the mu generation. Here, we propose a novel line-integral projection loss (LIP-loss) function that incorporates the PET attenuation physics for mu generation. Eighty training and twenty testing datasets of whole-body F-18-FDG PET and paired ground truth mu-CT were used. Quantitative evaluations showed that the model trained with the additional LIP-loss was able to significantly outperform the model trained solely based on the IM-loss function.