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

Abstract

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 (λ-MLAA) and attenuation map (μ-MLAA) based on the PET raw data only. However, μ-MLAA suffers from high noise and λ-MLAA suffers from large bias as compared to the reconstruction using the CT-based attenuation map (μ-CT). Recently, a convolutional neural network (CNN) was applied to predict the CT attenuation map (μ-CNN) from λ-MLAA and μ-MLAA, in which an image-domain loss (IM-loss) function between the μ-CNN and the ground truth μ-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 (μ) along the path of the two annihilation events, instead of the μ itself, is used for AC. Therefore, a network trained with the IM-loss may yield suboptimal performance in the μ generation. Here, we propose a novel line-integral projection loss (LIP-loss) function that incorporates the PET attenuation physics for μ generation. Eighty training and twenty testing datasets of whole-body 18 F-FDG PET and paired ground truth μ-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.

Deep-JASC: joint attenuation and scatter correction in whole-body 18F-FDG PET using a deep residual network

“…They reported the average voxel-wise RE 12.82% ± 2.45%, 5.61% ± 0.68% and 2.05% ± 1.51% for MLAA based AC, four segment-based AC and deep learning-based AC, respectively. Shi et al [39] proposed a line-integral projection loss (LIPloss) function that incorporates the physics of PET attenuation into attenuation map generation. They reported a MAE of 21.4%, 7.8%, 9.4%, 9.2% and 11.26% for MLAA; 3.5%, 4.2%, 4.8%, 4.4% and 4.1% for the deep learning method; and 3.2%, 3.7%, 4.1%, 3.6% and 3.6% for Deep-LIP in the head, neck/chest, abdomen, pelvis and whole-body regions, respectively.…”

A Review of Deep-Learning-Based Approaches for Attenuation Correction in Positron Emission Tomography

“…In the applications that do not require detailed anatomical information provided by CT, emission-only approaches, as described in the following sections, are effective for the realization of extremely low-dose studies. In particular, the DLbased conversion of non-attenuation-corrected PET to attenuation-corrected PET [29][30][31][32][33], in addition to the DLenhanced simultaneous activity and attenuation reconstruction [25][26][27][28], are suitable.…”

“…Alternative approaches are as follows: the derivation of pseudo-CT or attenuation-corrected PET images from non-attenuationcorrected (NAC) PET, and the improvement of the outputs of simultaneous activity and attenuation reconstruction using DL [25][26][27][28][29][30][31][32][33].…”

“…Another approach to improve the DL-enhanced MLAA is applying acquisition physics-based additional constraints in the projection domain of the μ-map. Shi et al enforced the similarity in the projection domain between the predicted and CT-based μ-maps based on the fact that the line integral of the attenuation coefficient along the LOR is used for AC instead of attenuation coefficient itself [25]. By adding the loss function that measures the line-integral difference between predicted and CT-based patches (projection domain) to the loss function that measures image intensity and gradient differences (image domain), more accurate μ-maps and corrected PET images could be obtained.…”

“…Many DL studies were focused on the transformation of MR images into a synthetic pseudo-CT or μ-map [34][35][36][37][38][39][40][41][42][43][44]52]. Other approaches that are not dependent on the anatomical images (CT or MRI) can overcome limitations with respect to current CT-and MRI-based ACs and allow for more accurate PET quantification in stand-alone PET scanners for the realization of low radiation doses [25][26][27][28][29][30][31][32][33].…”