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

arXiv: https://arxiv.org/abs/1909.01394 · HTML: https://mlsanity.com/paper/1909.01394/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2019.

## Built on by (most cited first, 4 of 4)

- [Physics-driven Deep Learning for PET/MRI](https://mlsanity.com/paper/2206.06788/) (2022)
- [TAI-GAN: A Temporally and Anatomically Informed Generative Adversarial Network for early-to-late frame conversion in dynamic cardiac PET inter-frame motion correction](https://mlsanity.com/paper/2402.09567/) (2024)
- [PC-UNet: An Enforcing Poisson Statistics U-Net for Positron Emission Tomography Denoising](https://mlsanity.com/paper/2510.14995/) (2025)
- [Geometry-anchored PET-aware multimodal pseudo-CT synthesis for whole-body attenuation correction: the BIC-MAC Challenge](https://mlsanity.com/paper/2609.27848/) (2026)

## Abstract (arXiv)

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 18F-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.