The significant statistical noise and limited spatial resolution of positron emission tomography (PET) data in sinogram space results in the degradation of the quality and accuracy of reconstructed images. Although high-dose radiotracers and long acquisition times improve the PET image quality, the patients’ radiation exposure increases and the patient is more likely to move during the PET scan. Recently, various data-driven techniques based on supervised deep neural network learning have made remarkable progress in reducing noise in images. However, these conventional techniques require clean target images that are of limited availability for PET denoising. Therefore, in this study, we utilized the Noise2Noise framework, which requires only noisy image pairs for network training, to reduce the noise in the PET images. A trainable wavelet transform was proposed to improve the performance of the network. The proposed network was fed wavelet-decomposed images consisting of low- and high-pass components. The inverse wavelet transforms of the network output produced denoised images. The proposed Noise2Noise filter with wavelet transforms outperforms the original Noise2Noise method in the suppression of artefacts and preservation of abnormal uptakes. The quantitative analysis of the simulated PET uptake confirms the improved performance of the proposed method compared with the original Noise2Noise technique. In the clinical data, 10 s images filtered with Noise2Noise are virtually equivalent to 300 s images filtered with a 6 mm Gaussian filter. The incorporation of wavelet transforms in Noise2Noise network training results in the improvement of the image contrast. In conclusion, the performance of Noise2Noise filtering for PET images was improved by incorporating the trainable wavelet transform in the self-supervised deep learning framework.

The lack of physically measured attenuation maps (μ-maps) for attenuation and scatter correction is an important technical challenge in brain-dedicated stand-alone positron emission tomography (PET) scanners. The accuracy of the calculated attenuation correction is limited by the nonuniformity of tissue composition due to pathologic conditions and the complex structure of facial bones. The aim of this study is to develop an accurate transmission-less attenuation correction method for amyloid-β (Aβ) brain PET studies. We investigated the validity of a deep convolutional neural network trained to produce a CT-derived μ-map (μ-CT) from simultaneously reconstructed activity and attenuation maps using the MLAA (maximum likelihood reconstruction of activity and attenuation) algorithm for Aβ brain PET. The performance of three different structures of U-net models (2D, 2.5D, and 3D) were compared. The U-net models generated less noisy and more uniform μ-maps than MLAA μ-maps. Among the three different U-net models, the patch-based 3D U-net model reduced noise and cross-talk artifacts more effectively. The Dice similarity coefficients between the μ-map generated using 3D U-net and μ-CT in bone and air segments were 0.83 and 0.67. All three U-net models showed better voxel-wise correlation of the μ-maps compared to MLAA. The patch-based 3D U-net model was the best. While the uptake value of MLAA yielded a high percentage error of 20% or more, the uptake value of 3D U-nets yielded the lowest percentage error within 5%. The proposed deep learning approach that requires no transmission data, anatomic image, or atlas/template for PET attenuation correction remarkably enhanced the quantitative accuracy of the simultaneously estimated MLAA μ-maps from Aβ brain PET.