# Deep-Learning-Based Framework for PET Image Reconstruction from Sinogram Domain
## 1 Introduction  
Positron emission tomography (PET) is an in vivo nuclear medicine imaging technique that is widely used in clinical trials and medical practice. Over several years, much effort has been devoted to promoting the wider application of PET in clinical and scientific research and enhancing PET imaging quality. In addition to improving the performance of PET imaging and acquisition systems, researchers have mainly focused on developing algorithms for image reconstruction. In PET, the raw tomographic data are typically stored in projection data histograms called sinograms, which cannot be interpreted directly by observers but can be shown through the projection-slice theorem, which can be mapped to images that reveal the radioactivity concentration distribution. However, owing to random noise in the data, PET image reconstruction is an ill-posed inverse problem [1]. Many solutions have been proposed to address this problem. In addition to the traditional analytic method, i.e., filtered backprojection (FBP) [2], various iterative strategies based on statistical data models have been widely used. The maximum-likelihood expectation maximum (MLEM) [3] is a classic iterative method that has a remarkable antinoise ability, but it also features slow convergence and has a large computational requirement. Compared with the MLEM, the maximum a posteriori (MAP) method [4] adds penalty terms that preserve regional smoothness and sharp variations of edges. Several studies attempted to design penalty terms using low-rank constraints [5], total variation (TV) [6], spatiotemporal spline modeling [7], tracer kinetics, and signal subspaces [8]. Regardless of the method chosen, it is necessary to assume a statistical model that produces a distribution close to the real data distribution,but there may be inconsistencies, and the difference between the two distributions causes a deviation between the reconstructed and real images. In addition, the system matrix plays an important role in these methods. To eliminate the dependence on hypothetical models and system matrices and reduce the complexity of the artificial setting and parameter training, the deep learning based image reconstruction as a promising option can be investigated to reconstruct from the sinogram data directly. In recent years, deep learning has demonstrated promising potential in the field of medical image reconstruction [9; 10; 11; 12] and has successfully generated high-quality images for PET [13; 14; 15]. Current medical image reconstruction methods using deep learning can be broadly classified into two categories: (category A) those achieving reconstruction from image domain to image domain and (category B) those completing reconstruction from the sinogram domain to the image domain. In recent years, there have been interesting changes in the approach and research of deep learning in image-to-image work. Deep learning was primarily used for postprocessing [16] or for accelerating [17; 18] the reconstruction task. [PERSON] et al. [19] used a deep convolutional neural network (CNN) to remove noise from low-dose computed tomography images. [PERSON] et al. [20] designed an offline CNN to accelerate the reconstruction of magnetic resonance images. [PERSON] et al. [21] proposed a cascaded CNN to remove the artifacts induced by denoising. As deep learning has achieved satisfactory results in image processing [22; 23], many researchers have attempted to introduce deep learning in PET image processing [24; 25; 26]. Of which most of the works belong to category A. [PERSON] et al. [27] proposed a framework combining a residual convolutional network with MLEM, and the dynamic data of prior patients were used to train a network for PET denoising. [PERSON] et al. [15] combined a denoising CNN with a local linear fitting function and trained the network using full-dose images as the ground truth and low-dose images reconstructed from downsampled data as the input.