# Dual-Tracer PET Image Separation by Deep Learning: A Simulation Study
## 1 Introduction  
Positron emission tomography (PET) is a potent functional molecular imaging technology having applications to the imaging of the heart [1], brain [2] and cancer [3]. Conventional PET scans rely on imaging a single tracer to provide detailed functional or molecular imaging information typically connected to disease, meaning that images of different processes can only be acquired separately through multiple scans, e.g., a 18F-fluorodeoxyglucose ([18]FDG) PET scan to examine glucose metabolism and a subsequent separate 11C-methionine ([19]MET) scan to image protein synthesis to determine the boundaries of a brain tumour [4, 5]. With multiplexed PET imaging, multiple targets of interest for different tracers can be observed simultaneously in a single scan, providing complementary information for clinical decision making [6, 7, 8, 9]. Additionally, using multi-tracers in a single PET scan was thought to be beneficial for shortening the examination time and thereby improving diagnostic efficiency [10]. Multiplexed PET involves injecting different tracers with an offset of several minutes or even simultaneously and recovering the dynamic/static imaging measurements of each individual tracer in a single PET scan. To the best of our knowledge, the initial proof-of-principle of such an approach, has been applied to studies with phantom [11], simulated brain imaging [12] and cardiac imaging [13]. The main challenge with simultaneous multiplexed PET imaging, however, is that positrons from the PET radionuclides will emit 511 keV photon pairs when they annihilate with electrons, resulting in no unique energyinformation for identifying or differentiating the source of each photon pair. As a result, the PET scanner measures the sum of the PET signals of all tracers [14]. Several dual-tracer separation methods based on staggered injection protocols and dynamic imaging techniques have been proposed. [PERSON] et al. [11] initially considered separating dual-tracer signals based on the difference in physical decay rates of tracers. A feasibility study of this method in small animals employing \([^{18}\)F]FDG and \([^{13}\)N]NH\({}_{4}^{+}\) was shown in [15]. Further investigations of this method were also conducted and presented in [6; 16]. However, this method requires significant differences between the half-lives of the two tracers. Another widely studied method is based on a parallel multi-tracer compartment model (CM), where the single-tracer signals are separated by fitting the superposed pharmacokinetic models of the corresponding tracers to the time activity curves (TACs) extracted from the reconstructed dynamic dual-tracer PET images; see Section 3.3 for details. The CM-based separation method was first introduced in [17] to estimate the kinetic parameters of \([^{11}\)C]-labeled tracers. The feasibility of this method for separating different tracer pairs was examined through simulation [18; 19; 20; 21; 22], animal studies [23; 24] and a three-tracer (\([^{18}\)F]FDG, \([^{62}\)Cu]ATSM and \([^{62}\)Cu]PTSM) separation task [25]. The CM-based method is susceptible to noise and is prone to fall into local minima, leading to inaccurate separation results. Several methods have been proposed to improve the separation quality based on the CM-based method, e.g., separating the linear from the non-linear in the fitting process to reduce the parameter space [26; 27], integrating the spatial and temporal information for dual-tracer separation by incorporating model fitting into the image reconstruction process [28] and simultaneous signal separation and reconstructions based on the dual-tracer kinetic model [29]. However, each of the aforementioned approaches was built on the assumption that the arterial input function (AIF) of each tracer is known, which restricts their practical feasibility. [PERSON] and [PERSON] [30; 31] tackled this problem by using a set of temporal basis functions to model the TACs of each tracer. This temporal model is then incorporated into a global 4D PET reconstruction strategy [32].