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1. The properties of the positronium lifetime image reconstruction based on maximum likelihood estimation

   https://doi.org/10.5604/01.3001.0054.1807  

   Chen, Zhuo; An, Lingling; Kao, Chien-Min; Huang, Hsin-Hsiung (December 2023, Bio-Algorithms and Med-Systems)

   The positronium lifetime imaging (PLI) reconstruction is a technique used in time-of-flight (TOF) positron emission tomography (PET) imaging that involves measuring the lifespan of positronium, which is a metastable electron-positron pair that arises when a PET molecule releases a positron, prior to its annihilation. We have previously developed a maximum likelihood (ML) algorithm for PLI reconstruction and demonstrated that it can generate quantitatively accurate lifetime images for a 570 ps (pico-seconds) TOF PET system. In this study, we conducted further investigations into the statistical properties of the algorithm, including the variability of the reconstruction results, the sensitivity of the algorithm to the number of acquired PLI events and its robustness to hyperparameter choices. Our findings indicate that the proposed ML method produces sufficiently stable lifetime images to enable reliable distinction of regions of interest. Moreover, the number of PLI events required to produce quantitatively accurate lifetime images is computationally plausible. These results demonstrate the potential of our ML algorithm for advancing the capabilities of TOF PET imaging. 

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2. Enhanced positronium lifetime imaging through two-component reconstruction in time-of-flight positron emission tomography

   https://doi.org/10.3389/fphy.2024.1429344  

   Chen, Zhuo; Kao, Chien-Min; Huang, Hsiun-Hsiung; An, Lingling (July 2024, Frontiers in Physics)

   Positronium lifetime imaging (PLI) is a newly demonstrated technique possible with time-of-flight (TOF) positron emission tomography (PET), capable of producing an image reflecting the lifetime of the positron, more precisely ortho-positronium (o-Ps), before annihilation, in addition to the traditional uptake image of the PET tracer. Due to the limited time resolution of TOF-PET systems and the added complexities in physics and statistics, lifetime image reconstruction presents a challenge. Recently, we described a maximum-likelihood approach for PLI by considering only o-Ps. In real-world scenarios, other populations of positrons that exhibit different lifetimes also exist. This paper introduces a novel two-component model aimed at enhancing the accuracy of o-Ps lifetime images. Through simulation studies, we compare this new model with the existing single-component model and demonstrate its superior performance in accurately capturing complex lifetime distributions. 

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3. An Integral Equation Model for PET Imaging

   Tang, Xinhuang; Schmidtlein, Charles Ross; Li, Si; Xu, Yuesheng (January 2021, International journal of numerical analysis and modeling)

   Positron emission tomography (PET) is traditionally modeled as discrete systems. Such models may be viewed as piecewise constant approximations of the underlying continuous model for the physical processes and geometry of the PET imaging. Due to the low accuracy of piecewise constant approximations, discrete models introduce an irreducible modeling error which fundamentally limits the quality of reconstructed images. To address this bottleneck, we propose an integral equation model for the PET imaging based on the physical and geometrical considerations, which describes accurately the true coincidences. We show that the proposed integral equation model is equivalent to the existing idealized model in terms of line integrals which is accurate but not suitable for numerical approximation. The proposed model allows us to discretize it using higher accuracy approximation methods. In particular, we discretize the integral equation by using the collocation principle with piecewise linear polynomials. The discretization leads to new ill-conditioned discrete systems for the PET reconstruction, which are further regularized by a novel wavelet-based regularizer. The resulting non-smooth optimization problem is then solved by a preconditioned proximity fixed-point algorithm. Convergence of the algorithm is established for a range of parameters involved in the algorithm. The proposed integral equation model combined with the discretization, regularization, and optimization algorithm provides a new PET image reconstruction method. Numerical results reveal that the proposed model substantially outperforms the conventional discrete model in terms of the consistency to simulated projection data and reconstructed image quality. This indicates that the proposed integral equation model with appropriate discretization and regularizer can significantly reduce modeling errors and suppress noise, which leads to improved image quality and projection data estimation. 

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4. Dynamic low-count PET image reconstruction using spatio-temporal primal dual network

   Hu R.; Cui J.; Li C.; Yu C.; Chen Y.; Liu H. (October 2023, Physics in medicine and biology)

   Objective. Dynamic positron emission tomography (PET) imaging, which can provide information on dynamic changes in physiological metabolism, is now widely used in clinical diagnosis and cancer treatment. However, the reconstruction from dynamic data is extremely challenging due to the limited counts received in individual frame, especially in ultra short frames. Recently, the unrolled modelbased deep learning methods have shown inspiring results for low-count PET image reconstruction with good interpretability. Nevertheless, the existing model-based deep learning methods mainly focus on the spatial correlations while ignore the temporal domain. Approach. In this paper, inspired by the learned primal dual (LPD) algorithm, we propose the spatio-temporal primal dual network (STPDnet) for dynamic low-count PET image reconstruction. Both spatial and temporal correlations are encoded by 3D convolution operators. The physical projection of PET is embedded in the iterative learning process of the network, which provides the physical constraints and enhances interpretability. Main results. The experiments of both simulation data and real rat scan data have shown that the proposed method can achieve substantial noise reduction in both temporal and spatial domains and outperform the maximum likelihood expectation maximization, spatio-temporal kernel method, LPD and FBPnet. Significance. Experimental results show STPDnet better reconstruction performance in the low count situation, which makes the proposed method particularly suitable in whole-body dynamic imaging and parametric PET imaging that require extreme short frames and usually suffer from high level of noise. 

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5. Structure and Tracer Kinetics-Driven Dynamic PET Reconstruction

   https://doi.org/10.1109/TRPMS.2019.2947860  

   Cui, Jianan; Qin, Zhongya; Chen, Shuhang; Chen, Yunmei; Liu, Huafeng (October 2019, IEEE transactions on radiation and plasma medical sciences)

   Dynamic positron emission tomography (dPET) is a nuclear medical imaging technology that shows the changes in radioactivity over time. In this article, we propose a structure and tracer kinetics-constrained reconstruction framework for dPET imaging. Given the Poisson nature of PET imaging, we integrate the sparse penalty on a dual dictionary into a Poisson-likelihood estimator. Explicit anatomical constraints with a structural dictionary constructed from magnetic resonance or computed tomography images are employed to take advantage of the anatomical imaging modalities. In the kinetic dictionary, we treat tracer kinetics as random variables in a physiologically plausible range based on a compartmental model. We demonstrate the performance of our proposed framework with a direct simulated data set and real patient data. 

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