This paper presents a statistical forward model for a Compton imaging system, called Compton imager. This system, under development at the University of Illinois Urbana Champaign, is a variant of Compton cameras with a single type of sensors which can simultaneously act as scatterers and absorbers. This imager is convenient for imaging situations requiring a wide field of view. The proposed statistical forward model is then used to solve the inverse problem of estimating the location and energy of point-like sources from observed data. This inverse problem is formulated and solved in a Bayesian framework by using a Metropolis within Gibbs algorithm for the estimation of the location, and an expectation-maximization algorithm for the estimation of the energy. This approach leads to more accurate estimation when compared with the deterministic standard back-projection approach, with the additional benefit of uncertainty quantification in the low photon imaging setting.

翻译：本文提出了一种针对康普顿成像系统（称为Compton imager）的统计正演模型。该系统由伊利诺伊大学厄巴纳-香槟分校开发，是康普顿相机的一种变体，采用单一类型传感器，可同时充当散射体和吸收体。该成像仪适用于需要宽视场的成像场景。所提出的统计正演模型被用于解决从观测数据中估计点状源位置和能量的反问题。该反问题在贝叶斯框架下进行表述和求解，通过使用Metropolis within Gibbs算法估计位置，并使用期望最大化算法估计能量。与确定性标准反投影方法相比，该方法能够实现更准确的估计，且在低光子成像场景中具有不确定性量化的额外优势。