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：本文针对一种称为康普顿成像仪（Compton imager）的康普顿成像系统，提出了一种统计正向模型。该系统由伊利诺伊大学厄巴纳-香槟分校研发，是康普顿相机的一种变体，采用单一类型传感器，可同时作为散射体和吸收体，适用于需要宽视场的成像场景。基于所提出的统计正向模型，我们解决了从观测数据中估计点状源位置与能量的反问题。该反问题在贝叶斯框架下构建并求解，采用吉布斯采样中的Metropolis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，该方法不仅能实现更精确的估计，还在低光子成像场景中具备不确定性量化的额外优势。