论文标题
基于康普顿散射的成像：模型 - 不确定性和数据驱动的重建方法
Imaging based on Compton scattering: model-uncertainty and data-driven reconstruction methods
论文作者
论文摘要
闪烁晶体的最新发展与$γ$ -rays的来源相结合，为基于康普顿散射的成像概念开辟了道路，即康普顿散射层析成像（CST）。相关的逆问题引起了许多挑战：非线性，多订单散射和高水平的噪声。这些挑战已经在文献中进行了研究，因此不可避免地会导致前进模型的不确定性。这项工作建议研究精确和近似的远期模型，并开发两种能够应对远期模型不确定的重建算法。第一个基于称为正则化顺序子空间优化（Resesop）的投影方法。我们在这里考虑半分化前向模型的有限维度限制，并显示其适当的性和正则化属性。第二个考虑了无监督的学习方法，即深图像先验（DIP），灵感来自Resesop中模型不确定性的启发。这些方法在蒙特卡洛数据上进行了验证。
The recent development of scintillation crystals combined with $γ$-rays sources opens the way to an imaging concept based on Compton scattering, namely Compton scattering tomography (CST). The associated inverse problem rises many challenges: non-linearity, multiple order-scattering and high level of noise. Already studied in the literature, these challenges lead unavoidably to uncertainty of the forward model. This work proposes to study exact and approximated forward models and develops two data-driven reconstruction algorithms able to tackle the inexactness of the forward model. The first one is based on the projective method called regularized sequential subspace optimization (RESESOP). We consider here a finite dimensional restriction of the semi-discrete forward model and show its well-posedness and regularisation properties. The second one considers the unsupervised learning method, deep image prior (DIP), inspired by the construction of the model uncertainty in RESESOP. The methods are validated on Monte-Carlo data.
