Background and Objective: The success of neural networks in a number of image processing tasks has motivated their application in image reconstruction problems in computed tomography (CT). While progress has been made in this area, the lack of stability and theoretical guarantees for accuracy, together with the scarcity of high-quality training data for specific imaging domains pose challenges for many CT applications. In this paper, we present a framework for iterative reconstruction (IR) in CT that leverages the hierarchical structure of neural networks, without the need for training. Our framework incorporates this structural information as a deep image prior (DIP), and uses a novel residual back projection (RBP) connection that forms the basis for our iterations. Methods: We propose using an untrained U-net in conjunction with a novel residual back projection to minimize an objective function and achieve high-accuracy reconstruction. In each iteration, the weights of the untrained U-net are optimized, and the output of the U-net in the current iteration is used to update the input of the U-net in the next iteration through the aforementioned RBP connection. Results: Experimental results demonstrate that the RBP-DIP framework offers improvements over other state-of-the-art conventional IR methods, as well as pre-trained and untrained models with similar network structures under multiple conditions. These improvements are particularly significant in the few-view, limited-angle, and low-dose imaging configurations. Conclusions: Applying to both parallel and fan beam X-ray imaging, our framework shows significant improvement under multiple conditions. Furthermore, the proposed framework requires no training data and can be adjusted on-demand to adapt to different conditions (e.g. noise level, geometry, and imaged object).

翻译：背景与目的：神经网络在多项图像处理任务中的成功，推动了其在计算机断层扫描（CT）图像重建问题中的应用。尽管该领域已取得进展，但稳定性不足、精度理论保证的缺失，以及特定成像领域高质量训练数据的稀缺，给许多CT应用带来了挑战。本文提出一种无需训练的CT迭代重建（IR）框架，该框架利用神经网络的层次结构作为深度图像先验（DIP），并引入一种新颖的残差反向投影（RBP）连接作为迭代基础。方法：我们提出将未训练的U-net与新型残差反向投影相结合，以最小化目标函数并实现高精度重建。每次迭代中，优化未训练U-net的权重，并通过前述RBP连接将当前迭代中U-net的输出用于更新下一次迭代中U-net的输入。结果：实验结果表明，在多种条件下，RBP-DIP框架相比其他先进传统IR方法，以及具有相似网络结构的预训练和未训练模型均展现出性能提升。这些提升在稀疏视图、有限角度和低剂量成像配置中尤为显著。结论：将该框架应用于平行束和扇束X射线成像时，在多种条件下均表现出显著改进。此外，该框架无需训练数据，可根据需求调整以适配不同条件（如噪声水平、几何构型和成像对象）。