The unrolling method has been investigated for learning variational models in X-ray computed tomography. However, it has been observed that directly unrolling the regularization model through gradient descent does not produce satisfactory results. In this paper, we present a novel deep learning-based CT reconstruction model, where the low-resolution image is introduced to obtain an effective regularization term for improving the network`s robustness. Our approach involves constructing the backbone network architecture by algorithm unrolling that is realized using the deep equilibrium architecture. We theoretically discuss the convergence of the proposed low-resolution prior equilibrium model and provide the conditions to guarantee convergence. Experimental results on both sparse-view and limited-angle reconstruction problems are provided, demonstrating that our end-to-end low-resolution prior equilibrium model outperforms other state-of-the-art methods in terms of noise reduction, contrast-to-noise ratio, and preservation of edge details.

翻译：展开方法已被研究用于在X射线计算机断层扫描中学习变分模型。然而，观察到通过梯度下降直接展开正则化模型并不能产生令人满意的结果。本文提出了一种新颖的基于深度学习的CT重建模型，其中引入低分辨率图像以获得有效的正则化项，从而提高网络的鲁棒性。我们的方法涉及通过算法展开构建骨干网络架构，该架构使用深度平衡架构实现。我们从理论上讨论了所提出的低分辨率先验平衡模型的收敛性，并给出了保证收敛的条件。提供了稀疏视图和有限角度重建问题的实验结果，表明我们的端到端低分辨率先验平衡模型在噪声抑制、对比度噪声比和边缘细节保持方面优于其他最先进方法。