X-ray computed tomography has been a useful technology in cancer detection and radiation therapy. However, high radiation dose during CT scans may increase the underlying risk of healthy organs. Usually, sparse-view X-ray projection is an effective method to reduce radiation. In this paper, we propose a constrained nonconvex truncated regularization model for this low-dose CT reconstruction. It preserves sharp edges very well. Although this model is quite complicated to analyze, we establish two useful theoretical results for its minimizers. Motivated by them, an iterative support shrinking algorithm is introduced. To handle more nondifferentiable points of the regularization function except zero point, we use a general proximally linearization technique at them, which is helpful to implement our algorithm. For this algorithm, we prove the convergence of the objective function, and give a lower bound theory of the iterative sequence. Numerical experiments and comparisons demonstrate that our model with the proposed algorithm performs good for low-dose CT reconstruction.

中文翻译：

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用于CT重建的非凸截断正则化和框约束模型

X射线计算机断层扫描已成为癌症检测和放射治疗中的有用技术。但是，CT扫描期间的高辐射剂量可能会增加健康器官的潜在风险。通常，稀疏X射线投影是减少辐射的有效方法。在本文中，我们为这种低剂量CT重建提出了一个受约束的非凸截短正则化模型。它很好地保留了锋利的边缘。尽管此模型的分析非常复杂，但我们为其最小化器建立了两个有用的理论结果。在他们的激励下，引入了迭代支持收缩算法。为了处理除零点以外的更多正则化函数的不可微点，我们在它们处使用了一般的近端线性化技术，这有助于实现我们的算法。对于此算法，我们证明了目标函数的收敛性，并给出了迭代序列的下界理论。数值实验和比较表明，我们的算法与所提出的算法在低剂量CT重建方面表现良好。