Comparison of three undersampling approaches in computed tomography reconstruction.
Comparison of three undersampling approaches in computed tomography reconstruction.
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DOI：
10.21037/qims.2019.07.07
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发表时间：
2019-07
影响因子：
2.8
通讯作者：
Chenyang Shen;Y. Lou;L. Chen;T. Zeng;Michael K. Ng;Lei Zhu;X. Jia
中科院分区：
文献类型：
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作者：
Chenyang Shen;Y. Lou;L. Chen;T. Zeng;Michael K. Ng;Lei Zhu;X. Jia
背景投影数据欠采样是减少计算机断层成像(CT)中X射线辐射剂量的有效方法。在现代CT技术中，欠采样也是减小投影数据量以便于快速CT扫描和成像的一种有利方法。一个有趣的问题是，在给定欠采样比的情况下，什么样的最佳欠采样方法才能实现最佳的CT图像重建。虽然这通常是一个具有挑战性的数学问题，但这是本文比较三种类型的欠采样操作的动机，我们希望能为这个问题提供一些启发。方法我们考虑了常规视图欠采样，即获取等角度投影的X射线投影；规则射线欠采样，获取所有角度的投影，但在周期模式下每个投影内的X射线线被遮挡；以及随机射线欠采样，以一定的概率获取每条X射线线。通过在全投影算子的奇异向量下表示欠采样投影算子，生成了这些欠采样算子的矩阵表示，并进行了奇异值分解(SVD)。比较了奇异值谱和奇异值向量。结果对于给定的欠采样率，随机射线欠采样法比其他两种方法更好地保留了全投影算子的性质。这转化为以较低的误差重建CT图像的优点，这在数值实验中也得到了证明。结论我们比较了三种欠采样策略，发现随机欠采样保留了最多的信息，并且在重建质量方面优于其他两种方法。
Background Projection data undersampling is an effective approach to reduce X-ray radiation dose in computed tomography (CT). In modern CT technologies, undersampling is also a favorable method to reduce projection data size to facilitate rapid CT scan and imaging. It is an intriguing question that given an undersampling ratio, what is the optimal undersampling approach that enables the best CT image reconstruction. While this is in general a challenging mathematical question, it is the motivation of this paper to compare three types of undersampling operations, which we hope to shed some light to this question. Methods We considered regular view undersampling that acquires X-ray projections at equiangular projection angles, regular ray undersampling that acquires projections at all angles but with X-ray lines blocked within each projection under a periodic pattern, and random ray undersampling that acquires each X-ray line with a certain probability. By representing the undersampling projection operators under the basis of singular vectors of full projection operator, we generated matrix representations of these undersampling operators and numerically perform singular value decomposition (SVD). Singular value spectra and singular vectors were compared. Results For a given undersampling ratio, the random ray undersampling approach preserves the properties of the full projection operator better than the other two approaches. This translates to advantages of reconstructing a CT image at a lower error, which has also been demonstrated in the numerical experiments. Conclusions We compared three undersampling strategies and found that random undersampling preserves the most information and outperforms the other two in terms of reconstruction quality.