New iterative reconstruction methods for fan-beam tomography
New iterative reconstruction methods for fan-beam tomography
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DOI：
10.1080/17415977.2017.1340946
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发表时间：
2018-06
影响因子：
1.3
通讯作者：
D. Kazantsev;V. Pickalov
中科院分区：
文献类型：
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作者：
D. Kazantsev;V. Pickalov
摘要在本文中，我们提出了一种新颖的迭代重建方法，用于严重角度采样或/和限量视图层析成像问题，并具有风扇梁扫描几何形状。所提出的算法基于一种新的分析变换，该变换将傅立叶定理推广到发散的梁扫描几何形状。使用非刚性坐标变换，可以将不同的射线重组为平行。因此，可以使用更简单的平行梁投影模型，而不是更复杂的发散梁几何形状。各种现有的迭代重建技术用于发散梁几何，很容易适应所提出的框架。该公式的显着优势在于可以利用有效的基于傅立叶的恢复方法而不会重新介绍投影。在高度稀疏的测量（少量视图数据）的情况下，由于涉及错误的角度插值，重新介绍方法不适合。在这项工作中，介绍了基于风扇束几何形状的新分析框架的三种新方法：Gerchberg-Papoulis算法，Neumann分解方法及其总变异正则化版本。提出的数值实验表明，这些方法可以从少量视图嘈杂的层析成像测量中重建有竞争力。
Abstract In this paper, we present a novel class of iterative reconstruction methods for severely angular undersampled or/and limited-view tomographic problems with fan-beam scanning geometry. The proposed algorithms are based on a new analytical transform which generalizes Fourier-slice theorem to divergent-beam scanning geometries. Using a non-rigid coordinate transform, divergent rays can be reorganized into parallel ones. Therefore, one can employ a simpler parallel-beam projection model instead of more complicated divergent-beam geometries. Various existing iterative reconstruction techniques for divergent-beam geometries can be easily adapted to the proposed framework. The significant advantage of this formulation is the possibility of exploiting efficient Fourier-based recovery methods without rebinning of the projections. In case of highly sparse measurements (few-view data), rebinning methods are not suitable due to error-prone angular interpolation involved. In this work, three new methods based on the novel analytical framework for fan-beam geometry are presented: the Gerchberg-Papoulis algorithm, the Neumann decomposition method and its total variation regularized version. Presented numerical experiments demonstrate that the methods can be competitive in reconstructing from few-view noisy tomographic measurements.