xml:id='mma4480-para-0001'>A two‐dimensional sparse‐data tomographic problem is studied. '/> Shape recovery for sparse‐data tomography
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Shape recovery for sparse‐data tomography

机译:稀疏数据断层扫描的形状恢复

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xml:id="mma4480-para-0001">A two‐dimensional sparse‐data tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A nonuniform rational basis splines (NURBS) curve is used as a computational representation of the boundary. This approach conveniently provides the result in a format readily compatible with computer‐aided design software. However, the linear tomography task becomes a nonlinear inverse problem because of the NURBS‐based parameterization. Therefore, Bayesian inversion with Markov chain Monte Carlo sampling is used for calculating an estimate of the NURBS control points. The reconstruction method is tested with both simulated data and measured X‐ray projection data. The proposed method recovers the shape and the attenuation coefficient significantly better than the baseline algorithm (optimally thresholded total variation regularization), but at the cost of heavier computation.
机译: xml:id =“ MMA4480-PARA-0001“>研究了二维稀疏数据断层切换问题。假设目标是由平滑曲线限定的均匀对象。非均匀的理性基础样条(NURBS)曲线用作边界的计算表示。这种方法方便地提供了与计算机辅助设计软件易于兼容的格式的结果。但是,由于基于NURBS的参数化,线性断层扫描任务成为非线性逆问题。因此,使用马尔可夫链蒙特卡罗采样的贝叶斯反演用于计算NURBS控制点的估计。使用模拟数据和测量的X射线投影数据测试重建方法。该方法恢复了形状和衰减系数明显优于基线算法(最佳阈值的总变化正则化),但以较重计算的成本。

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