[论文解读] Full Characterization of Reconstruction Artifacts from Arbitrary Incomplete X-ray CT Data

Leise Borg, Jürgen Frikel+2 more|arXiv (Cornell University)|Jul 4, 2017

Medical Imaging Techniques and Applications参考文献 47被引用 3

一句话总结

本文使用微局部分析对不完整X射线CT中的重建伪影进行了数学分类，表明伪影源于数据集边界的边界。它识别出两类伪影：由物体奇点引起的、沿直线延伸的与物体相关的伪影，以及由边界几何形状决定的、与物体无关的伪影（非光滑边界时为直线状，光滑边界时为曲线状），并以Sobolev空间中的强度特征进行表征。

ABSTRACT

This article provides a mathematical classification of artifacts from arbitrary incomplete X-ray tomography data when using the classical filtered backprojection algorithm. Using microlocal analysis, we prove that all artifacts arise from points at the boundary of the data set. Our results show that, depending on the geometry of the data set boundary, two types of artifacts can arise object-dependent and object-independent artifacts. The object-dependent artifacts are generated by singularities of the object being scanned and these artifacts can extend all along lines. This is a generalization of the streak artifacts observed in limited angle CT. The article also characterizes two new phenomena: the object-independent artifacts are caused only by the geometry of the data set boundary; they occur along lines if the boundary of the data set is not smooth and along curves if the boundary of the data set is smooth. In addition to the geometric description of artifacts, the article also provides characterizations of their strength in Sobolev scale in certain cases. Moreover, numerical reconstructions from simulated and real data are presented illustrating our theorems. This work is motivated by a reconstruction we present from a synchrotron data set in which artifacts along lines appeared that were independent of the object. The results of this article apply to a wide range of well-known incomplete data problems, including limited angle CT and region of interest tomography, as well as to unconventional x-ray CT imaging setups. Some of those problems are explicitly addressed in this article, theoretically and numerically.

研究动机与目标

• 对使用滤波反投影法进行不完整X射线CT数据重建时的伪影进行数学分类。
• 通过分析数据集边界的几何形状，确定伪影的来源。
• 区分由物体奇点引起的与物体相关的伪影（物体依赖性伪影）和仅由数据边界几何形状引起的与物体无关的伪影（物体独立性伪影）。
• 在特定情况下，以Sobolev空间表征伪影的强度。
• 通过模拟和真实同步辐射数据的数值重建验证理论结果。

提出的方法

• 采用微局部分析研究不完整X射线数据重建图像中奇点的传播特性。
• 分析奇点通过滤波反投影算法的传播路径，将伪影的起源追溯至数据集边界的边界。
• 根据数据集边界的光滑性与几何形状对伪影进行分类：非光滑边界产生线状伪影，光滑边界产生曲线状伪影。
• 在特定几何与解析条件下，推导伪影强度在Sobolev尺度下的表征公式。
• 通过模拟和真实同步辐射X射线CT数据的数值重建验证理论预测。
• 使用真实同步辐射数据集的重建结果作为示例，说明与物体无关的线状伪影的产生机制。

实验结果

研究问题

• RQ1 是什么决定了在不完整X射线CT数据的滤波反投影重建中伪影的起源？
• RQ2 数据集边界几何形状与光滑性如何影响伪影的形状与结构？
• RQ3 在形成机制与空间分布方面，如何区分与物体相关的伪影与与物体无关的伪影？
• RQ4 能否在Sobolev空间中量化伪影的强度？在何种条件下可以实现？
• RQ5 理论预测与真实及模拟数据的数值重建结果在多大程度上一致？

主要发现

• 所有来自不完整X射线CT数据的滤波反投影重建伪影，其根源均来自数据集边界的边界。
• 与物体相关的伪影源于被扫描物体的奇点，并沿直线方向延伸，推广了有限角CT中常见的条纹伪影。
• 与物体无关的伪影完全由数据集边界的几何形状引起：若边界非光滑，则伪影呈线状；若边界光滑，则伪影呈曲线状。
• 在特定几何与解析条件下，伪影强度可在Sobolev空间中进行表征，从而提供伪影强度的定量度量。
• 来自模拟与真实同步辐射数据的数值重建结果均证实了理论预测，包括与物体无关的线状伪影的存在。