A Local Approach to Resolution Analysis of Image Reconstruction in Tomography
A Local Approach to Resolution Analysis of Image Reconstruction in Tomography
复制标题
层析成像图像重建分辨率分析的局部方法
DOI：
10.1137/17m1112108
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
A. Katsevich
中科院分区：
文献类型：
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作者：
A. Katsevich
提出了一种新的分析层析重建分辨率的方法。而不是按照传统的方法来获得一个全球性的精度估计，我们研究如何重建函数$f_\n $近似的奇异性的原始对象$f$。数据是f$的离散化2D Radon变换。对象可以是静态的或随时间变化的（动态断层扫描）。假设步长沿着角度和仿射变量是O（\n）。我们选取一个点$\bar x_0$，其中$f$有一个跳跃奇点，并得到$f_\n $在$\bar x_0$的一个O（\n）$-邻域中的领先奇异行为为$\epsilon\to 0 $。事实证明，$f_\n $的极限行为只依赖于被重构的奇点附近的数据。这大大简化了分析，并允许我们研究复杂的设置，例如，动态体层摄影此外，我们的分辨率分析是算法特定的-同样的方法可以用于分析。
We propose a novel approach to analyzing resolution of tomographic reconstruction. Instead of following a conventional approach to obtain a global accuracy estimate, we investigate how the reconstructed function $f_\epsilon$ approximates the singularities of the original object $f$. The data is a discretized 2D Radon transform of $f$. The object could be static or change with time (dynamic tomography). Suppose the step-sizes along the angular and affine variables are $O(\epsilon)$. We pick a point $\bar x_0$, where $f$ has a jump singularity, and obtain the leading singular behavior of $f_\epsilon$ in an $O(\epsilon)$-neighborhood of $\bar x_0$ as $\epsilon\to0$. It turns out that the limiting behavior of $f_\epsilon$ depends only on the data microlocally near the singularity being reconstructed. This significantly simplifies the analysis and allows us to investigate complicated settings, e.g., dynamic tomography. Also, our resolution analysis is algorithm-specific---the same approach can be used for anal...