The attenuated geodesic x-ray transform
The attenuated geodesic x-ray transform
复制标题
衰减测地 X 射线变换
DOI：
10.1088/1361-6420/aab8bc
复制
发表时间：
2018
期刊：
影响因子：
2.1
通讯作者：
Stefanov, Plamen
中科院分区：
文献类型：
--
作者：
Holman, Sean;Monard, François;Stefanov, Plamen
本文讨论与测地线x射线变换相关的稳定性问题，其中变换中的(衰减类型)权重与底层几何体之间的相互作用强烈影响问题的稳定性或不稳定性。在不稳定的情况下，我们还解释了根据潜在的共轭点和这些点处的微局部权重预期的人工产物的类型。特别是，我们证明了著名的迭代重建Landweber算法在问题不稳定的情况下不能提供准确的重建，尽管重建算法所产生的伪影可以被适当地描述。
This article deals with stability issues related to geodesic x-ray transforms, where an interplay between the (attenuation type) weight in the transform and the underlying geometry strongly impact whether the problem is stable or unstable. In the unstable case, we also explain what types of artifacts are expected in terms of the underlying conjugate points and the microlocal weights at those points. We show in particular that the well-known iterative reconstruction Landweber algorithm cannot provide accurate reconstruction when the problem is unstable, though the artifacts generated, specific for the reconstruction algorithm, can be properly described.