关于由定中心轴锥变换确定函数的问题
On the determination of a function from its cone transform with fixed central axis
摘要：
在过去的十年中，在单光子发射计算机断层扫描中使用的康普顿相机的研究的背景下，出现了一种称为锥变换的氡型变换，其将其在各种锥集合上的积分分配给给定函数。在这里，我们研究的锥变换的中心轴的积分锥是固定的。我们提出了它的许多性质，如两个反演公式，稳定性估计，唯一性和重建的局部数据问题。
英文摘要：
A Radon-type transform called a cone transform that assigns to a given function its integral over various sets of cones has arisen in the last decade in the context of the study of Compton cameras used in Single Photon Emission Computed Tomography. Here, we study the cone transform for which the central axis of the cones of integration is fixed. We present many of its properties, such as two inversion formulas, a stability estimate, and uniqueness and reconstruction for a local data problem.
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