论文标题
通过离散层析成像进行三维重建的线性时间方法
A linear time approach to three-dimensional reconstruction by discrete tomography
论文作者
论文摘要
离散层析成像的目的是通过给定的一组线和通过一组线路重建一个未知功能$ f $。除了需要准确的重建外，也有利于及时执行任务。鬼的存在使这一点变得复杂，这使许多解决方案总体上存在。在本文中，我们考虑函数$ f的情况：先前的工作表明，在二维情况下，无论解决方案是否唯一，都可以在线性时间（相对于方向数和网格大小）以线性时间（相对于方向数和网格大小）来确定所有解决方案。在这项工作中，我们表明在非比例的条件下以三个维度存在类似的线性方法。我们表明，在三维边界幽灵的情况下，非比例性的状况已实现。
The goal of discrete tomography is to reconstruct an unknown function $f$ via a given set of line sums. In addition to requiring accurate reconstructions, it is favourable to be able to perform the task in a timely manner. This is complicated by the presence of ghosts, which allow many solutions to exist in general. In this paper we consider the case of a function $f : A \to \mathbb{R}$ where $A$ is a finite grid in $\mathbb{Z}^3$. Previous work has shown that in the two-dimensional case it is possible to determine all solutions in parameterized form in linear time (with respect to the number of directions and the grid size) regardless of whether the solution is unique. In this work, we show that a similar linear method exists in three dimensions under the condition of nonproportionality. We show that the condition of nonproportionality is fulfilled in the case of three-dimensional boundary ghosts.
