利用重影恢复离散傅里叶变换的缺失切片
Recovering Missing Slices of the Discrete Fourier Transform using Ghosts
摘要：
离散傅立叶变换（DFT）是解决许多通常含有缺失或不可测频率信息的逆问题的基础。傅立叶空间的这种不完全覆盖总是产生称为鬼的系统性伪影。本文提出了一种快速、准确的去卷积方法，用于消除DFT缺失切片引起的循环伪影。这里讨论的切片源自投影离散Radon变换（称为离散傅里叶切片定理）下DFT空间的精确划分。该方法的计算复杂度为O（n log2 n）（其中n = N^2），并由一个新的有限鬼理论构造。这一理论也被证明是统一的几个方面的工作所做的鬼在过去的三十年。本文的结论是一个重要的应用快速，准确，非迭代图像重建从有限范围内的投影角度获得的离散切片集。
英文摘要：
The Discrete Fourier Transform (DFT) underpins the solution to many inverse problems commonly possessing missing or un-measured frequency information. This incomplete coverage of Fourier space always produces systematic artefacts called Ghosts. In this paper, a fast and exact method for de-convolving cyclic artefacts caused by missing slices of the DFT is presented. The slices discussed here originate from the exact partitioning of DFT space, under the projective Discrete Radon Transform, called the Discrete Fourier Slice Theorem. The method has a computational complexity of O(n log2 n) (where n = N^2) and is constructed from a new Finite Ghost theory. This theory is also shown to unify several aspects of work done on Ghosts over the past three decades. The paper concludes with a significant application to fast, exact, non-iterative image reconstruction from sets of discrete slices obtained for a limited range of projection angles.
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