Australian e-Health Research Center, CSIRO, Brisbane 4029, Australia.
IEEE Trans Image Process. 2012 Oct;21(10):4431-41. doi: 10.1109/TIP.2012.2206033. Epub 2012 Jun 26.
The discrete Fourier transform (DFT) underpins the solution to many inverse problems commonly possessing missing or unmeasured frequency information. This incomplete coverage of the Fourier space always produces systematic artifacts called Ghosts. In this paper, a fast and exact method for deconvolving cyclic artifacts caused by missing slices of the DFT using redundant image regions is presented. The slices discussed here originate from the exact partitioning of the Discrete Fourier Transform (DFT) space, under the projective Discrete Radon Transform, called the discrete Fourier slice theorem. The method has a computational complexity of O(n log(2) n) (for an n=N×N image) and is constructed from a new cyclic theory of Ghosts. This theory is also shown to unify several aspects of work done on Ghosts over the past three decades. This paper concludes with an application to fast, exact, non-iterative image reconstruction from a highly asymmetric set of rational angle projections that give rise to sets of sparse slices within the DFT.
离散傅里叶变换 (DFT) 是解决许多逆问题的基础，这些问题通常具有缺失或未测量的频率信息。傅里叶空间的这种不完全覆盖总是会产生系统伪影，称为“幽灵”。本文提出了一种快速、精确的方法，用于使用冗余图像区域消除由于 DFT 中缺失切片而引起的循环伪影。这里讨论的切片源自离散傅里叶变换 (DFT) 空间的精确划分，在投影离散 Radon 变换下，称为离散傅里叶切片定理。该方法的计算复杂度为 O(nlog(2)n)（对于 n=N×N 图像），并且是由新的循环幽灵理论构建的。该理论还展示了统一过去三十年中在幽灵方面所做的几个方面的工作。本文最后应用于从高度非对称的有理角度投影集快速、精确、非迭代地重建图像，这些投影集在 DFT 中产生稀疏切片集。
