  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.
