Recovering Missing Slices of the Discrete Fourier Transform using Ghosts

Details Recovering Missing Slices of the Discrete Fourier Transform using Ghosts Recovering Missing Slices of the Discrete Fourier Transform using Ghosts

2010-12-30

arxiv.org/abs/1101.0076v1

Physics

Mathematical Physics

10 pages, 18 figures (submitted to IEEE Image Proc.)

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Recovering Missing Slices of the Discrete Fourier Transform using Ghosts does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Recovering Missing Slices of the Discrete Fourier Transform using Ghosts, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Recovering Missing Slices of the Discrete Fourier Transform using Ghosts will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-400835