Recovering missing slices of the discrete fourier transform using ghosts

Chandra, Shekhar S., Svalbe, Imants D., Guedon, Jeanpierre, Kingston, Andrew M. and Normand, Nicolas (2012) Recovering missing slices of the discrete fourier transform using ghosts. IEEE Transactions on Image Processing, 21 10: 4431-4441. doi:10.1109/TIP.2012.2206033

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Author Chandra, Shekhar S.
Svalbe, Imants D.
Guedon, Jeanpierre
Kingston, Andrew M.
Normand, Nicolas
Title Recovering missing slices of the discrete fourier transform using ghosts
Journal name IEEE Transactions on Image Processing   Check publisher's open access policy
ISSN 1057-7149
1941-0042
Publication date 2012-10
Year available 2012
Sub-type Article (original research)
DOI 10.1109/TIP.2012.2206033
Open Access Status File (Author Post-print)
Volume 21
Issue 10
Start page 4431
End page 4441
Total pages 11
Place of publication Piscataway, NJ, United States
Publisher Institute of Electrical and Electronics Engineers
Collection year 2013
Language eng
Formatted abstract
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(nlog2n) (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.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: Non HERDC
School of Information Technology and Electrical Engineering Publications
 
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Citation counts: TR Web of Science Citation Count  Cited 6 times in Thomson Reuters Web of Science Article | Citations
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Created: Fri, 14 Mar 2014, 14:44:18 EST by Shekhar Chandra on behalf of School of Information Technol and Elec Engineering