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Recovering missing slices of the discrete fourier transform using ghosts

Chandra, Shekhar S; Svalbe, Imants D; Guedon, Jeanpierre; Kingston, Andrew; Normand, Nicolas

Description

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...[Show more]

dc.contributor.authorChandra, Shekhar S
dc.contributor.authorSvalbe, Imants D
dc.contributor.authorGuedon, Jeanpierre
dc.contributor.authorKingston, Andrew
dc.contributor.authorNormand, Nicolas
dc.date.accessioned2015-12-10T23:23:21Z
dc.date.available2015-12-10T23:23:21Z
dc.identifier.issn1057-7149
dc.identifier.urihttp://hdl.handle.net/1885/66921
dc.description.abstractThe 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\times 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.
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE Inc)
dc.sourceIEEE Transactions on Image Processing
dc.subjectKeywords: Cyclic ghost theory; Discrete radon transform; Discrete tomography; Fourier slice theorem; Ghosts; limited angle; Mojette transform; Number theoretic transform; Image reconstruction; Inverse problems; Mathematical transformations; Discrete Fourier transfo Cyclic ghost theory; discrete Fourier slice theorem; discrete Radon transform; discrete tomography; Ghosts; image reconstruction; limited angle; Mojette transform; number theoretic transform
dc.titleRecovering missing slices of the discrete fourier transform using ghosts
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume21
dc.date.issued2012
local.identifier.absfor080202 - Applied Discrete Mathematics
local.identifier.absfor080106 - Image Processing
local.identifier.absfor080401 - Coding and Information Theory
local.identifier.ariespublicationf5625xPUB1368
local.type.statusPublished Version
local.contributor.affiliationChandra, Shekhar S, CSIRO
local.contributor.affiliationSvalbe, Imants D, Monash University
local.contributor.affiliationGuedon, Jeanpierre, LUNAM Universite, Universite de Nantes
local.contributor.affiliationKingston, Andrew, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationNormand, Nicolas, University of Nantes
local.bibliographicCitation.issue10
local.bibliographicCitation.startpage4431
local.bibliographicCitation.lastpage4441
local.identifier.doi10.1109/TIP.2012.2206033
local.identifier.absseo970102 - Expanding Knowledge in the Physical Sciences
dc.date.updated2016-02-24T08:45:42Z
local.identifier.scopusID2-s2.0-84866648949
local.identifier.thomsonID000309056700010
CollectionsANU Research Publications

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