Recovering missing slices of the discrete fourier transform using ghosts
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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.author | Chandra, Shekhar S | |
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dc.contributor.author | Svalbe, Imants D | |
dc.contributor.author | Guedon, Jeanpierre | |
dc.contributor.author | Kingston, Andrew | |
dc.contributor.author | Normand, Nicolas | |
dc.date.accessioned | 2015-12-10T23:23:21Z | |
dc.date.available | 2015-12-10T23:23:21Z | |
dc.identifier.issn | 1057-7149 | |
dc.identifier.uri | http://hdl.handle.net/1885/66921 | |
dc.description.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(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.publisher | Institute of Electrical and Electronics Engineers (IEEE Inc) | |
dc.source | IEEE Transactions on Image Processing | |
dc.subject | Keywords: 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.title | Recovering missing slices of the discrete fourier transform using ghosts | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.identifier.citationvolume | 21 | |
dc.date.issued | 2012 | |
local.identifier.absfor | 080202 - Applied Discrete Mathematics | |
local.identifier.absfor | 080106 - Image Processing | |
local.identifier.absfor | 080401 - Coding and Information Theory | |
local.identifier.ariespublication | f5625xPUB1368 | |
local.type.status | Published Version | |
local.contributor.affiliation | Chandra, Shekhar S, CSIRO | |
local.contributor.affiliation | Svalbe, Imants D, Monash University | |
local.contributor.affiliation | Guedon, Jeanpierre, LUNAM Universite, Universite de Nantes | |
local.contributor.affiliation | Kingston, Andrew, College of Physical and Mathematical Sciences, ANU | |
local.contributor.affiliation | Normand, Nicolas, University of Nantes | |
local.bibliographicCitation.issue | 10 | |
local.bibliographicCitation.startpage | 4431 | |
local.bibliographicCitation.lastpage | 4441 | |
local.identifier.doi | 10.1109/TIP.2012.2206033 | |
local.identifier.absseo | 970102 - Expanding Knowledge in the Physical Sciences | |
dc.date.updated | 2016-02-24T08:45:42Z | |
local.identifier.scopusID | 2-s2.0-84866648949 | |
local.identifier.thomsonID | 000309056700010 | |
Collections | ANU Research Publications |
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