AustralieFrV1, Main, Exploration, bibRecord, 005956

Recovering Missing Slices of the Discrete Fourier Transform Using Ghosts

Identifieur interne : 005956 ( Main/Exploration ); précédent : 005955; suivant : 005957

Recovering Missing Slices of the Discrete Fourier Transform Using Ghosts

Auteurs : Shekhar S. Chandra [Australie] ; Imants D. Svalbe [Australie] ; Jeanpierre Guedon [France] ; Andrew M. Kingston [Australie] ; Nicolas Normand [France]

Source :

IEEE transactions on image processing [ 1057-7149 ] ; 2012.

RBID : Pascal:12-0392417

Descripteurs français

Pascal (Inist)
- Transformation Fourier discrète, Problème inverse, Couverture, Artefact, Partitionnement, Méthode partition, Transformation discrète, Transformation Radon, Complexité calcul, Méthode itérative, Reconstruction image, Tomographie, Théorie nombre.

English descriptors

KwdEn :
- Artefact, Computational complexity, Coverage, Discrete Fourier transformation, Discrete transformation, Image reconstruction, Inverse problem, Iterative method, Number theory, Partition method, Partitioning, Radon transformation, Tomography.

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 log₂ n) (for an n = N x 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.

Affiliations:

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Le document en format XML

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<front><div type="abstract" xml:lang="en">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<sub>2</sub>
 n) (for an n = N x 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.</div>
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Recovering Missing Slices of the Discrete Fourier Transform Using Ghosts

Recovering Missing Slices of the Discrete Fourier Transform Using Ghosts

Source :

Descripteurs français

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri