Comptes Rendus
no. 1
Physics/Mathematical physics, theoretical physics
A new reconstruction method in the Fourier domain for 3D positron emission tomography
[Une nouvelle méthode de reconstruction 3D dans le domaine de Fourier en tomographie par émission de positons]

Présenté par : Maurice Goldman

Denis Mariano-Goulart1  ; Jean-François Crouzet2
1 Department of nuclear medicine, Montpellier Medical University, 371, avenue du Doyen Giraud, 34295 Montpellier, France
2 Department of mathematics, Montpellier Science University, place Eugène Bataillon, 34095 Montpellier, France
Comptes Rendus. Physique, Volume 6 (2005) no. 1, pp. 133-137.

Cet article décrit un nouvel algorithme exact de reconstruction 3D dédié aux tomographes par émission de positons cylindriques. Il ne nécessite pas l'estimation des données de projection manquantes ni d'interpolations délicates dans l'espace 3D. Il utilise la transformée de Fourier 2D de signaux construits à partir des projections obliques acquises pour calculer la transformée de Fourier 3D de la distribution de radioactivité à déterminer. On obtient ainsi un algorithme de reconstruction tridimensionnel rapide qui ne nécessite que des interpolations 1D et tire profit de la redondance des données de projection 3D pour autoriser un meilleur rapport signal sur bruit dans l'objet reconstruit.

This article describes a new exact 3D reconstruction algorithm dedicated to cylindrical positron emission tomographs that does not require an estimation of missing projection data nor complex 3D interpolation procedures. This algorithm uses the 2D Fast Fourier Transform of non-transaxial projections to place suitable voxel values in the 3D FFT of the radioactive distribution. This leads to a direct fully 3D reconstruction algorithm with a limited amount of computation that requires only 1D interpolation procedures and benefits from redundant projection data to improve the signal to noise ratio in the radioactive distribution.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crhy.2004.11.011
Keywords: Positron emission tomography, 3D reconstruction, Noise, Fourier transform
Mot clés : Tomographie par émission de positons, Reconstruction 3D, Bruit, Transformation de Fourier
Denis Mariano-Goulart 1 ; Jean-François Crouzet 2

1 Department of nuclear medicine, Montpellier Medical University, 371, avenue du Doyen Giraud, 34295 Montpellier, France
2 Department of mathematics, Montpellier Science University, place Eugène Bataillon, 34095 Montpellier, France 
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     title = {A new reconstruction method in the {Fourier} domain for {3D} positron emission tomography},
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Denis Mariano-Goulart; Jean-François Crouzet. A new reconstruction method in the Fourier domain for 3D positron emission tomography. Comptes Rendus. Physique, Volume 6 (2005) no. 1, pp. 133-137. doi : 10.1016/j.crhy.2004.11.011. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2004.11.011/

[1] S.S. Orlov Theory of three dimensional reconstruction. I. Conditions for a complete set of projections, Sov. Phys. Crystal., Volume 20 (1976), pp. 312-314

[2] S.S. Orlov Theory of three dimensional reconstruction. II. The recovery operato, Sov. Phys. Crystal., Volume 20 (1976), pp. 429-433

[3] J.G. Colsher Fully three-dimensional PET, Phys. Med. Biol., Volume 25 (1980), pp. 103-115

[4] J.G. Rogers; R. Harrop; P.E. Kinahan The theory of three-dimensional image reconstruction for PET, IEEE T. Med. Imaging, Volume 6 (1987), pp. 239-243

[5] M. Defrise; D.W. Townsend; R. Clack Image reconstruction from truncated two-dimensional projections, Inverse Probl., Volume 11 (1995), pp. 287-313

[6] P.E. Kinahan; J.G. Rogers Analytic 3D image reconstruction using all detected events, IEEE T. Nucl. Sci., Volume 36 (1989), pp. 964-968

[7] M. Defrise; P.E. Kinahan; W. Townsend; C. Michel; M. Sibomana; D.F. Newport Exact and approximate rebinning algorithms for 3D PET data, IEEE T. Med. Imaging, Volume 16 (1997), pp. 145-158

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