Comptes Rendus
no. 1
Physics/Mathematical physics, theoretical physics
A new reconstruction method in the Fourier domain for 3D positron emission tomography

Presented by: 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, Self-organization on surfaces, Volume 6 (2005) no. 1, pp. 133-137.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crhy.2004.11.011
Keywords: Positron emission tomography, 3D reconstruction, Noise, Fourier transform
Mots-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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Denis Mariano-Goulart; Jean-François Crouzet. A new reconstruction method in the Fourier domain for 3D positron emission tomography. Comptes Rendus. Physique, Self-organization on surfaces, 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/

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