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International Journal of Biomedical Imaging
Volume 2012 (2012), Article ID 452910, 11 pages
Research Article

High Performance 3D PET Reconstruction Using Spherical Basis Functions on a Polar Grid

1Instituto de Física Corpuscular, Universitat de València/CSIC, Edificio Institutos de Investigación, 22085 Valencia, Spain
2Departamento de Física Atómica, Molecular y Nuclear, Universitat de València, 46100 Valencia, Spain

Received 14 October 2011; Revised 18 January 2012; Accepted 26 January 2012

Academic Editor: Habib Zaidi

Copyright © 2012 J. Cabello et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Statistical iterative methods are a widely used method of image reconstruction in emission tomography. Traditionally, the image space is modelled as a combination of cubic voxels as a matter of simplicity. After reconstruction, images are routinely filtered to reduce statistical noise at the cost of spatial resolution degradation. An alternative to produce lower noise during reconstruction is to model the image space with spherical basis functions. These basis functions overlap in space producing a significantly large number of non-zero elements in the system response matrix (SRM) to store, which additionally leads to long reconstruction times. These two problems are partly overcome by exploiting spherical symmetries, although computation time is still slower compared to non-overlapping basis functions. In this work, we have implemented the reconstruction algorithm using Graphical Processing Unit (GPU) technology for speed and a precomputed Monte-Carlo-calculated SRM for accuracy. The reconstruction time achieved using spherical basis functions on a GPU was 4.3 times faster than the Central Processing Unit (CPU) and 2.5 times faster than a CPU-multi-core parallel implementation using eight cores. Overwriting hazards are minimized by combining a random line of response ordering and constrained atomic writing. Small differences in image quality were observed between implementations.