Use of a fast EM algorithm for 3D image reconstruction with the YAP-PET tomograph

Abstract

Objective: We would like to improve the image reconstructions for both signal-to-noise ratio (SNR) and spatial resolution characteristics for the small animal positron emission tomograph YAP-PET, built at the Department of Physics of Ferrara University. The three-dimensional (3D) filtered backprojection (FBP) algorithm, usually used for image reconstruction, has a limited angle restriction due to the tomograph geometry, which causes a serious loss in sensitivity.

Methods: We implemented a 3D iterative reconstruction program using the symmetry and sparse properties of the 'probability matrix', which correlates the emission from each voxel to the detector within a coincidence tube. A fraction only of matrix elements are calculated before the reconstruction and stored on disk: this allows us to avoid on-line computation. A depth dependent function differentiates the voxels in a coincidence tube. Three experimental phantoms with no background were reconstructed by using the program, in comparison with traditionally used FBP.

Results: The adopted method allowed us to reduce the computation time significantly. Furthermore, the simple depth dependent function improved the spatial resolution. With 64 x 64 x 20 voxels of 0.625 x 0.625 x 2.0 mm(3) in the field of view, the computation time was less than 4 min per iteration on a Sparc Ultra 450 Workstation, and less than 6 min per iteration on a Mac-PPC G3 300 MHz: the spatial resolution measured with a 0.8 mm diameter 18F-FDG filled capillary reconstructed in this way was 2.0 mm FWHM. By decreasing the voxel size to 0.3125 x 0.3125 x 2.0 mm(3) per voxel the transaxial FWHM was 1.7 mm with a computation time of 15 min per iteration on a Sparc Ultra 450. By using all the acquired data, the SNR improves from 1.3 to 6.0 in the worst measured case, a pair of 0.8mm diameter 18F-FDG filled capillaries, which are 2.5 mm apart each other.

Conclusion: The adoption of iterative reconstruction allowed us to overcome the loss in sensitivity of previously used FBP: this improved the SNR. The studies of symmetry and sparse properties avoided a severe increase of the reconstruction time and of storing space on disk. This fast EM Algorithm is now routinely used for the image reconstruction with the YAP-PET tomograph.