Abstract
Objectives: Tomographic reconstruction algorithms estimate the 3D map of radiotracer concentration without any systematic uncertainty estimate. We explore a new reconstruction paradigm in which the error is estimated as part of the reconstruction process.
Methods: Our algorithm NIBEM (Non sommative Interval Based Expectation Maximization) is based on directed interval arithmetic. It uses non-additive modeling of the forward and back-projection operators that provides intervals instead of single-valued projections and back-projections. To show the ability of NIBEM to jointly estimate the activity concentration and associated uncertainty, we simulated the PET acquisition of an ellipsoidal water phantom including 4 spheres (sphere-to-background activity ratios of 2, 4, 6 and 8). Fifty Poisson noise realizations were reconstructed with MLEM and one realization was reconstructed with NIBEM. All reconstructions included attenuation correction. For 5 volumes of interest (VOI) drawn in the background and in each sphere, we calculated: 1/ the L2 distance D_MLEM between each MLEM reconstruction and the phantom and the L2 distance D_NIBEM between the median image of the NIBEM intervals and the phantom, from 1 to 100 iterations; 2/ the number of voxels i for which the true activity Ri was included in the NIBEM interval of width Li and the relative width of these intervals defined as Li/Ri.
Results: NIBEM median images looked similar to MLEM images. The smallest value of D_NIBEM along the iterations occurred between 10 and 30 iterations depending on the VOI and was always less than the smallest D_MLEM. At 18 iterations, the NIBEM interval included the true activity value in 68% to 85% voxels as a function of the VOI and Li/Ri varied from 22% to 30%.
Conclusions: The NIBEM median image gives an excellent estimate of the real activity distribution while NIBEM intervals provide uncertainty estimates. NIBEM shows promises to assign confidence intervals to reconstructed voxel values although the statistical distribution of Li still needs to be determined.
Research Support INCA STIPPI grant