A study of lesion contrast recovery for statistical PET image reconstruction with accurate system models

Iterative methods for the reconstruction of PET images can produce results superior to filtered backprojection since they are able to explicitly model the Poisson statistics of photon pair coincidence detection. However, many implementations of these methods use simple forward and backward projection schemes based either on linear interpolation or on computing the volume of intersection of detection tubes with each voxel. Other important physical system factors, such as depth dependent geometric sensitivity and spatially variant detector pair resolution are often ignored. In this paper, we examine the effect of a more accurate system model on algorithm performance. A second factor that limits the performance of the iterative algorithms is the chosen objective function and the manner in which it is optimized. Here we compare performance of filtered backprojection (FBP) with the OSEM (ordered subsets EM) algorithm, which approximately maximizes the likelihood, and a MAP (maximum a posteriori) method using a Gibbs prior with convex potential functions. Using the contrast recovery coefficient (CRC) as a performance measure, we performed various phantom experiments to investigate how the choice of algorithm and projection matrix affect reconstruction accuracy. Plots of CRC versus background variance were generated by varying cut-off frequency in FBP, subset size and iteration number or post-smoothing kernel in OSEM, and smoothing parameter in the MAP reconstructions. The results of these studies show that all of the iterative methods tested produce superior CRCs than FBP at matched background variance. However, there is also considerable variation in performance within the class of statistical methods depending on the choice of projection matrix and reconstruction algorithm.