Theoretical Comparison of Motion Correction Techniques for PET Image Reconstruction

We theoretically compare the bias and variance properties of two motion correction techniques for regularized PET image reconstruction from motion-gated datasets. The first method (RRA) consists of independent reconstructions of all gates followed by registration to a reference gate and averaging. The second method (MBMC) uses the entire dataset simultaneously to reconstruct the motion corrected reference gate image by including the motion information in the system model as a warping matrix. Both methods are capable of correcting for non-rigid motion and assume the presence of accurate gate-to-gate motion information, which can be obtained by co-registering gated anatomical images. In order to compare the two techniques, we simulated a motion phantom where a circular phantom warps into an ellipse and a modified version of the NCAT phantom with respiratory motion. We determined differences in voxelwise variances between the two methods as a function of the smoothing parameter when biases are matched. We showed that the MBMC approach results in lower variance for maximum-likelihood (ML) image reconstruction with or without linear post-smoothing. In penalized-likelihood (PL) image reconstruction with quadratic penalties, the MBMC approach outperforms the RRA approach up to a certain degree of smoothing beyond which both methods have approximately equal variance.