Spatial resolution and noise properties of regularized motion-compensated image reconstruction

Reducing motion artifacts is an important problem in medical image reconstruction. Using gating to partition data into separate frames can reduce motion artifacts but can increase noise in images reconstructed from individual frames. One can pool the frames to reduce noise by using motion-compensated image reconstruction (MCIR) methods. MCIR methods have been studied in many medical imaging modalities to reduce both noise and motion artifacts. However, there has been less analysis of the spatial resolution and noise properties of MCIR methods. This paper analyzes the spatial resolution and noise properties of MCIR methods based on a general parametric motion model. For simplicity we consider the motion to be given. We present a method to choose quadratic spatial regularization parameters to provide predictable resolution properties that are independent of the object and the motion. The noise analysis shows that the estimator variance depends on both the measurement covariance and the Jacobian determinant values of the motion. A 2D PET simulation demonstrates the theoretical results.