Regularization design for isotropic spatial resolution in motion-compensated image reconstruction

Patient motion degrades image quality in medical imaging. Gating can reduce motion artifacts by using part of the acquired data, but can increase noise. Motion-compensated image reconstruction (MCIR) utilizes all collected data with motion information to reduce motion artifacts and noise. Interactions between Poisson log-likelihood and quadratic regularizers lead to nonuniform and anisotropic spatial resolution in the static case. These undesirable problems can become worse in MCIR due to local motion. We previously compensated for local volume changes in MCIR to provide approximately uniform spatial resolution, but achieved isotropic resolution only for the static case. This paper proposes a quadratic spatial regularizer design that achieves nearly uniform and isotropic spatial resolution in MCIR. We consider "analytical approach" to regularization design that was developed for static image reconstruction and extend it to MCIR methods based on a general parametric motion model. Our proposed regularizer can compensate not only for the effects of interactions between the Poisson log likelihood and the spatial regularizer but also for the effects of nonrigid motion. A 2D PET simulation demonstrates the theoretical results.