Motion-Compensated PET Image Reconstruction via Separable Parabolic Surrogates

The effective resolution of positron emission tomography (PET) can be significantly degraded by patient motion during data acquisition. This is especially true in the thorax due to respiratory motion. This study concentrates on the improvement of motion correction algorithms both in terms of image quality and computational cost. In this paper, we present a novel motion-compensated image reconstruction (MCIR) algorithm based on a parabolic surrogate likelihood function instead of the loglikelihood function of the expectation maximization (EM) algorithm. The theoretical advantage of the parabolic surrogate algorithm lies within the fact that its loglikelihood is upper bounded by the EM loglikelihood, thus it will converge faster than EM. This is of particular importance in PET motion correction, where reconstructions are very computationally demanding. Relaxation parameters were also introduced to converge closer to the maximum likelihood (ML) solution and achieve lower noise levels. Image reconstructions with embedded relaxation parameters actually converged to better solutions than the corresponding ones without relaxation. Motion-compensated parabolic surrogates were indeed shown to accelerate convergence compared to EM, without reaching a limit cycle. Nonetheless, with the incorporation of ordered subsets in the reconstruction setting, the improvement was less evident.