Strategies to Improve Direct EM Patlak Reconstructions

Abstract

Direct Expectation-Maximization (EM) reconstruction of parametric images from PET data has been proposed, to take advantage of the known Poisson character of raw PET data. However, direct reconstruction algorithms are then dependent on the properties of the kinetic model and of the radiotracer used. Moreover, the first direct EM reconstruction algorithm proposed, the Parametric Iterative Reconstruction (PIR) algorithm, based on the Patlak plot, converges slowly when applied to [$^{18\mathrm{F}}$]FDG data. Thus, alternative algorithms have been proposed to accelerate convergence. In this study, we propose additional strategies to improve the PIR algorithm. One strategy is to use a line search procedure to increase the size of steps taken at each iteration (PIR-LS). Another group of strategies is to apply physiological constraints (PIR-PC) on the intercept parameter of the Patlak plot, since this parameter has a small dynamic range and is more stable across subjects and across physiological and disease states. The third strategy is to apply a linear transform to the independent variables of the Patlak model (PIR-LTIV) to obtain new independent variables more favorable for convergence. PIR-LS, PIR-PC and PIR-LTIV were first compared to PIR and the Nested EM algorithm on simulated 2D data. Results showed that all new methods could increase the convergence speed of PIR, with PIR-LTIV having the fastest convergence among the new methods, and similar to that of the Nested EM algorithm. Then, PIR and PIR-LS were compared using a simulated dynamic brain dataset, PIR andPIR-PC were compared on a real lung tumor data set, and PIR-LTIV was tested on simulated brain data, real brain data, and the real lung tumor dataset. These data confirmed that all new methodscould increase PIR convergence, with PIR-LTIV being the most promising since convergence speed was visually similar to that of indirect reconstructions, with lower image noise.