title: A fast fully 4-D incremental gradient reconstruction algorithm for list mode PET data.
abstract: We describe a fast and globally convergent fully four-dimensional incremental gradient (4DIG) algorithm to estimate the continuous-time tracer density from list mode positron emission tomography (PET) data. Detection of 511-keV photon pairs produced by positron-electron annihilation is modeled as an inhomogeneous Poisson process whose rate function is parameterized using cubic B-splines. The rate functions are estimated by minimizing the cost function formed by the sum of the negative log-likelihood of arrival times, spatial and temporal roughness penalties, and a negativity penalty. We first derive a computable bound for the norm of the optimal temporal basis function coefficients. Based on this bound we then construct and prove convergence of an incremental gradient algorithm. Fully 4-D simulations demonstrate the substantially faster convergence behavior of the 4DIG algorithm relative to preconditioned conjugate gradient. Four-dimensional reconstructions of real data are also included to illustrate the performance of this method.
authors.affiliation: Signal and Image Processing Institute, University of Southern California, Los Angeles, CA 90089, USA.
authors.forename: Quanzheng
authors.initials: Q
authors.lastname: Li
authors.forename: Evren
authors.initials: E
authors.lastname: Asma
authors.forename: Sangtae
authors.initials: S
authors.lastname: Ahn
authors.forename: Richard M
authors.initials: RM
authors.lastname: Leahy
mesh_terms: D000465:Algorithms; D000818:Animals; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D051379:Mice; D049268:Positron-Emission Tomography / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013382:Subtraction Technique; D013997:Time Factors