ITERATIVE ALGEBRAIC RECONSTRUCTION ALGORITHMS FOR EMISSION COMPUTED-TOMOGRAPHY - A UNIFIED FRAMEWORK AND ITS APPLICATION TO POSITRON EMISSION TOMOGRAPHY

In this paper, a unified framework of iterative algebraic reconstructi on for emission computed tomography (ECT) and its application to posit ron emission tomography (PET) is presented. The unified framework is b ased on an algebraic image restoration model and contains conventional iterative algebraic reconstruction algorithms: ART, SIRT, Landweber i teration (LWB), the generalized Landweber iteration (GLWB), the steepe st descent method (STP), as well as iterative filtered backprojection (IFBP) reconstruction algorithms: Chang's method, Walters' method, and a modified iterative MAP. The framework provides an effective tool to systematically study conventional iterative algebraic algorithms and IFBP algorithms. Based on this framework, conventional iterative algeb raic algorithms and IFBP algorithms are generalized. It is shown from the algebraic point of view that IFBP algorithms are not only excellen t methods for correction of attenuation (either uniform or nonuniform) but are also good general iterative reconstruction algorithms (they c an be applied to either attenuated or attenuation-free projections and converge very fast). The convergence behavior of iterative algebraic algorithms is discussed and insight is drawn into the fast convergence proper-ty of IFBP algorithms. A simulated PET system is used to evalu ate IFBP algorithms and LWB in comparison with the maximum likelihood estimation via expectation maximization algorithm (MLE-EM) and the fil tered backprojection (FBP) algorithm. The simulation results indicate that for both attenuation-free projection and attenuated projection ca ses IFBP algorithms have a significant computational advantage over LW B and MLE-EM, and have performance advantages over FBP in terms of con trast recovery and/or noise-to-signal ratios (NSRs) in regions of inte rest.