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Iterative algebraic reconstruction algorithms for emission computed tomography: A unified framework and its application to positron emission tomography
Author(s) -
Xu XiaoLiang,
Liow JeihSan,
Strother Stephen C.
Publication year - 1993
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.596954
Subject(s) - algorithm , algebraic reconstruction technique , iterative reconstruction , iterative method , expectation–maximization algorithm , projection (relational algebra) , convergence (economics) , mathematics , algebraic number , radon transform , computer science , mathematical optimization , artificial intelligence , maximum likelihood , mathematical analysis , statistics , economics , economic growth
In this paper, a unified framework of iterative algebraic reconstruction for emission computed tomography (ECT) and its application to positron emission tomography (PET) is presented. The unified framework is based on an algebraic image restoration model and contains conventional iterative algebraic reconstruction algorithms: ART, SIRT, Landweber iteration (LWB), the generalized Landweber iteration (GLWB), the steepest 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 algebraic algorithms and IFBP algorithms are generalized. It is shown from the algebraic point of view that IFBP algorithms are not only excellent methods for correction of attenuation (either uniform or nonuniform) but are also good general iterative reconstruction algorithms (they can 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 property of IFBP algorithms. A simulated PET system is used to evaluate IFBP algorithms and LWB in comparison with the maximum likelihood estimation via expectation maximization algorithm (MLE‐EM) and the filtered backprojection (FBP) algorithm. The simulation results indicate that for both attenuation‐free projection and attenuated projection cases IFBP algorithms have a significant computational advantage over LWB and MLE‐EM, and have performance advantages over FBP in terms of contrast recovery and/or noise‐to‐signal ratios (NSRs) in regions of interest.