title: Weighted least-squares reconstruction methods for positron emission tomography.
abstract: We present unpenalized and penalized weighted least-squares (WLS) reconstruction methods for positron emission tomography (PET), where the weights are based on the covariance of a model error and depend on the unknown parameters. The penalty function for the latter method is chosen so that certain a priori information is incorporated. The algorithms used to minimize the WLS objective functions guarantee nonnegative estimates and, experimentally, they converged faster than the maximum likelihood expectation-maximization (ML-EM) algorithm and produced images that had significantly better resolution and contrast. Although simulations suggest that the proposed algorithms are globally convergent, a proof of convergence has not yet been found. Nevertheless, we are able to show that the unpenalized method produces estimates that decrease the objective function monotonically with increasing iterations.
authors.affiliation: Department of Electrical and Computer Engineering, University of Florida, Gainesville 32611, USA. anderson@eel.ufl.edu
authors.forename: J M
authors.initials: JM
authors.lastname: Anderson
authors.forename: B A
authors.initials: BA
authors.lastname: Mair
authors.forename: M
authors.initials: M
authors.lastname: Rao
authors.forename: C H
authors.initials: CH
authors.lastname: Wu
mesh_terms: D000465:Algorithms; D001921:Brain / Q000000981:diagnostic imaging; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D016018:Least-Squares Analysis; D019047:Phantoms, Imaging; D014055:Tomography, Emission-Computed / Q000379:methods*