Interior-point methodology for 3-D PET reconstruction.
Interior-point methods have been successfully applied to a wide variety of linear and nonlinear programming applications. This paper presents a class of algorithms, based on path-following interior-point methodology, for performing regularized maximum-likelihood (ML) reconstructions on three-dimensional (3-D) emission tomography data. The algorithms solve a sequence of subproblems that converge to the regularized maximum likelihood solution from the interior of the feasible region (the nonnegative orthant). We propose two methods, a primal method which updates only the primal image variables and a primal-dual method which simultaneously updates the primal variables and the Lagrange multipliers. A parallel implementation permits the interior-point methods to scale to very large reconstruction problems. Termination is based on well-defined convergence measures, namely, the Karush-Kuhn-Tucker first-order necessary conditions for optimality. We demonstrate the rapid convergence of the path-following interior-point methods using both data from a small animal scanner and Monte Carlo simulated data. The proposed methods can readily be applied to solve the regularized, weighted least squares reconstruction problem.
Center for Information Technology, National Institutes of Health, Bethesda, MD 20892-5624, USA. johnson@mail.nih.gov
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Johnson
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Seidel
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Sofer
D000465:Algorithms; D000818:Animals; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D016013:Likelihood Functions; D009010:Monte Carlo Method; D014055:Tomography, Emission-Computed