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 perf orming regularized maximum-likelihood (ML) reconstructions on three-dimensi onal (3-D) emission tomography data. The algorithms solve a sequence of sub problems that converge to the regularized maximum likelihood solution from the interior of the feasible region (the nonnegative orthant), We propose t wo methods, a primal method which updates only the primal image variables a nd a primal-dual method which simultaneously updates the primal variables a nd 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-Tuck er first-order necessary conditions for optimality, We demonstrate the rapi d convergence of the path-following interior-point methods using both data from a small animal scanner and Monte Carlo simulated data. The proposed me thods can readily be applied to solve the regularized, weighted least squar es reconstruction problem.