Interior-Point Methodology for Large-Scale Regularized Maximum Likelihood Reconstruction in Emission Tomography

Interior-point methods possess strong theoretical properties and have been successfully applied to a wide variety of linear and nonlinear programming applications. This paper presents a class of algorithms, based on interior-point methodology, for performing regularized maximum likelihood reconstructions on 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 non-negative 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. Termination to a solution of desired accuracy is based on well-defined convergence measures. We demonstrate the rapid convergence of the interior-point methods using both data from a small animal scanner and Monte Carlo simulated data. We present a parallel implementation that permits the interior-point methods to scale to very large reconstruction problems.