Interior-point methodology for 3-D PET reconstruction.

C A Johnson; J Seidel; A Sofer

doi:10.1109/42.848179

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PubMed · 10909923

Interior-point methodology for 3-D PET reconstruction.

C A Johnson·J Seidel·A Sofer

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Abstract

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.

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Algorithms Animals Image Processing, Computer-Assisted Likelihood Functions Monte Carlo Method Tomography, Emission-Computed Journal Article Research Support, U.S. Gov't, Non-P.H.S.

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C A Johnson, J Seidel, A Sofer. 2000. Interior-point methodology for 3-D PET reconstruction.. https://doi.org/10.1109/42.848179

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