Statistical PET image reconstruction using duality of nonlinear programming

In recent years technology has been in practical use which performs PET image reconstruction using a Maximum Likelihood (ML) estimation or a Maximum A Posteriori (MAP) estimation to improve the quality of the reconstructed images. Generally speaking, these methods require minimization of a convex cost function based on an iterative method and are accompanied by many problems related to the computational complexity. In this paper we propose a new Row‐Action type image reconstruction method that uses duality of nonlinear programming to rapidly converge with a small computational complexity per iteration. The proposed method has various advantages compared to the conventional methods. Examples of the advantages include: (1) avoids limit cycles and rapidly converges to true solutions, (2) can easily handle nonnegative constraint, (3) sufficient reconstructed images are obtained in one iteration, (4) easy to implement with a small number of empirically set parameters. The effectiveness of the proposed method is presented through simulated experiments and results of applications to clinical PET data are also presented.