Accelerated direct reconstruction of PET parametric images using augmented Lagrangian optimization

Abstract

Direct estimation of physiologically or biochemically important parameters from raw projection data is challenging in dynamic positron emission tomography (PET) due to the coupling between tomographic image reconstruction and nonlinear kinetic parameter estimation. Optimization transfer algorithms have been previously developed to solve the complex optimization problem. These algorithms, however, can suffer from slow convergence rate. This paper proposes an accelerated iterative algorithm for direct reconstruction of kinetic parameters through variable splitting under the framework of augmented Lagrangian optimization. Similar to the optimization transfer algorithms, the proposed algorithm splits each iteration of direct reconstruction into two separate steps: dynamic image reconstruction and pixel-wise nonlinear least squares kinetic fitting. The unique advantage of the new algorithm is its flexibility to employ any existing reconstruction algorithms in the reconstruction step, which can substantially accelerate the convergence speed. Computer simulations show that the proposed direct algorithm can be efficiently implemented and achieve much faster convergence speed than the optimization transfer algorithm.