Penalized direct estimation of parametric images in PET

Abstract

Direct positron emission tomography (PET) reconstruction has been developed for acquiring accurate parametric imaging from raw measurement. Direct reconstruction estimates physiological kinetic parameters in iterative reconstruction process that contains two steps such as updating dynamic images and calculating nonlinear least square (NLS) parameter fitting. Although the quality of dynamic images has been significantly improved using the direct reconstruction, the small kinetic values related to the binding potential are still noisy due to high noise variance of the conventional pixel-by-pixel NLS. To improve the performance, we propose a penalized direct reconstruction that contains the Poisson likelihood, ridge regression with NLS, and total variation (TV) terms. In particular, because the kinetic parameters are three dimensional images and we can assume that the kinetic parameters of neighbor voxels varies smoothly, we can impose a 3-D TV regularization to the kinetic parameter images directly. To solve the cost function, we use a splitting method exploiting an alternating direction method of multipliers (ADMM) algorithm. In computer simulation, we use a segmented brain phantom in which different kinetic parameters are used for different regions. We compare binding potential images of conventional methods and the proposed method. We demonstrate that the proposed method is significantly accurate and improves the quality of binding potential image compared to the conventional direct method.