Iterative nonlinear least squares algorithms for direct reconstruction of parametric images from dynamic PET

Indirect and direct methods have been developed for reconstructing parametric images from dynamic PET data. Indirect methods are relatively simple and easy to implement because the reconstruction and kinetic modeling are performed in two separate steps. Direct methods estimate the parametric images directly from the dynamic PET data and are statistically more efficient, but the algorithms are often difficult to implement. This paper presents a simple, monotonically convergent iterative algorithm for direct reconstruction of parametric images. Each iteration of the proposed algorithm consists of two separate steps: reconstruction of dynamic images followed by a pixel-wise weighted nonlinear least squares fitting. This algorithm resembles the empirical iterative implementation of the indirect approach, but converges to the solution of the direct formulation.