Direct 4D reconstruction of parametric images incorporating anato-functional joint entropy

We developed an anatomy-guided 4D closed-form algorithm to directly reconstruct parametric images from projection data for (nearly) irreversible tracers. Conventional methods consist of individually reconstructing 2D/3D PET data, followed by graphical analysis on the sequence of reconstructed image frames. The proposed direct reconstruction approach maintains the simplicity and accuracy of the expectation-maximization (EM) algorithm by extending the system matrix to include the relation between the parametric images and the measured data. A closed-form solution was achieved using a different hidden complete-data formulation within the EM framework. Furthermore, the proposed method was extended to maximum a posterior reconstruction via incorporation of MR image information, taking the joint entropy between MR and parametric PET features as the prior. Using realistic simulated noisy [(11)C]-naltrindole PET and MR brain images/data, the quantitative performance of the proposed methods was investigated. Significant improvements in terms of noise versus bias performance were demonstrated when performing direct parametric reconstruction, and additionally upon extending the algorithm to its Bayesian counterpart using the MR-PET joint entropy measure.