Conventional Reconstruction Followed by Kinetic Modelling PET Scanner P F B K1 k2 k3 k4 Kinetic Model Back-Project sinograms for each time-frame separately; Estimate parameters, j, for a sinlge region: Draw regions and make time-activity curves. j = [K1 = ?, k2 = ?, k3 = ? , k4 = ?]

Step-by-step: Conventional Recon Followed by Kinetic Modelling PET Scanner P F B K1 k2 k3 k4 Kinetic Model Back-Project sinograms for each time-frame separately; Estimate parameters, j, for a sinlge region: Draw regions and make time-activity curves. j = [K1 = ?, k2 = ?, k3 = ? , k4 = ?]

Direct Reconstruction Scheme k1 measured data k3 PET Scanner K1 Kinetic Model F P F B K1 k2 k3 k4 k2 k4 Guess Parametric Images, Solve Model for Emission Forward Project Emisisons, F E[Y |F(j)] = AF(j) + m Calculate Fit of Sinograms min {-LL(Y|j)}

Step-by-step: Direct Reconstruction k1 measured data k3 PET Scanner K1 Kinetic Model F P F B K1 k2 k3 k4 k2 k4 Guess Parametric Images, Solve Model for Emission Forward Project Emisisons, F E[Y |F(j)] = AF(j) + m Calculate Fit of Sinograms min {-LL(Y|j)}

Direct Reconstruction Scheme measured data k3 PET Scanner K1 Kinetic Model F P F B K1 k2 k3 k4 k2 k4 Guess NEW Parametric Images, Solve Model for Emission Forward Project Emisisons, F E[Y |F(j)] = AF(j) + m Calculate Regularized Fit of Sinograms min {-LL(Y|j) + S(j)}

Direct Recon. with Regularization k3 measured data PET Scanner K1 Kinetic Model F P F B K1 k2 k3 k4 k2 k4 Convergence! Guess Regularized Parametric Images, Solve Model for Emission Forward Project Emisisons, F E[Y |F(j)] = AF(j) + m Calculate Regularized Fit of Sinograms min {-LL(Y|j) + S(j)}