1. 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 = ?]

2. 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 = ?]

3. Direct Reconstruction Schemek1
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)}

4. Step-by-step: Direct Reconstructionk1
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)}

5. 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)}

6. Direct Recon. with Regularizationk3
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)}