Kinetic Model Fitting with Forced Convexification

During dynamic tomography reconstruction, kinetic models, e.g. the two-tissue compartment model, should be fitted to the reconstructed activity values in each voxel and frame, which is equivalent to the solution of a huge number of general optimization problems. Newton's and Levenberg's methods have quadratic convergence speed close to the optimum, but they may get stuck in local extrema, and their convergence is not guaranteed at all. The failure of convergence of the voxel time activity functions may slow down the convergence of the global reconstruction. To solve this, we propose the dynamic transformation of the target function to shrink those regions of the domain where Newton's method would not go into the direction of the optimum. We specify the conditions of such transformations and provide concrete solutions. We also make the transformation scale or time dependent to allow its gradual elimination when it is not needed anymore.