  As a generalization of the optimal mass transport (OMT) approach of Benamou
and Brenier's, the regularized optimal mass transport (rOMT) formulates a
transport problem from an initial mass configuration to another with the
optimality defined by the total kinetic energy, but subject to an
advection-diffusion constraint equation. Both rOMT and the Benamou and
Brenier's formulation require the total initial and final masses to be equal;
mass is preserved during the entire transport process. However, for many
applications, e.g., in dynamic image tracking, this constraint is rarely if
ever satisfied. Therefore, we propose to employ an unbalanced version of rOMT
to remove this constraint together with a detailed numerical solution procedure
and applications to analyzing fluid flows in the brain.
