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.

翻译：作为Benamou和Brenier最优质量传输（OMT）方法的推广，正则化最优质量传输（rOMT）通过总动能定义最优性，构建了从初始质量分布到目标质量分布的传输问题，但需满足平流-扩散约束方程。rOMT与Benamou和Brenier的公式均要求初始与最终总质量相等，且整个传输过程中质量守恒。然而在诸多应用中（如动态图像追踪），这一约束几乎难以满足。为此，我们提出采用非平衡版本的rOMT以消除该约束，并给出了详细的数值求解流程及其在分析大脑流体流动中的应用。