论文标题
关于动态最佳传输与功能提升之间的连接
On the Connection between Dynamical Optimal Transport and Functional Lifting
论文作者
论文摘要
功能提升方法通过将它们嵌入更大的空间来近似困难的非凸问题解决方案。在这项工作中，我们研究了一种基于嵌入固定范围$γ$的概率测量空间的数学严格公式。有趣的是，这种方法可以作为动力学最佳运输理论的概括。将已建立的连续性方程施加为约束，对应于具有一阶正则化的变异模型。通过修改连续性方程，该方法也可以扩展到具有高阶正则化的模型。
Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the space of pointwise probability measures over a fixed range $Γ$. Interestingly, this approach can be derived as a generalization of the theory of dynamical optimal transport. Imposing the established continuity equation as a constraint corresponds to variational models with first-order regularization. By modifying the continuity equation, the approach can also be extended to models with higher-order regularization.
