A Vectorial Approach to Unbalanced Optimal Mass Transport

TL;DR

This paper integrates unbalanced optimal mass transport into the vector-valued OMT framework by incorporating a source term into the continuity equation, expanding the theoretical understanding of mass variation in transport problems.

Contribution

It demonstrates how unbalanced OMT can be formulated within the vector-valued OMT framework by adding a source term to the continuity equation.

Findings

Unbalanced OMT fits into the vector-valued OMT framework.

The source term effectively models mass creation or destruction.

The approach broadens the applicability of vectorial OMT methods.

Abstract

Unbalanced optimal mass transport (OMT) seeks to remove the conservation of mass constraint by adding a source term to the standard continuity equation in the Benamou-Brenier formulation of OMT. In this note, we show how the addition of the source fits into the vector-valued OMT framework.