Multiview Sensing With Unknown Permutations: An Optimal Transport Approach
This work addresses a specific challenge in multiview sensing for fields like robotics and imaging, offering an incremental improvement by incorporating regularization into existing frameworks.
The paper tackles the problem of recovering signals measured under unknown permutations, common in applications like imaging deformable objects and simultaneous localization and mapping, by introducing a regularization function to promote likely permutations and developing a tractable algorithm using optimal transport relaxations.
In several applications, including imaging of deformable objects while in motion, simultaneous localization and mapping, and unlabeled sensing, we encounter the problem of recovering a signal that is measured subject to unknown permutations. In this paper we take a fresh look at this problem through the lens of optimal transport (OT). In particular, we recognize that in most practical applications the unknown permutations are not arbitrary but some are more likely to occur than others. We exploit this by introducing a regularization function that promotes the more likely permutations in the solution. We show that, even though the general problem is not convex, an appropriate relaxation of the resulting regularized problem allows us to exploit the well-developed machinery of OT and develop a tractable algorithm.