Multiview Sensing With Unknown Permutations: An Optimal Transport Approach

• URL: http://arxiv.org/abs/2103.07458v1
• Date: Fri, 12 Mar 2021 18:48:18 GMT
• Title: Multiview Sensing With Unknown Permutations: An Optimal Transport Approach
• Authors: Yanting Ma, Petros T. Boufounos, Hassan Mansour, Shuchin Aeron
• Abstract summary: We take a fresh look at the problem of recovering a signal subject to unknown permutations through the lens of optimal transport. 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.
• Score: 42.62524143925126
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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