# Multiview Sensing With Unknown Permutations: An Optimal Transport Approach

arXiv: https://arxiv.org/abs/2103.07458 · HTML: https://mlsanity.com/paper/2103.07458/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 25 references that are in the map.
- First posted on arXiv 12 Mar 2021.

## Builds on (most cited first, 10 of 10)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [Continuum limit of total variation on point clouds](https://mlsanity.com/paper/1403.6355/) (2014)
- [Linear regression without correspondence](https://mlsanity.com/paper/1705.07048/) (2017)
- [A Transportation Lp Distance for Signal Analysis](https://mlsanity.com/paper/1609.08669/) (2016)
- [Denoising Linear Models with Permuted Data](https://mlsanity.com/paper/1704.07461/) (2017)
- [Signal Recovery from Unlabeled Samples](https://mlsanity.com/paper/1701.08701/) (2017)
- [Permutations Unlabeled beyond Sampling Unknown](https://mlsanity.com/paper/1812.00498/) (2018)
- [Machine Learning Methods for Data Association in Multi-Object Tracking](https://mlsanity.com/paper/1802.06897/) (2018)

## Built on by (most cited first, 1 of 1)

- [Regularization for Shuffled Data Problems via Exponential Family Priors on the Permutation Group](https://mlsanity.com/paper/2111.01767/) (2021)

## Abstract (arXiv)

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.