R-local unlabeled sensing: A novel graph matching approach for multiview unlabeled sensing under local permutations

TL;DR

This paper introduces a new graph matching algorithm for multi-view unlabeled sensing with local permutations, effectively estimating local permutations in scenarios like sensor networks and point cloud alignment.

Contribution

It proposes a novel, scalable algorithm that leverages graph and Gromov-Wasserstein alignment to solve local permutation problems in multi-view unlabeled sensing.

Findings

Algorithm is computationally efficient and scalable.

Effective in low to moderate SNR regimes.

Applicable to practical scenarios like sensor networks and point cloud registration.

Abstract

Unlabeled sensing is a linear inverse problem where the measurements are scrambled under an unknown permutation leading to loss of correspondence between the measurements and the rows of the sensing matrix. Motivated by practical tasks such as mobile sensor networks, target tracking and the pose and correspondence estimation between point clouds, we study a special case of this problem restricting the class of permutations to be local and allowing for multiple views. In this setting, namely unlabeled multi-view sensing with local permutation, previous results and algorithms are not directly applicable. In this paper, we propose a computationally efficient algorithm that creatively exploits the machinery of graph alignment and Gromov-Wasserstein alignment and leverages the multiple views to estimate the local permutations. Simulation results on synthetic data sets indicate that the proposed algorithm is scalable and applicable to the challenging regimes of low to moderate SNR.