R-local unlabeled sensing: A novel graph matching approach for multiview unlabeled sensing under local permutations
This addresses a practical problem in mobile sensor networks, target tracking, and point cloud alignment, but it is incremental as it builds on existing unlabeled sensing methods by adding local permutations and multiple views.
The paper tackles the problem of unlabeled multi-view sensing with local permutations, where measurements are scrambled under unknown local permutations, by proposing a computationally efficient algorithm that uses graph alignment and Gromov-Wasserstein alignment. Simulation results show the algorithm is scalable and works in low to moderate SNR regimes.
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.