R-Local Unlabeled Sensing: A Novel Graph Matching Approach for Multiview Unlabeled Sensing Under Local Permutations

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 multi-view unlabeled sensing under local permutations, previous results and algorithms are not directly applicable. In this paper, we propose a computationally efficient algorithm, R-local unlabeled sensing (RLUS), that creatively exploits the machinery of indefinite relaxations of the graph matching problem 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.