Unlabeled Sensing With Local Permutations

Unlabeled sensing is a linear inverse problem where the measurements are scrambled with an unknown permutation resulting in a loss of correspondence to the measurement matrix. In this paper, we consider a special case of the unlabeled sensing problem where we restrict the class of permutations to be local and allow for multiple views. This setting is motivated via some practical problems. In this setting, we consider a regime where none of the previous results and algorithms are applicable and provide a computationally efficient algorithm, which exploits the Gromov-Wasserstein alignment framework locally. Simulation results are provided on synthetic data sets.