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.
Highlights
Motivated by several practical problems such as sampling in the presence of clock jitter, mobile sensor networks and multiple target tracking in radar, the problem of unlabeled sensing was first considered in [1]
We study a specific case of the unlabeled sensing problem where the set of permutations, modeling the loss of correspondence, is local
We consider the task of estimating the unknown permutation P∗ ∈ n,r from the views Y ∈ Rn×m such that
Summary
Motivated by several practical problems such as sampling in the presence of clock jitter, mobile sensor networks and multiple target tracking in radar, the problem of unlabeled sensing was first considered in [1]. There, the authors derived information theoretic results for identification of unknown signal under linear measurements when the measurement correspondence is lost Several generalizations of this problem as well as specific cases have been considered in [2]–[13]. We study a specific case of the unlabeled sensing problem where the set of permutations, modeling the loss of correspondence, is local. The block diagonal permutation structure we consider has been discussed in [11] but with the following additional assumptions on the model in (1): (a) The data matrix X∗ ∈ Rd×d is orthonormal, and (b) The block diagonal permutation P∗ is sparse. 4) One of the main conclusions of this paper is that, for the r-local model, multiple views significantly help in permutation recovery.
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