Multi-marginal optimal transport using partial information with applications in robust localization and sensor fusion

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Multi-marginal optimal transport using partial information with applications in robust localization and sensor fusion. / Elvander, Filip; Haasler, Isabel; Jakobsson, Andreas; Karlsson, Johan.

In: Signal Processing, Vol. 171, 107474, 2020.

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TY - JOUR

T1 - Multi-marginal optimal transport using partial information with applications in robust localization and sensor fusion

AU - Elvander, Filip

AU - Haasler, Isabel

AU - Jakobsson, Andreas

AU - Karlsson, Johan

PY - 2020

Y1 - 2020

N2 - During recent decades, there has been a substantial development in optimal mass transport theory and methods. In this work, we consider multi-marginal problems wherein only partial information of each marginal is available, a common setup in many inverse problems in, e.g., remote sensing and imaging. By considering an entropy regularized approximation of the original transport problem, we propose an algorithm corresponding to a block-coordinate ascent of the dual problem, where Newton’s algorithm is used to solve the sub-problems. In order to make this computationally tractable for large-scale settings, we utilize the tensor structure that arises in practical problems, allowing for computing projections of the multi-marginal transport plan using only matrix-vector operations of relatively small matrices. As illustrating examples, we apply the resulting method to tracking and barycenter problems in spatial spectral estimation. In particular, we show that the optimal mass transport framework allows for fusing information from different time steps, as well as from different sensor arrays, also when the sensor arrays are not jointly calibrated. Furthermore, we show that by incorporating knowledge of underlying dynamics in tracking scenarios, one may arrive at accurate spectral estimates, as well as faithful reconstructions of spectra corresponding to unobserved time points.

AB - During recent decades, there has been a substantial development in optimal mass transport theory and methods. In this work, we consider multi-marginal problems wherein only partial information of each marginal is available, a common setup in many inverse problems in, e.g., remote sensing and imaging. By considering an entropy regularized approximation of the original transport problem, we propose an algorithm corresponding to a block-coordinate ascent of the dual problem, where Newton’s algorithm is used to solve the sub-problems. In order to make this computationally tractable for large-scale settings, we utilize the tensor structure that arises in practical problems, allowing for computing projections of the multi-marginal transport plan using only matrix-vector operations of relatively small matrices. As illustrating examples, we apply the resulting method to tracking and barycenter problems in spatial spectral estimation. In particular, we show that the optimal mass transport framework allows for fusing information from different time steps, as well as from different sensor arrays, also when the sensor arrays are not jointly calibrated. Furthermore, we show that by incorporating knowledge of underlying dynamics in tracking scenarios, one may arrive at accurate spectral estimates, as well as faithful reconstructions of spectra corresponding to unobserved time points.

KW - optimal mass transport

KW - multi-marginal problems

KW - entropy regularization

KW - spectral estimation

KW - array signal processing

KW - sensor fusion

U2 - 10.1016/j.sigpro.2020.107474

DO - 10.1016/j.sigpro.2020.107474

M3 - Article

VL - 171

JO - Signal Processing

JF - Signal Processing

SN - 0165-1684

M1 - 107474

ER -