Multi-marginal optimal transport using partial information with applications in robust localization and sensor fusion
Elvander, Filip LU ; Haasler, Isabel ; Jakobsson, Andreas LU
and Karlsson, Johan
(2020)
In Signal Processing
171.
- Abstract
- 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... (More)
- 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/ffc57cad-9d61-4a84-b4d3-a50b9565ec9c
- author
- Elvander, Filip
LU
; Haasler, Isabel
; Jakobsson, Andreas
LU
and Karlsson, Johan
- organization
- publishing date
- 2020
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- optimal mass transport, multi-marginal problems, entropy regularization, spectral estimation, array signal processing, sensor fusion
- in
- Signal Processing
- volume
- 171
- article number
- 107474
- publisher
- Elsevier
- external identifiers
-
- scopus:85079545878
- ISSN
- 0165-1684
- DOI
- 10.1016/j.sigpro.2020.107474
- language
- English
- LU publication?
- yes
- id
- ffc57cad-9d61-4a84-b4d3-a50b9565ec9c
- date added to LUP
- 2020-04-29 16:30:14
- date last changed
- 2022-04-18 21:56:20
@article{ffc57cad-9d61-4a84-b4d3-a50b9565ec9c,
abstract = {{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.}},
author = {{Elvander, Filip and Haasler, Isabel and Jakobsson, Andreas and Karlsson, Johan}},
issn = {{0165-1684}},
keywords = {{optimal mass transport; multi-marginal problems; entropy regularization; spectral estimation; array signal processing; sensor fusion}},
language = {{eng}},
publisher = {{Elsevier}},
series = {{Signal Processing}},
title = {{Multi-marginal optimal transport using partial information with applications in robust localization and sensor fusion}},
url = {{http://dx.doi.org/10.1016/j.sigpro.2020.107474}},
doi = {{10.1016/j.sigpro.2020.107474}},
volume = {{171}},
year = {{2020}},
}