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Multi-marginal opti...
Multi-marginal optimal transport using partial information with applications in robust localization and sensor fusion
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- Elvander, Filip (författare)
- Lund University,Lunds universitet,Statistical Signal Processing Group,Forskargrupper vid Lunds universitet,Matematisk statistik,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Lund University Research Groups,Mathematical Statistics,Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
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- Haasler, Isabel (författare)
- KTH,KTH Royal Institute of Technology,Optimeringslära och systemteori
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- Jakobsson, Andreas (författare)
- Lund University,Lunds universitet,Biomedical Modelling and Computation,Forskargrupper vid Lunds universitet,Statistical Signal Processing Group,Lund University Research Groups
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- Karlsson, Johan (författare)
- KTH,KTH Royal Institute of Technology,Optimeringslära och systemteori
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(creator_code:org_t)
- Elsevier BV, 2020
- 2020
- Engelska.
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Ingår i: Signal Processing. - : Elsevier BV. - 0165-1684 .- 1872-7557. ; 171
- Relaterad länk:
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http://dx.doi.org/10...
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https://lup.lub.lu.s...
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https://doi.org/10.1...
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https://urn.kb.se/re...
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Signalbehandling (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Signal Processing (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering (hsv//eng)
Nyckelord
- optimal mass transport
- multi-marginal problems
- entropy regularization
- spectral estimation
- array signal processing
- sensor fusion
- Array signal processing
Publikations- och innehållstyp
- art (ämneskategori)
- ref (ämneskategori)
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