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

Research output: Contribution to journalArticle

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.

Details

Authors
Organisations
External organisations
  • KTH Royal Institute of Technology
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Probability Theory and Statistics
  • Signal Processing
  • Computational Mathematics

Keywords

  • optimal mass transport, multi-marginal problems, entropy regularization, spectral estimation, array signal processing, sensor fusion
Original languageEnglish
Article number107474
JournalSignal Processing
Volume171
Publication statusPublished - 2020
Publication categoryResearch
Peer-reviewedYes

Related research output

Filip Elvander, 2020, Centre for the Mathematical sciences, Lund University. 256 p.

Research output: ThesisDoctoral Thesis (compilation)

View all (1)