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Distributed basis pursuit

Mota, JFC; Xavier, JMF; Aguiar, PMQ; Puschel, M; (2012) Distributed basis pursuit. IEEE Transactions on Signal Processing , 60 (4) pp. 1942-1956. 10.1109/TSP.2011.2182347.

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Abstract

We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP). BP finds the least ℓ 1-norm solution of the underdetermined linear system Ax = b and is used, for example, in compressed sensing for reconstruction. Our algorithm solves BP on a distributed platform such as a sensor network, and is designed to minimize the communication between nodes. The algorithm only requires the network to be connected, has no notion of a central processing node, and no node has access to the entire matrix A at any time. We consider two scenarios in which either the columns or the rows of A are distributed among the compute nodes. Our algorithm, named D-ADMM, is a decentralized implementation of the alternating direction method of multipliers. We show through numerical simulation that our algorithm requires considerably less communications between the nodes than the state-of-the-art algorithms. © 2011 IEEE.

Type: Article
Title: Distributed basis pursuit
DOI: 10.1109/TSP.2011.2182347
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Electronic and Electrical Eng
URI: http://discovery.ucl.ac.uk/id/eprint/1490484
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