Distributed Basis Pursuit

Details Distributed Basis Pursuit Distributed Basis Pursuit

2010-09-06

arxiv.org/abs/1009.1128v3

Mathematics

Optimization and Control

Preprint of the journal version of the paper; IEEE Transactions on Signal Processing, Vol. 60, Issue 4, April, 2012

Scientific paper

10.1109/TSP.2011.2182347

We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP). BP finds the least L1-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.

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