Distributed Compressed Sensing for Static and Time-Varying Networks

@article{Patterson2014DistributedCS,
  title={Distributed Compressed Sensing for Static and Time-Varying Networks},
  author={Stacy Patterson and Yonina C. Eldar and Idit Keidar},
  journal={IEEE Transactions on Signal Processing},
  year={2014},
  volume={62},
  pages={4931-4946}
}
We consider the problem of in-network compressed sensing from distributed measurements. Every agent has a set of measurements of a signal x, and the objective is for the agents to recover x from their collective measurements using only communication with neighbors in the network. Our distributed approach to this problem is based on the centralized Iterative Hard Thresholding algorithm (IHT). We first present a distributed IHT algorithm for static networks that leverages standard tools from… 

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References

SHOWING 1-10 OF 62 REFERENCES
Distributed sparse signal recovery for sensor networks
TLDR
A distributed algorithm for sparse signal recovery in sensor networks based on Iterative Hard Thresholding (IHT) is proposed, which can dramatically reduce this communication cost by leveraging solutions to the distributed top-K problem in the database literature.
D-ADMM: A Communication-Efficient Distributed Algorithm for Separable Optimization
TLDR
D-ADMM is proven to converge when the network is bipartite or when all the functions are strongly convex, although in practice, convergence is observed even when these conditions are not met.
Distributed soft thresholding for sparse signal recovery
TLDR
A new class of distributed algorithms to solve Lasso regression problems, when the communication to a fusion center is not possible, e.g., due to communication cost or privacy reasons, are proposed.
Distributed Basis Pursuit
TLDR
The algorithm, named D-ADMM, is a decentralized implementation of the alternating direction method of multi- pliers, and it is shown through numerical simulation that the algorithm requires considerably less communications between the nodes than the state-of-the-art algorithms.
Distributed Spectrum Sensing for Cognitive Radio Networks by Exploiting Sparsity
TLDR
A cooperative approach to the sensing task of wireless cognitive radio (CR) networks is introduced based on a basis expansion model of the power spectral density map in space and frequency that reduces spatial and frequency spectrum leakage by 15 dB relative to least-squares alternatives.
Sparse event detection in wireless sensor networks using compressive sensing
TLDR
This paper forms the problem for sparse event detection in wireless sensor networks as a compressive sensing problem, and proposes a Bayesian detection algorithm that has much better performance than the l1-magic algorithm proposed in the literature.
Cooperative Sensing and Compression in Vehicular Sensor Networks for Urban Monitoring
TLDR
The results show that the cooperative data sensing and compression approach is superior to the conventional sampling and interpolation strategy which propagates data in an uncompressed form, with 4-5dB gain in reconstruction quality and 21-55% savings in communication cost for the same sampling times.
Cooperative Convex Optimization in Networked Systems: Augmented Lagrangian Algorithms With Directed Gossip Communication
TLDR
This work solves the problem for generic connected network topologies with asymmetric random link failures with a novel distributed, de-centralized algorithm, and proposes a novel, Gauss-Seidel type, randomized algorithm, at a fast time scale.
Distributed algorithms for basis pursuit
TLDR
Methods for solving the Basis Pursuit problem in a distributed environment, i.e., when the computational resources and the matrix A are distributed over several interconnected nodes, are explored.
Compressed Sensing With Nonlinear Observations and Related Nonlinear Optimization Problems
  • T. Blumensath
  • Computer Science
    IEEE Transactions on Information Theory
  • 2013
TLDR
It is shown that, under conditions similar to those required in the linear setting, the iterative hard thresholding algorithm can be used to accurately recover sparse or structured signals from few nonlinear observations.
...
...