8 research outputs found
Distributed Recovery of Jointly Sparse Signals Under Communication Constraints
The problem of the distributed recovery of jointly sparse signals has attracted much attention recently. Let us assume that the nodes of a network observe different sparse signals with common support; starting from linear, compressed measurements, and exploiting network communication, each node aims at reconstructing the support and the non-zero values of its observed signal. In the literature, distributed greedy algorithms have been proposed to tackle this problem, among which the most reliable ones require a large amount of transmitted data, which barely adapts to realistic network communication constraints. In this work, we address the problem through a reweighted l1 soft thresholding technique, in which the threshold is iteratively tuned based on the current estimate of the support. The proposed method adapts to constrained networks, as it requires only local communication among neighbors, and the transmitted messages are indices from a finite set. We analytically prove the convergence of the proposed algorithm and we show that it outperforms the state-of-the-art greedy methods in terms of balance between recovery accuracy and communication load
Low-power distributed sparse recovery testbed on wireless sensor networks
Recently, distributed algorithms have been proposed
for the recovery of sparse signals in networked systems, e.g. wire-
less sensor networks. Such algorithms allow large networks to
operate autonomously without the need of a fusion center, and are
very appealing for smart sensing problems employing low-power
devices. They exploit local communications, where each node of
the network updates its estimates of the sensed signal also based
on the correlated information received from neighboring nodes.
In the literature, theoretical results and numerical simulations
have been presented to prove convergence of such methods to
accurate estimates. Their implementation, however, raises some
concerns in terms of power consumption due to iterative inter-
node communications, data storage, computation capabilities,
global synchronization, and faulty communications. On the other
hand, despite these potential issues, practical implementations on
real sensor networks have not been demonstrated yet. In this
paper we fill this gap and describe a successful implementation
of a class of randomized, distributed algorithms on a real
low-power wireless sensor network testbed with very scarce
computational capabilities. We consider a distributed compressed
sensing problem and we show how to cope with the issues
mentioned above. Our tests on synthetic and real signals show
that distributed compressed sensing can successfully operate in
a real-world environment
Online Optimization in Dynamic Environments: A Regret Analysis for Sparse Problems
Time-varying systems are a challenge in many scientific and engineering areas. Usually, estimation of time-varying parameters or signals must be performed online, which calls for the development of responsive online algorithms. In this paper, we consider this problem in the context of the sparse optimization; specifically, we consider the Elastic-net model. Following the rationale in [1], we propose a novel online algorithm and we theoretically prove that it is successful in terms of dynamic regret. We then show an application to recursive identification of time-varying autoregressive models, in the case when the number of parameters to be estimated is unknown. Numerical results show the practical efficiency of the proposed method