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