Distributed Recovery of Jointly Sparse Signals Under Communication Constraints

Abstract

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 1 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.

Online Optimization in Dynamic Environments: A Regret Analysis for Sparse Problems

“…On the one hand, its simplicity allows a straightforward implementation and makes its theoretical analysis affordable. On the other hand, IST is prone to decentralization and parallel implementation [26,14,15,12]. In this work, we deal with a centralized setting, but the extension to a distributed setting (for example, a sensor network) might be investigated in the future.…”

Estimate exchange over network is good for distributed hard thresholding pursuit

“…Next, we mention that there exist several signal models in the literature where sparse signals are not the same for all nodes of a network. For example, denoting the signal at node l by x l , supports of x l are the same in [17], [31], [32], [33], but not their signal values; further, x l have common and private support and/or signal parts in [34], [12], [18]. In this article, we consider the setup (1) where ∀l, x l = x.…”

Low-power distributed sparse recovery testbed on wireless sensor networks

“…Specifically, they envisaged a network in which each node acquires and compresses data according to the CS paradigm; after that, each node transmits such compressed data to the FC, which performs (centralized) sparse signal recovery. More recent works [8], [9], [10], [11], [12], [13], instead, focus on the fully distributed case where no FC is used: both acquisition and recovery are performed in-network, leveraging on local cooperation between nodes. This is a good choice when a FC is not available or far to reach.…”

“…Distributed iterative algorithms for in-network recovery (without FC) of sparse signals have been lately proposed and theoretically analysed. In particular, there are methods based on iterative thresholding [8], [10], [11], [13], alternating direction method of multipliers [12], [15], and greedy algorithms [9]. In all these works, local cooperation is envisaged, that is, each node of the network can share information with its neighbors.…”

“…For this motivation, solutions to decrease the transmission load have been proposed, exploiting, e.g., randomization [10] and binary messaging [12], [13]. These schemes have been shown to dramatically reduce the number of required transmissions with respect to earlier methods.…”