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

A Decentralized Bayesian Algorithm for Distributed Compressive Sensing in Networked Sensing Systems

Compressive sensing (CS), as a new sensing/sampling paradigm, facilitates signal acquisition by reducing the number of samples required for reconstruction of the original signal, and thus appears to be a promising technique for applications where the sampling cost is high, e.g., the Nyquist rate exceeds the current capabilities of analog-to-digital converters (ADCs). Conventional CS, although effective for dealing with one signal, only leverages the intra-signal correlation for reconstruction. This paper develops a decentralized Bayesian reconstruction algorithm for networked sensing systems to jointly reconstruct multiple signals based on the distributed compressive sensing (DCS) model that exploits both intra- and inter-signal correlations. The proposed approach is able to address networked sensing system applications with privacy concerns and/or for a fusion-centre-free scenario, where centralized approaches fail. Simulation results demonstrate that the proposed decentralized approaches have good recovery performance and converge reasonably quicklyThis is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/TWC.2015.248798

Simultaneous Bayesian Sparse Approximation with Structured Sparse Models

Sparse approximation is key to many signal processing, image processing and machine learning applications. If multiple signals maintain some degree of dependency, for example the support sets are statistically related, then it will generally be advantageous to jointly estimate the sparse representation vectors from the measurements vectors as opposed to solving for each signal individually. In this paper, we propose simultaneous sparse Bayesian learning (SBL) for joint sparse approximation with two structured sparse models (SSMs), where one is row-sparse with embedded element-sparse, and the other one is row-sparse plus element-sparse. While SBL has attracted much attention as a means to deal with a single sparse approximation problem, it is not obvious how to extend SBL to SSMs. By capitalizing on a dual-space view of existing convex methods for SMs, we showcase the precision component model and covariance component model for SSMs, where both models involve a common hyperparameter and an innovation hyperparameter that together control the prior variance for each coefficient. The statistical perspective of precision component vs. covariance component models unfolds the intrinsic mechanism in SSMs, and also leads to our development of SBL-inspired cost functions for SSMs. Centralized algorithms, that include ℓ1 and ℓ2 reweighting algorithms, and consensus based decentralized algorithms are developed for simultaneous sparse approximation with SSMs. In addition, theoretical analysis is conducted to provide valuable insights into the proposed approach, which includes global minima analysis of the SBLinspired nonconvex cost functions and convergence analysis of the proposed ℓ1 reweighting algorithms for SSMs. Superior performance of the proposed algorithms is demonstrated by numerical experiments.This is the author accepted manuscript. The final version is available from IEEE at http://dx.doi.org/10.1109/TSP.2016.2605067