Compressive sensing is a signal acquisition framework based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable recovery. In this paper we introduce a new theory for distributed compressive sensing (DCS) that enables new distributed coding algorithms for multi-signal ensembles that exploit both intra-and inter-signal correlation structures. The DCS theory rests on a new concept that we term the joint sparsity of a signal ensemble. Our theoretical contribution is to characterize the fundamental performance limits of DCS recovery for jointly sparse signal ensembles in the noiseless measurement setting; our result connects single-signal, joint, and distributed (multi-encoder) compressive sensing. To demonstrate the efficacy of our framework and to show that additional challenges such as computational tractability can be addressed, we study in detail three example models for jointly sparse signals. For these models, we develop practical algorithms for joint recovery of multiple signals from incoherent projections. In two of our three models, the results are asymptotically best-possible, meaning that both the upper and lower bounds match the performance of our practical algorithms. Moreover, simulations indicate that the asymptotics take effect with just a moderate number of signals. DCS is immediately applicable to a range of problems in sensor arrays and networks.

Compressive sensing (CS) is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable, sub-Nyquist signal acquisition. When a statistical characterization of the signal is available, Bayesian inference can complement conventional CS methods based on linear programming or greedy algorithms. We perform approximate Bayesian inference using belief propagation (BP) decoding, which represents the CS encoding matrix as a graphical model. Fast computation is obtained by reducing the size of the graphical model with sparse encoding matrices. To decode a length-N signal containing K large coefficients, our CS-BP decoding algorithm uses O(K log(N )) measurements and O(N log 2 (N )) computation. Finally, although we focus on a two-state mixture Gaussian model, CS-BP is easily adapted to other signal models.

Abstract-Compressed sensing is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for reconstruction. In this paper we expand our theory for distributed compressed sensing (DCS) that enables new distributed coding algorithms for multi-signal ensembles that exploit both intra-and inter-signal correlation structures. The DCS theory rests on a new concept that we term the joint sparsity of a signal ensemble. We present a second new model for jointly sparse signals that allows for joint recovery of multiple signals from incoherent projections through simultaneous greedy pursuit algorithms. We also characterize theoretically and empirically the number of measurements per sensor required for accurate reconstruction.

No abstract

No abstract

No abstract

Abstract-In compressive sensing, a small collection of linear projections of a sparse signal contains enough information to permit signal recovery. Distributed compressive sensing (DCS) extends this framework by defining ensemble sparsity models, allowing a correlated ensemble of sparse signals to be jointly recovered from a collection of separately acquired compressive measurements. In this paper, we introduce a framework for modeling sparse signal ensembles that quantifies the intra-and inter-signal dependencies within and among the signals. This framework is based on a novel bipartite graph representation that links the sparse signal coefficients with the measurements obtained for each signal. Using our framework, we provide fundamental bounds on the number of noiseless measurements that each sensor must collect to ensure that the signals are jointly recoverable.

Abstract-Most network traffic analysis and modelingstudies lump all connections together into a single flow. Such aggregate traffic typically exhibits long-range-dependent (LRD) correlations and non-Gaussian marginal distributions. Importantly, in a typical aggregate traffic model, traffic bursts arise from many connections being active simultaneously. In this paper, we develop a new framework for analyzing and modeling network traffic that moves beyond aggregation by incorporating connection-level information. A careful study of many traffic traces acquired in different networking situations reveals (in opposition to the aggregate modeling ideal) that traffic bursts typically arise from just a few high-volume connections that dominate all others. We term such dominating connections alpha traflc. Alpha traffic is caused by large file transmissions over high bandwidth links and is extremely bursty (non-Gaussian). Stripping the alpha traffic from an aggregate trace leaves a beta traf/ic residual that is Gaussian, LRD, and shares the same fractal scaling exponent as the aggregate traffic. Beta traffic is caused by both small and large file transmissions over low bandwidth links. In our alpha/beta traffic model, the heterogeneity of the network resources give rise to burstiness and heavy-tailed connection durations give rise to LRD. Queuing experiments suggest that the alpha component dictates the tail queue behavior for large queue sizes, whereas the beta component controls the tail queue behavior for small queue sizes.