Results 1  10
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21
Collaborative Spectrum Sensing from Sparse Observations Using Matrix Completion for Cognitive Radio Networks
"... Abstract — In cognitive radio, spectrum sensing is a key component to detect spectrum holes (i.e., channels not used by any primary users). Collaborative spectrum sensing among the cognitive radio nodes is expected to improve the ability of checking complete spectrum usage states. Unfortunately, due ..."
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Cited by 37 (5 self)
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Abstract — In cognitive radio, spectrum sensing is a key component to detect spectrum holes (i.e., channels not used by any primary users). Collaborative spectrum sensing among the cognitive radio nodes is expected to improve the ability of checking complete spectrum usage states. Unfortunately, due to power limitation and channel fading, available channel sensing information is far from being sufficient to tell the unoccupied channels directly. Aiming at breaking this bottleneck, we apply recent matrix completion techniques to greatly reduce the sensing information needed. We formulate the collaborative sensing problem as a matrix completion subproblem and a jointsparsity reconstruction subproblem. Results of numerical simulations that validated the effectiveness and robustness of the proposed approach are presented. In particular, in noiseless cases, when number of primary user is small, exact detection was obtained with no more than 8 % of the complete sensing information, whilst as number of primary user increases, to achieve a detection rate of 95.55%, the required information percentage was merely 16.8%. I.
Distributed basis pursuit
 IEEE Trans. Sig. Proc
, 2012
"... Abstract—We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP). BP finds the leastnorm solution of the underdetermined linear system and is used, for example, in compressed sensing for reconstruction. Our algorithm solves BP on a distributed platform such as a s ..."
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Cited by 28 (7 self)
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Abstract—We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP). BP finds the leastnorm solution of the underdetermined linear system and is used, for example, in compressed sensing for reconstruction. Our algorithm solves BP on a distributed platform such as a sensor network, and is designed to minimize the communication between nodes. The algorithm only requires the network to be connected, has no notion of a central processing node, and no node has access to the entire matrix at any time. We consider two scenarios in which either the columns or the rows of are distributed among the compute nodes. Our algorithm, named DADMM, is a decentralized implementation of the alternating direction method of multipliers. We show through numerical simulation that our algorithm requires considerably less communications between the nodes than the stateoftheart algorithms. Index Terms—Augmented Lagrangian, basis pursuit (BP), distributed optimization, sensor networks.
Global Testing under Sparse Alternatives: ANOVA, Multiple Comparisons and the Higher Criticism
"... Testing for the significance of a subset of regression coefficients in a linear model, a staple of statistical analysis, goes back at least to the work of Fisher who introduced the analysis of variance (ANOVA). We study this problem under the assumption that the coefficient vector is sparse, a commo ..."
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Cited by 25 (2 self)
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Testing for the significance of a subset of regression coefficients in a linear model, a staple of statistical analysis, goes back at least to the work of Fisher who introduced the analysis of variance (ANOVA). We study this problem under the assumption that the coefficient vector is sparse, a common situation in modern highdimensional settings. Suppose we have p covariates and that under the alternative, the response only depends upon on the order of p 1−α of those, 0 ≤ α ≤ 1. Under moderate sparsity levels, i.e. 0 ≤ α ≤ 1/2, we show that ANOVA is essentially optimal under some conditions on the design. This is no longer the case under strong sparsity constraints, i.e. α> 1/2. In such settings, a multiple comparison procedure is often preferred and we establish its optimality when α ≥ 3/4. However, these two very popular methods are suboptimal, and sometimes powerless, under moderately strong sparsity where 1/2 < α < 3/4. We suggest a method based on the Higher Criticism that is powerful in the whole range α> 1/2. This optimality property is true for a variety of designs, including the classical (balanced) multiway designs and more modern ‘p> n ’ designs arising in genetics and signal processing. In addition to the standard fixed effects model, we establish similar results for a random effects model where the nonzero coefficients of the regression vector are normally distributed.
Sparse target counting and localization in sensor networks based on compressive sensing
 in INFOCOM
, 2011
"... Abstract—In this paper, we propose a novel compressive sensing (CS) based approach for sparse target counting and positioning in wireless sensor networks. While this is not the first work on applying CS to count and localize targets, it is the first to rigorously justify the validity of the problem ..."
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Cited by 22 (2 self)
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Abstract—In this paper, we propose a novel compressive sensing (CS) based approach for sparse target counting and positioning in wireless sensor networks. While this is not the first work on applying CS to count and localize targets, it is the first to rigorously justify the validity of the problem formulation. Moreover, we propose a novel greedy matching pursuit algorithm (GMP) that complements the wellknown signal recovery algorithms in CS theory and prove that GMP can accurately recover a sparse signal with a high probability. We also propose a framework for counting and positioning targets from multiple categories, a novel problem that has never been addressed before. Finally, we perform a comprehensive set of simulations whose results demonstrate the superiority of our approach over the existing CS and nonCS based techniques.
Random access compressed sensing for energyefficient underwater sensor networks
 IEEE Journal on Selected Areas in Communications
, 2011
"... Abstract—Inspired by the theory of compressed sensing and employing random channel access, we propose a distributed energyefficient sensor network scheme denoted by Random Access Compressed Sensing (RACS). The proposed scheme is suitable for longterm deployment of large underwater networks, in whi ..."
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Cited by 16 (1 self)
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Abstract—Inspired by the theory of compressed sensing and employing random channel access, we propose a distributed energyefficient sensor network scheme denoted by Random Access Compressed Sensing (RACS). The proposed scheme is suitable for longterm deployment of large underwater networks, in which saving energy and bandwidth is of crucial importance. During each frame, a randomly chosen subset of nodes participate in the sensing process, then share the channel using random access. Due to the nature of random access, packets may collide at the fusion center. To account for the packet loss that occurs due to collisions, the network design employs the concept of sufficient sensing probability. With this probability, sufficiently many data packets – as required for field reconstruction based on compressed sensing – are to be received. The RACS scheme prolongs network lifetime while employing a simple and distributed scheme which eliminates the need for scheduling. Index Terms—Sensor networks, compressed sensing, wireless communications, underwater acoustic networks, random access. I.
BASIS PURSUIT IN SENSOR NETWORKS
"... Basis Pursuit (BP) finds a minimum ℓ1norm vector z that satisfies the underdetermined linear system Mz = b, where the matrix M and vector b are given. Lately, BP has attracted attention because of its application in compressed sensing, where it is used to reconstruct signals by finding the sparsest ..."
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Cited by 12 (4 self)
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Basis Pursuit (BP) finds a minimum ℓ1norm vector z that satisfies the underdetermined linear system Mz = b, where the matrix M and vector b are given. Lately, BP has attracted attention because of its application in compressed sensing, where it is used to reconstruct signals by finding the sparsest solutions of linear systems. In this paper, we propose a distributed algorithm to solve BP. This means no central node is used for the processing and no node has access to all the data: the rows ofM and the vectorbare distributed over a set of interconnected compute nodes. A typical scenario is a sensor network. The novelty of our method is in using an optimal firstorder method to solve an augmented Lagrangianbased reformulation of BP. We implemented our algorithm in a computer cluster, and show that it can solve problems that are too large to be stored in and processed by a single node. Index Terms — Convex optimization, basis pursuit, distributed algorithm, sensor network, compressed sensing 1.
Distributed sparse signal recovery for sensor networks
 in Proc. IEEE Int. Conf. on Acoust., Speech, and Sig. Proc. (ICASSP
"... We propose a distributed algorithm for sparse signal recovery in sensor networks based on Iterative Hard Thresholding (IHT). Every agent has a set of measurements of a signal x, and the objective is for the agents to recover x from their collective measurements at a minimal communication cost and ..."
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Cited by 7 (3 self)
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We propose a distributed algorithm for sparse signal recovery in sensor networks based on Iterative Hard Thresholding (IHT). Every agent has a set of measurements of a signal x, and the objective is for the agents to recover x from their collective measurements at a minimal communication cost and with low computational complexity. A naı̈ve distributed implementation of IHT would require global communication of every agent’s full state in each iteration. We find that we can dramatically reduce this communication cost by leveraging solutions to the distributed topK problem in the database literature. Evaluations show that our algorithm requires up to three orders of magnitude less total bandwidth than the bestknown distributed basis pursuit method. Index Terms — compressed sensing, distributed algorithm, iterative hard thresholding, topK 1.
Local Access to Sparse and Large Global Information in P2P Networks: a Case for Compressive Sensing
"... Abstract—In this paper we face the following problem: how to provide each peer local access to the full information (not just a summary) that is distributed over all edges of an overlay network? How can this be done if local access is performed at a given rate? We focus on large and sparse informati ..."
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Cited by 5 (0 self)
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Abstract—In this paper we face the following problem: how to provide each peer local access to the full information (not just a summary) that is distributed over all edges of an overlay network? How can this be done if local access is performed at a given rate? We focus on large and sparse information and we propose to exploit the compressive sensing (CS) theory to efficiently collect and proactively disseminate this information across a large overlay network. We devise an approach based on random walks (RW) to spread CS random combinations to participants in a random peertopeer (P2P) overlay network. CS allows the peer to compress the RW payload in a distributed fashion: given a constraint on the RW size, e.g., the maximum UDP packet payload size, this amounts to being able to distribute larger information and to guarantee that a large fraction of the global information is obtained by each peer. We analyze the performance of the proposed method by means of a simple (yet accurate) analytical model describing the structure of the so called CS sensing matrix in presence of peer dynamics and communication link failures. We validate our model predictions against a simulator of the system at the peer and network level on different models of random overlay networks. The model we developed can be exploited to select the parameters of the RW and the criteria to build the sensing matrix in order to achieve successful information recovery. Finally, a prototype has been developed and deployed over the PlanetLab network to prove the feasibility of the proposed approach in a realistic environment. Our analysis reveals that the method we propose is feasible, accurate and robust to peer and information dynamics. We also argue that centralized and other distributed approaches, i.e., flooding and gossiping, are unfit in the context we consider. I.
1 Distributed Compressed Sensing For Static and TimeVarying Networks
"... Abstract—We consider the problem of innetwork compressed sensing from distributed measurements. Every agent has a set of measurements of a signal x, and the objective is for the agents to recover x from their collective measurements using only communication with neighbors in the network. Our distri ..."
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Cited by 2 (1 self)
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Abstract—We consider the problem of innetwork compressed sensing from distributed measurements. Every agent has a set of measurements of a signal x, and the objective is for the agents to recover x from their collective measurements using only communication with neighbors in the network. Our distributed approach to this problem is based on the centralized Iterative Hard Thresholding algorithm (IHT). We first present a distributed IHT algorithm for static networks that leverages standard tools from distributed computing to execute innetwork computations with minimized bandwidth consumption. Next, we address distributed signal recovery in networks with timevarying topologies. The network dynamics necessarily introduce inaccuracies to our innetwork computations. To accommodate these inaccuracies, we show how centralized IHT can be extended to include inexact computations while still providing the same recovery guarantees as the original IHT algorithm. We then leverage these new theoretical results to develop a distributed version of IHT for timevarying networks. Evaluations show that our distributed algorithms for both static and timevarying networks outperform previously proposed solutions in time and bandwidth by several orders of magnitude. Index Terms—compressed sensing, distributed algorithm, iterative hard thresholding, distributed consensus I.
Technology Email:
"... Many realworld systems and applications such as World Wide Web, and social interactions can be modeled as networks of interacting dynamical nodes. However, in many cases, one encounters the situation where the pattern of the nodetonode interactions (i.e., edges) or the structure of a network is u ..."
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Many realworld systems and applications such as World Wide Web, and social interactions can be modeled as networks of interacting dynamical nodes. However, in many cases, one encounters the situation where the pattern of the nodetonode interactions (i.e., edges) or the structure of a network is unknown. We address this issue by studying the Network Reconstruction Problem: Given a network with missing edges, how is it possible to uncover the network structure based on certain observable quantities extracted from partial measurements? We propose a novel framework called CSNetRec based on a newly emerged paradigm in sparse signal recovery called Compressive Sensing (CS). The general idea of using CS is that if the presentation of information is sparse, then it can be recovered by using a few number of linear measurements. In particular, we utilize the observed data of information cascades in the context of CS for network reconstruction. Our comprehensive empirical analysis over both synthetic and real datasets demonstrates that the proposed framework leads to an efficient and effective reconstruction. More specifically, the results demonstrate that our framework can perform accurately even on low number of cascades (e.g. when the number of cascades is around half of the number of existing edges in the desired network). Furthermore, our framework is capable of nearperfect reconstruction of the desired network in presence of 95 % sparsity. In addition, we compared the performance of our framework with NetInf; one of the stateoftheart methods in inferring the networks of diffusion. The results suggest that the proposed method outperforms NetInf by an average of 10 % improvement based on the Fmeasure. I