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40
Signal reconstruction from noisy random projections
- IEEE Trans. Inform. Theory
, 2006
"... Recent results show that a relatively small number of random projections of a signal can contain most of its salient information. It follows that if a signal is compressible in some orthonormal basis, then a very accurate reconstruction can be obtained from random projections. We extend this type of ..."
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Cited by 239 (26 self)
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Recent results show that a relatively small number of random projections of a signal can contain most of its salient information. It follows that if a signal is compressible in some orthonormal basis, then a very accurate reconstruction can be obtained from random projections. We extend this type of result to show that compressible signals can be accurately recovered from random projections contaminated with noise. We also propose a practical iterative algorithm for signal reconstruction, and briefly discuss potential applications to coding, A/D conversion, and remote wireless sensing. Index Terms sampling, signal reconstruction, random projections, denoising, wireless sensor networks
Computation over Multiple-Access Channels
- IEEE TRANSACTIONS ON INFORMATION THEORY
, 2007
"... The problem of reliably reconstructing a function of sources over a multiple-access channel is considered. It is shown that there is no source-channel separation theorem even when the individual sources are independent. Joint sourcechannel strategies are developed that are optimal when the structure ..."
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Cited by 139 (24 self)
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The problem of reliably reconstructing a function of sources over a multiple-access channel is considered. It is shown that there is no source-channel separation theorem even when the individual sources are independent. Joint sourcechannel strategies are developed that are optimal when the structure of the channel probability transition matrix and the function are appropriately matched. Even when the channel and function are mismatched, these computation codes often outperform separation-based strategies. Achievable distortions are given for the distributed refinement of the sum of Gaussian sources over a Gaussian multiple-access channel with a joint source-channel lattice code. Finally, computation codes are used to determine the multicast capacity of finite field multiple-access networks, thus linking them to network coding.
Compressive Wireless Sensing
, 2006
"... Compressive Sampling is an emerging theory that is based on the fact that a relatively small number of random projections of a signal can contain most of its salient information. In this paper, we introduce the concept of Compressive Wireless Sensing for sensor networks in which a fusion center retr ..."
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Cited by 109 (4 self)
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Compressive Sampling is an emerging theory that is based on the fact that a relatively small number of random projections of a signal can contain most of its salient information. In this paper, we introduce the concept of Compressive Wireless Sensing for sensor networks in which a fusion center retrieves signal field information from an ensemble of spatially distributed sensor nodes. Energy and bandwidth are scarce resources in sensor networks and the relevant metrics of interest in our context are 1) the latency involved in information retrieval; and 2) the associated power-distortion trade-off. It is generally recognized that given sufficient prior knowledge about the sensed data (e.g., statistical characterization, homogeneity etc.), there exist schemes that have very favorable power-distortion-latency trade-offs. We propose a distributed matched source-channel communication scheme, based in part on recent results in compressive sampling theory, for estimation of sensed data at the fusion center and analyze, as a function of number of sensor nodes, the trade-offs between power, distortion and latency. Compressive wireless sensing is a universal scheme in the sense that it requires no prior knowledge about the sensed data. This universality, however, comes at the cost of optimality (in terms of a less favorable power-distortion-latency trade-off) and we quantify this cost relative to the case when sufficient prior information about the sensed data is assumed.
Estimation diversity and energy efficiency in distributed sensing
- IEEE Transactions on Signal Processing
, 2007
"... Abstract—Distributed estimation based on measurements from multiple wireless sensors is investigated. It is assumed that a group of sensors observe the same quantity in independent ad-ditive observation noises with possibly different variances. The observations are transmitted using amplify-and-forw ..."
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Cited by 63 (1 self)
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Abstract—Distributed estimation based on measurements from multiple wireless sensors is investigated. It is assumed that a group of sensors observe the same quantity in independent ad-ditive observation noises with possibly different variances. The observations are transmitted using amplify-and-forward (analog) transmissions over nonideal fading wireless channels from the sensors to a fusion center, where they are combined to generate an estimate of the observed quantity. Assuming that the best linear unbiased estimator (BLUE) is used by the fusion center, the equal-power transmission strategy is first discussed, where the system performance is analyzed by introducing the concept of estimation outage and estimation diversity, and it is shown that there is an achievable diversity gain on the order of the number of sensors. The optimal power allocation strategies are then consid-ered for two cases: minimum distortion under power constraints; and minimum power under distortion constraints. In the first case, it is shown that by turning off bad sensors, i.e., sensors with bad channels and bad observation quality, adaptive power gain can be achieved without sacrificing diversity gain. Here, the adaptive power gain is similar to the array gain achieved in multiple-input single-output (MISO) multiantenna systems when channel conditions are known to the transmitter. In the second case, the sum power is minimized under zero-outage estimation distortion constraint, and some related energy efficiency issues in sensor networks are discussed. Index Terms—Distributed estimation, energy efficiency, estima-tion diversity, estimation outage.
Joint Source-Channel Communication for Distributed Estimation in Sensor Networks
"... Power and bandwidth are scarce resources in dense wireless sensor networks and it is widely recognized that joint optimization of the operations of sensing, processing and communication can result in significant savings in the use of network resources. In this paper, a distributed joint source-chan ..."
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Cited by 53 (3 self)
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Power and bandwidth are scarce resources in dense wireless sensor networks and it is widely recognized that joint optimization of the operations of sensing, processing and communication can result in significant savings in the use of network resources. In this paper, a distributed joint source-channel communication architecture is proposed for energy-efficient estimation of sensor field data at a distant destination and the corresponding relationships between power, distortion, and latency are analyzed as a function of number of sensor nodes. The approach is applicable to a broad class of sensed signal fields and is based on distributed computation of appropriately chosen projections of sensor data at the destination – phase-coherent transmissions from the sensor nodes enable exploitation of the distributed beamforming gain for energy efficiency. Random projections are used when little or no prior knowledge is available about the signal field. Distinct features of the proposed scheme include: 1) processing and communication are combined into one distributed projection operation; 2) it virtually eliminates the need for innetwork processing and communication; 3) given sufficient prior knowledge about the sensed data, consistent estimation is possible with increasing sensor density even with vanishing total network power; and 4) consistent signal estimation is possible with power and latency requirements growing at most sub-linearly with the number of sensor nodes even when little or no prior knowledge about the sensed data is assumed at the sensor nodes.
Linear Coherent Decentralized Estimation
"... Abstract—We consider the distributed estimation of an unknown vector signal in a resource constrained sensor network with a fusion center. Due to power and bandwidth limitations, each sensor compresses its data in order to minimize the amount of information that needs to be communicated to the fusio ..."
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Cited by 47 (1 self)
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Abstract—We consider the distributed estimation of an unknown vector signal in a resource constrained sensor network with a fusion center. Due to power and bandwidth limitations, each sensor compresses its data in order to minimize the amount of information that needs to be communicated to the fusion center. In this context, we study the linear decentralized estimation of the source vector, where each sensor linearly encodes its observations and the fusion center also applies a linear mapping to estimate the unknown vector signal based on the received messages. We adopt the mean squared error (MSE) as the performance criterion. When the channels between sensors and the fusion center are orthogonal, it has been shown previously that the complexity of designing the optimal encoding matrices is NP-hard in general. In this paper, we study the optimal linear decentralized estimation when the multiple access channel (MAC) is coherent. For the case when the source and observations are scalars, we derive the optimal power scheduling via convex optimization and show that it admits a simple distributed implementation. Simulations show that the proposed power scheduling improves the MSE performance by a large margin when compared to the uniform power scheduling. We also show that under a finite network power budget, the asymptotic MSE performance (when the total number of sensors is large) critically depends on the multiple access scheme. For the case when the source and observations are vectors, we study the optimal linear decentralized estimation under both bandwidth and power constraints. We show that when the MAC between sensors and the fusion center is noiseless, the resulting problem has a closed-form solution (which is in sharp contrast to the orthogonal MAC case), while in the noisy MAC case, the problem can be efficiently solved by semi-definite programming (SDP). Index Terms—Distributed estimation, energy efficiency, multiple access channel, linear source-channel coding, convex optimization. I.
Decentralized Detection in Wireless Sensor Networks with Channel Fading Statistics
- EURASIP J. Wirel. Commun. Netw
, 2007
"... Abstract—Distributed detection strategies for wireless sensor networks are studied under the assumption of spatially and tempo-rally independent and identically distributed (i.i.d.) observations at the sensor nodes. Both intelligent (with knowledge of obser-vation statistics) and dumb (oblivious of ..."
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Cited by 31 (2 self)
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Abstract—Distributed detection strategies for wireless sensor networks are studied under the assumption of spatially and tempo-rally independent and identically distributed (i.i.d.) observations at the sensor nodes. Both intelligent (with knowledge of obser-vation statistics) and dumb (oblivious of observation statistics) sensors are considered. Two types of communication channels are studied: a parallel access channel (PAC) in which each sensor has a dedicated additive white Gaussian noise (AWGN) channel to a decision center, and a multiple-access channel (MAC) in which the decision center receives a coherent superposition of the sensor transmissions. Our results show that the MAC yields significantly superior detection performance for any network power constraint. For intelligent sensors, uncoded (finite duration) communication of local log-likelihood ratios over the MAC achieves the optimal error exponent of the centralized (noise-free channel) benchmark as the number of nodes increases, even with sublinear network power scaling. Motivated by this result, we propose a distributed detection strategy for dumb sensors—histogram fusion—in which each node appropriately quantizes its temporal data and commu-nicates its type or histogram to the decision center. It is shown that uncoded histogram fusion over the MAC is also asymptotically optimal under sublinear network power scaling with an additional advantage: knowledge of observation statistics is needed only at the decision center. Histogram fusion achieves exponential decay in error probability with the number of nodes even under a finite total network power. In principle, a vanishing error probability at a slower subexponential rate can be attained even with vanishing total network power in the limit. These remarkable power/energy savings with the number of nodes are due to the inherent beam-forming gain in the MAC. Index Terms—Distributed beamforming, distributed detection, energy efficiency, error exponents, low latency, types. I.
Random access compressed sensing for energy-efficient 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 energy-efficient sensor network scheme denoted by Random Access Compressed Sensing (RACS). The proposed scheme is suitable for long-term 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 energy-efficient sensor network scheme denoted by Random Access Compressed Sensing (RACS). The proposed scheme is suitable for long-term 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 life-time 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.
Approximating signals supported on graphs
, 2011
"... In this paper, we investigate the notion of smoothness for signals supported on the vertices of a graph. We provide theoretical explanations when and why the Laplacian eigenbasis can be regarded as a meaningful “Fourier ” transform of such signals. Moreover, we analyze the desired properties of the ..."
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Cited by 16 (2 self)
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In this paper, we investigate the notion of smoothness for signals supported on the vertices of a graph. We provide theoretical explanations when and why the Laplacian eigenbasis can be regarded as a meaningful “Fourier ” transform of such signals. Moreover, we analyze the desired properties of the underlying graphs for better compressibility of the signals. We verify our theoretical work by experiments on real world data.
