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50
Distributed compressed sensing
, 2005
"... 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 introduce a new theory for distributed compressed sensing (DCS) that enables new distributed coding algori ..."
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Cited by 137 (25 self)
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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 introduce a new theory for distributed compressed sensing (DCS) that enables new distributed coding algorithms for multisignal ensembles that exploit both intra and intersignal correlation structures. The DCS theory rests on a new concept that we term the joint sparsity of a signal ensemble. We study in detail three simple models for jointly sparse signals, propose algorithms for joint recovery of multiple signals from incoherent projections, and characterize theoretically and empirically the number of measurements per sensor required for accurate reconstruction. We establish a parallel with the SlepianWolf theorem from information theory and establish upper and lower bounds on the measurement rates required for encoding jointly sparse signals. In two of our three models, the results are asymptotically bestpossible, 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. In some sense DCS is a framework for distributed compression of sources with memory, which has remained a challenging problem for some time. DCS is immediately applicable to a range of problems in sensor networks and arrays.
Compressive radar imaging
 Proc. 2007 IEEE Radar Conf
, 2007
"... Abstract—We introduce a new approach to radar imaging based on the concept of compressive sensing (CS). In CS, a lowdimensional, nonadaptive, linear projection is used to acquire an efficient representation of a compressible signal directly using just a few measurements. The signal is then reconstr ..."
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Cited by 104 (9 self)
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Abstract—We introduce a new approach to radar imaging based on the concept of compressive sensing (CS). In CS, a lowdimensional, nonadaptive, linear projection is used to acquire an efficient representation of a compressible signal directly using just a few measurements. The signal is then reconstructed by solving an inverse problem either through a linear program or a greedy pursuit. We demonstrate that CS has the potential to make two significant improvements to radar systems: (i) eliminating the need for the pulse compression matched filter at the receiver, and (ii) reducing the required receiver analogtodigital conversion bandwidth so that it need operate only at the radar reflectivity’s potentially low “information rate” rather than at its potentially high Nyquist rate. These ideas could enable the design of new, simplified radar systems, shifting the emphasis from expensive receiver hardware to smart signal recovery algorithms. I.
Information fusion for wireless sensor networks
 Methods, models, and classifications, ACM Computing Surveys, Volume 39, Issue 3, Article 9
, 2007
"... ..."
Joint SourceChannel 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 sourcechan ..."
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Cited by 51 (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 sourcechannel communication architecture is proposed for energyefficient 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 – phasecoherent 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 sublinearly with the number of sensor nodes even when little or no prior knowledge about the sensed data is assumed at the sensor nodes.
Distributed compressive spectrum sensing in cooperative multihop cognitive networks
 IEEE Journal of Selected Topics in Signal Processing
, 2010
"... Abstract—In wideband cognitive radio (CR) networks, spectrum sensing is an essential task for enabling dynamic spectrum sharing, but entails several major technical challenges: very high sampling rates required for wideband processing, limited power and computing resources per CR, frequencyselectiv ..."
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Cited by 43 (0 self)
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Abstract—In wideband cognitive radio (CR) networks, spectrum sensing is an essential task for enabling dynamic spectrum sharing, but entails several major technical challenges: very high sampling rates required for wideband processing, limited power and computing resources per CR, frequencyselective wireless fading, and interference due to signal leakage from other coexisting CRs. In this paper, a cooperative approach to wideband spectrum sensing is developed to overcome these challenges. To effectively reduce the data acquisition costs, a compressive sampling mechanism is utilized which exploits the signal sparsity induced by network spectrum underutilization. To collect spatial diversity against wireless fading, multiple CRs collaborate during the sensing task by enforcing consensus among local spectral estimates; accordingly, a decentralized consensus optimization algorithm is derived to attain high sensing performance at a reasonable computational cost and power overhead. To identify spurious spectral estimates due to interfering CRs, the orthogonality between the spectrum of primary users and that of CRs is imposed as constraints for consensus optimization during distributed collaborative sensing. These decentralized techniques are developed for both cases of with and without channel knowledge. Simulations testify the effectiveness of the proposed cooperative sensing approach in multihop CR networks. Index Terms—Collaborative sensing, compressive sampling, consensus optimization, distributed fusion, spectrum sensing. I.
DISTRIBUTED COMPRESSIVE VIDEO SENSING
"... Lowcomplexity video encoding has been applicable to several emerging applications. Recently, distributed video coding (DVC) has been proposed to reduce encoding complexity to the order of that for still image encoding. In addition, compressive sensing (CS) has been applicable to directly capture co ..."
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Cited by 36 (4 self)
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Lowcomplexity video encoding has been applicable to several emerging applications. Recently, distributed video coding (DVC) has been proposed to reduce encoding complexity to the order of that for still image encoding. In addition, compressive sensing (CS) has been applicable to directly capture compressed image data efficiently. In this paper, by integrating the respective characteristics of DVC and CS, a distributed compressive video sensing (DCVS) framework is proposed to simultaneously capture and compress video data, where almost all computation burdens can be shifted to the decoder, resulting in a very lowcomplexity encoder. At the decoder, compressed video can be efficiently reconstructed using the modified GPSR (gradient projection for sparse reconstruction) algorithm. With the assistance of the proposed initialization and stopping criteria for GRSR, derived from statistical dependencies among successive video frames, our modified GPSR algorithm can terminate faster and reconstruct better video quality. The performance of our DCVS method is demonstrated via simulations to outperform three known CS reconstruction algorithms. Index Terms—compressive video sensing, (distributed) compressive sampling/sensing, distributed video coding
Learning Compressed Sensing
"... Abstract — Compressed sensing [7], [6] is a recent set of mathematical results showing that sparse signals can be exactly reconstructed from a small number of linear measurements. Interestingly, for ideal sparse signals with no measurement noise, random measurements allow perfect reconstruction whil ..."
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Cited by 25 (0 self)
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Abstract — Compressed sensing [7], [6] is a recent set of mathematical results showing that sparse signals can be exactly reconstructed from a small number of linear measurements. Interestingly, for ideal sparse signals with no measurement noise, random measurements allow perfect reconstruction while measurements based on principal component analysis (PCA) or independent component analysis (ICA) do not. At the same time, for other signal and noise distributions, PCA and ICA can significantly outperform random projections in terms of enabling reconstruction from a small number of measurements. In this paper we ask: given a training set typical of the signals we wish to measure, what are the optimal set of linear projections for compressed sensing? We show that the optimal projections are in general not the principal components nor the independent components of the data, but rather a seemingly novel set of projections that capture what is still uncertain about the signal, given the training set. We also show that the projections onto the learned uncertain components may far outperform random projections. This is particularly true in the case of natural images, where random projections have vanishingly small signal to noise ratio as the number of pixels becomes large. I.
Thresholded Basis Pursuit: Quantizing Linear Programming Solutions for Optimal Support Recovery and Approximation in Compressed Sensing
, 2008
"... We consider the Compressed Sensing problem. We have a large underdetermined set of noisy measurements Y = GX + N, where X is a sparse signal and G is drawn from a random ensemble. In our previous work, we had shown that a signaltonoise ratio, SNR = O(log n) is necessary and sufficient for support ..."
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Cited by 17 (1 self)
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We consider the Compressed Sensing problem. We have a large underdetermined set of noisy measurements Y = GX + N, where X is a sparse signal and G is drawn from a random ensemble. In our previous work, we had shown that a signaltonoise ratio, SNR = O(log n) is necessary and sufficient for support recovery from an informationtheoretic perspective. In this paper we present a linear programming solution for support recovery. The solution of the problem amounts to solving min ‖Z‖1 s.t. Y = GZ, and quantizing/thresholding the resulting solution Z. We show that this scheme is guaranteed to perfectly reconstruct a discrete signal or control the elementwise reconstruction error for a continuous signal for specific values of sparsity. We show that in the linear regime when the sparsity, k, increases linearly with signal dimension, n, the sign pattern of X can be recovered with SNR = O(log n) and m = O(k) measurements. Our proof technique is based on perturbation of the noiseless ℓ1 problem. Consequently, the achievable sparsity level in the noisy problem is comparable to that of the noiseless problem. Our result offers a sharp characterization in that neither the SNR nor the sparsity ratio can be significantly improved. In contrast previous results based on LASSO and MAXCorrelation techniques assume significantly larger SNR or sublinear sparsity. We also show that our final result can be obtained from Dvoretsky theorem rather than the restricted isometry property (RIP). The advantage of this line of reasoning is that Dvoretsky’s theorem continues to hold for nonsingular transformations while RIP property may not be satisfied for the latter case. We also consider approximation in terms of ℓ2 and show that our bounds match existing bounds for LASSO in this case.
Performance Analysis for Sparse Support Recovery
, 2009
"... In this paper, the performance of estimating the common support for jointly sparse signals based on their projections onto lowerdimensional space is analyzed. Support recovery is formulated as a multiplehypothesis testing problem and both upper and lower bounds on the probability of error are deri ..."
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Cited by 17 (1 self)
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In this paper, the performance of estimating the common support for jointly sparse signals based on their projections onto lowerdimensional space is analyzed. Support recovery is formulated as a multiplehypothesis testing problem and both upper and lower bounds on the probability of error are derived for general measurement matrices, by using the Chernoff bound and Fano’s inequality, respectively. The form of the upper bound shows that the performance is determined by a single quantity that is a measure of the incoherence of the measurement matrix, while the lower bound reveals the importance of the total measurement gain. To demonstrate its immediate applicability, the lower bound is applied to derive the minimal number of samples needed for accurate direction of arrival (DOA) estimation for an algorithm based on sparse representation. When applied to Gaussian measurement ensembles, these bounds give necessary and sufficient conditions to guarantee a vanishing probability of error for majority realizations of the measurement matrix. Our results offer surprising insights into the sparse signal reconstruction based on their projections. For example, as far as support recovery is concerned, the wellknown bound in compressive sensing is generally not sufficient if the Gaussian ensemble is used. Our study provides an alternative performance measure, one that is natural and important in practice, for signal recovery in compressive sensing as well as other application areas taking advantage of signal sparsity.