On sensing capacity of sensor networks for a class of linear observation models

Aeron, Shuchin; Zhao, Manqi; Saligrama, Venkatesh

doi:10.1109/ssp.2007.4301286

Cited by 13 publications

(14 citation statements)

References 20 publications

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“…However, in many practical applications, obtaining some large fraction of these positions would be sufficient. Neither the limits of partial sparsity recovery nor the performance of practical algorithms are completely understood, though some results have been reported in [20]- [22], [24].…”

Section: Discussionmentioning

confidence: 99%

Necessary and Sufficient Conditions for Sparsity Pattern Recovery

Fletcher

Rangan

Goyal

2009

IEEE Trans. Inform. Theory

188

229

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The problem of detecting the sparsity pattern of a k-sparse vector in R n from m random noisy measurements is of interest in many areas such as system identification, denoising, pattern recognition, and compressed sensing. This paper addresses the scaling of the number of measurements m, with signal dimension n and sparsity-level nonzeros k, for asymptotically-reliable detection. We show a necessary condition for perfect recovery at any given SNR for all algorithms, regardless of complexity, is m = Ω(k log(n − k)) measurements. Conversely, it is shown that this scaling of Ω(k log(n − k)) measurements is sufficient for a remarkably simple "maximum correlation" estimator. Hence this scaling is optimal and does not require more sophisticated techniques such as lasso or matching pursuit. The constants for both the necessary and sufficient conditions are precisely defined in terms of the minimum-toaverage ratio of the nonzero components and the SNR. The necessary condition improves upon previous results for maximum likelihood estimation. For lasso, it also provides a necessary condition at any SNR and for low SNR improves upon previous work. The sufficient condition provides the first asymptotically-reliable detection guarantee at finite SNR.

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Section: Discussionmentioning

confidence: 99%

Necessary and Sufficient Conditions for Sparsity Pattern Recovery

Fletcher

Rangan

Goyal

2009

IEEE Trans. Inform. Theory

188

229

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“…For a strict sparse scene, we have 2 0 0 σ → , which means absence of clutter in a radar scene. We can simplify its rate distortion function [39]:…”

Section: Sparse Radar Scenes and Rate-distortion Characterizationmentioning

confidence: 99%

Information-Theoretic Characterization and Undersampling Ratio Determination for Compressive Radar Imaging in a Simulated Environment

Zhang

Yang

Liu

et al. 2015

Entropy

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Abstract:Assuming sparsity or compressibility of the underlying signals, compressed sensing or compressive sampling (CS) exploits the informational efficiency of under-sampled measurements for increased efficiency yet acceptable accuracy in information gathering, transmission and processing, though it often incurs extra computational cost in signal reconstruction. Shannon information quantities and theorems, such as source rate-distortion, trans-information and rate distortion theorem concerning lossy data compression, provide a coherent framework, which is complementary to classic CS theory, for analyzing informational quantities and for determining the necessary number of measurements in CS. While there exists some information-theoretic research in the past on CS in general and compressive radar imaging in particular, systematic research is needed to handle issues related to scene description in cluttered environments and trans-information quantification in complex sparsity-clutter-sampling-noise settings. The novelty of this paper lies in furnishing a general strategy for information-theoretic analysis of scene compressibility, trans-information of radar echo data about the scene and the targets of interest, respectively, and limits to undersampling ratios necessary for scene reconstruction subject to distortion given sparsity-clutter-noise constraints. A computational experiment was performed to demonstrate informational analysis regarding the scene-sampling-reconstruction process and to generate phase transition diagrams showing relations between undersampling ratios and sparsity-clutter-noise-distortion constraints. The strategy proposed in this paper is valuable for information-theoretic analysis and undersampling theorem developments in compressive

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“…They drive the bounds on the sufficient number of measurements for distributed encoding exploiting CS theory. [10] also addressed the problem of finding sensing capacity of sensor networks that is defined as the maximum number of signal dimensions per sensor observation. It showed that sensing capacity decreases as sensing diversity per sensor decreases.…”

Section: B Compressive Sensing Based Wireless Sensor Networkmentioning

confidence: 99%

SNR efficient transmission for compressive sensing based wireless sensor networks

Hwang

Park

Kim

et al. 2013

6th Joint IFIP Wireless and Mobile Networking Conference (WMNC)

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Compressive sensing(CS) is an emerging technology that can recover a signal from under sampled measurements based on sparsity of the signal in some basis domain. Even though CS associated with wireless sensor networks (WSNs) has contributed in developing efficient compression and detection algorithms, most research has focused on detection problem with a simple model without considering properties of physical channels. This paper considers a compressive sensing based WSN, that exploits channel gain to transmit and detect signals efficiently. Assuming that measured signals at each sensor are correlated and sparse at some basis domain, we propose a novel sensor selection scheme and associated signaling channel design to improve detection performance. The simulation results show that the proposed method support reduction in the number of measurmenets by 60~80% for a wide range of sparsity level at high and low SNRs.

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On sensing capacity of sensor networks for a class of linear observation models

Abstract: In this paper we address the problem of finding the sensing capacity of sensor networks for a class of linear observation models and a fixed SNR regime. Sensing capacity is defined as the maximum number October 27, 2018 DRAFT

Cited by 13 publications

References 20 publications

Necessary and Sufficient Conditions for Sparsity Pattern Recovery

Necessary and Sufficient Conditions for Sparsity Pattern Recovery

Information-Theoretic Characterization and Undersampling Ratio Determination for Compressive Radar Imaging in a Simulated Environment

SNR efficient transmission for compressive sensing based wireless sensor networks

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