TY - JOUR
T1 - Measurement Bounds for Compressed Sensing in Sensor Networks with Missing Data
AU - Joseph, Geethu
AU - Varshney, Pramod K.
N1 - Funding Information:
Manuscript received April 3, 2020; revised October 6, 2020 and November 29, 2020; accepted January 7, 2021. Date of publication January 14, 2021; date of current version February 5, 2021. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Subhro Das. This work was supported by the National Science Foundation under Grant ENG 60064237. This work was presented in part at the IEEE International Workshop on Signal Processing Advances in Wireless Communications, May 2020, Atlanta, GA, USA. (Corresponding author: Geethu Joseph.) The authors are with the Department of EECS at Syracuse University, Syracuse, New York 13244 USA (e-mail: gjoseph@syr.edu; varshney@syr.edu). Digital Object Identifier 10.1109/TSP.2021.3051743
Publisher Copyright:
© 1991-2012 IEEE.
PY - 2021
Y1 - 2021
N2 - In this paper, we study the problem of sparse vector recovery at the fusion center of a sensor network from linear sensor measurements when there is missing data. In the presence of missing data, the random sampling approach employed in compressed sensing provides excellent reconstruction accuracy. However, the theoretical guarantees associated with this sparse recovery problem have not been well studied. Therefore, in this paper, we derive a sufficient condition on the number of measurements required to ensure faithful recovery of a sparse signal using random (subGaussian) projections when the generation of missing data is modeled using a Bernoulli erasure channel. We analyze three different network topologies, namely, star, (relay aided-)tree, and serial-star topologies. Our analysis establishes how the minimum required number of measurements for recovery scales with the network parameters, the properties of the random measurement matrix, and the recovery algorithm. Finally, through numerical simulations, we study the minimum required number of measurements as a function of different system parameters and validate our theoretical results.
AB - In this paper, we study the problem of sparse vector recovery at the fusion center of a sensor network from linear sensor measurements when there is missing data. In the presence of missing data, the random sampling approach employed in compressed sensing provides excellent reconstruction accuracy. However, the theoretical guarantees associated with this sparse recovery problem have not been well studied. Therefore, in this paper, we derive a sufficient condition on the number of measurements required to ensure faithful recovery of a sparse signal using random (subGaussian) projections when the generation of missing data is modeled using a Bernoulli erasure channel. We analyze three different network topologies, namely, star, (relay aided-)tree, and serial-star topologies. Our analysis establishes how the minimum required number of measurements for recovery scales with the network parameters, the properties of the random measurement matrix, and the recovery algorithm. Finally, through numerical simulations, we study the minimum required number of measurements as a function of different system parameters and validate our theoretical results.
KW - Compressed sensing
KW - measurement bounds
KW - missing data
KW - restricted isometric property
KW - sensor networks
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U2 - 10.1109/TSP.2021.3051743
DO - 10.1109/TSP.2021.3051743
M3 - Article
AN - SCOPUS:85099730887
SN - 1053-587X
VL - 69
SP - 905
EP - 916
JO - IRE Transactions on Audio
JF - IRE Transactions on Audio
M1 - 9325096
ER -