{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:02:38Z","timestamp":1760241758996,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2018,8,6]],"date-time":"2018-08-06T00:00:00Z","timestamp":1533513600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61501139,61371100,61401118"],"award-info":[{"award-number":["61501139,61371100,61401118"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Information acquisition in underwater sensor networks is usually limited by energy and bandwidth. Fortunately, the received signal can be represented sparsely on some basis. Therefore, a compressed sensing method can be used to collect the information by selecting a subset of the total sensor nodes. The conventional compressed sensing scheme is to select some sensor nodes randomly. The network lifetime and the correlation of sensor nodes are not considered. Therefore, it is significant to adjust the sensor node selection scheme according to these factors for the superior performance. In this paper, an optimized sensor node selection scheme is given based on Bayesian estimation theory. The advantage of Bayesian estimation is to give the closed-form expression of posterior density function and error covariance matrix. The proposed optimization problem first aims at minimizing the mean square error (MSE) of Bayesian estimation based on a given error covariance matrix. Then, the non-convex optimization problem is transformed as a convex semidefinite programming problem by relaxing the constraints. Finally, the residual energy of each sensor node is taken into account as a constraint in the optimization problem. Simulation results demonstrate that the proposed scheme has better performance than a conventional compressed sensing scheme.<\/jats:p>","DOI":"10.3390\/s18082568","type":"journal-article","created":{"date-parts":[[2018,8,7]],"date-time":"2018-08-07T03:44:18Z","timestamp":1533613458000},"page":"2568","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Bayesian Compressive Sensing Based Optimized Node Selection Scheme in Underwater Sensor Networks"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3559-5759","authenticated-orcid":false,"given":"Ruisong","family":"Wang","sequence":"first","affiliation":[{"name":"Harbin Institute of Technology, Weihai 264209, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gongliang","family":"Liu","sequence":"additional","affiliation":[{"name":"Harbin Institute of Technology, Weihai 264209, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenjing","family":"Kang","sequence":"additional","affiliation":[{"name":"Harbin Institute of Technology, Weihai 264209, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Li","sequence":"additional","affiliation":[{"name":"Harbin Institute of Technology, Weihai 264209, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruofei","family":"Ma","sequence":"additional","affiliation":[{"name":"Harbin Institute of Technology, Weihai 264209, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunsheng","family":"Zhu","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1109\/MCOM.2017.1700212","article-title":"Secure multimedia big data in trust-assisted sensor-cloud for smart city","volume":"55","author":"Zhu","year":"2017","journal-title":"IEEE Commun. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1125","DOI":"10.1109\/JSYST.2014.2300535","article-title":"A novel sensory data processing framework to integrate sensor networks with mobile cloud","volume":"10","author":"Zhu","year":"2016","journal-title":"IEEE Syst. J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/j.apacoust.2017.08.007","article-title":"Error control and adjustment method for underwater wireless sensor network localization","volume":"130","author":"Han","year":"2018","journal-title":"Appl. Acoust."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"161","DOI":"10.2514\/1.B36533","article-title":"Experimental and numerical parametric studies on two-Phase underwater ramjet","volume":"34","author":"Zhang","year":"2018","journal-title":"J. Propuls. Power"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"774","DOI":"10.1016\/j.cej.2017.07.142","article-title":"Underwater superoleophobicity cellulose nanofibril aerogel through regioselective sulfonation for oil\/water separation","volume":"330","author":"Sun","year":"2017","journal-title":"Chem. Eng. J."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2602","DOI":"10.1109\/LCOMM.2017.2744638","article-title":"Blind detection for SPAD-based underwater VLC system under P-G mixed noise model","volume":"21","author":"Wang","year":"2017","journal-title":"IEEE Commun. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1109\/MCOM.2015.7321974","article-title":"Routing protocols for underwater wireless sensor networks","volume":"53","author":"Han","year":"2015","journal-title":"IEEE Commun. Mag."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1109\/MCOM.2015.7180508","article-title":"Secure communication for underwater acoustic sensor networks","volume":"53","author":"Han","year":"2015","journal-title":"IEEE Commun. Mag."},{"key":"ref_9","unstructured":"Zhu, C.S., Li, X.H., Leung, V.C.M., and Yang, L.T. (2017). Towards pricing for sensor-cloud. IEEE Trans. Cloud Comput."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1109\/MCOM.2017.1600822","article-title":"Multi-method data delivery for green sensor-cloud","volume":"55","author":"Zhu","year":"2017","journal-title":"IEEE Commun. Mag."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2177","DOI":"10.1109\/TII.2012.2189222","article-title":"Compressed sensing signal and data acquisition in wireless sensor networks and internet of things","volume":"9","author":"Li","year":"2013","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1109\/TSP.2011.2170977","article-title":"Fast and efficient compressive sensing using structurally random matrices","volume":"60","author":"Do","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4053","DOI":"10.1109\/TSP.2011.2161982","article-title":"Structured compressed sensing: From theory to applications","volume":"59","author":"Duarte","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"764","DOI":"10.1109\/TIT.2010.2094817","article-title":"The dynamics of message passing on dense graphs, with applications to compressed sensing","volume":"57","author":"Bayati","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1007\/s10208-015-9276-6","article-title":"Generalized sampling and infinite-dimensional compressed sensing","volume":"16","author":"Adcock","year":"2016","journal-title":"Found. Comput. Math."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1058","DOI":"10.1109\/JPROC.2010.2042415","article-title":"Compressed channel sensing: A new approach to estimating sparse multipath channels","volume":"98","author":"Bajwa","year":"2010","journal-title":"Proc. IEEE"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"5862","DOI":"10.1109\/TIT.2010.2070191","article-title":"Toeplitz compressed sensing matrices with applications to sparse channel estimation","volume":"56","author":"Haupt","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3828","DOI":"10.1109\/TAP.2013.2256093","article-title":"Directions-of-arrival estimation through Bayesian compressive sensing strategies","volume":"61","author":"Carlin","year":"2013","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1182","DOI":"10.1002\/mrm.21391","article-title":"Sparse MRI: The application of compressed sensing for rapid MR imaging","volume":"58","author":"Lustig","year":"2007","journal-title":"Magn. Reson. Med."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"706","DOI":"10.1109\/TBC.2017.2669641","article-title":"Iterative clipping noise recovery of OFDM signals based on compressed sensing","volume":"63","author":"Yang","year":"2017","journal-title":"IEEE Trans. Broadcast."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1109\/TCI.2017.2675708","article-title":"Non-linear inverse scattering via sparsity regularized contrast source inversion","volume":"3","author":"Bevacqua","year":"2017","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"37","DOI":"10.2528\/PIER16111404","article-title":"Shape reconstruction via equivalence principles, constrained inverse source problems and sparsity promotion","volume":"158","author":"Bevacqua","year":"2017","journal-title":"Prog. Electromagn. Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1109\/TMI.2015.2490340","article-title":"A compressive sensing approach for 3D breast cancer microwave imaging with magnetic nanoparticles as contrast agent","volume":"35","author":"Bevacqua","year":"2016","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"7038","DOI":"10.1109\/TVT.2017.2669920","article-title":"Interference mitigation based on Bayesian compressive sensing for wireless localization systems in unlicensed band","volume":"66","author":"Sung","year":"2017","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.infrared.2017.04.005","article-title":"Bayesian compressive sensing for thermal imagery using Gaussian-Jeffreys prior","volume":"83","author":"Gu","year":"2017","journal-title":"Infrared Phys. Technol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1357","DOI":"10.1109\/TAP.2017.2655013","article-title":"Bayesian compressive sensing approaches for direction of arrival estimation with mutual coupling effects","volume":"65","author":"Hawes","year":"2017","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2022","DOI":"10.1109\/JSAC.2016.2566140","article-title":"Spectrally efficient CSI acquisition for power line communications: A Bayesian compressive sensing perspective","volume":"34","author":"Ding","year":"2016","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_28","first-page":"211","article-title":"Sparse Bayesian learning and the relevance vector machine","volume":"1","author":"Tipping","year":"2001","journal-title":"J. Mach. Learn. Res."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/s11235-014-9902-7","article-title":"Bayesian compressive sensing for ultra-wideband channel estimation: Algorithm and performance analysis","volume":"59","author":"Ozgor","year":"2015","journal-title":"Telecommun. Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1937","DOI":"10.1109\/LCOMM.2015.2427806","article-title":"Block-FFT based OMP for compressed channel estimation in underwater acoustic communications","volume":"19","author":"Yu","year":"2015","journal-title":"IEEE Commun. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1660","DOI":"10.1109\/JSAC.2011.110915","article-title":"Random access compressed sensing for energy-efficient underwater sensor networks","volume":"29","author":"Fazel","year":"2011","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1985","DOI":"10.1007\/s11276-015-1076-z","article-title":"Energy-efficient compressed data aggregation in underwater acoustic sensor networks","volume":"22","author":"Lin","year":"2016","journal-title":"Wirel. Netw."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"25577","DOI":"10.3390\/s151025577","article-title":"Underwater acoustic matched field imaging based on compressed sensing","volume":"15","author":"Yan","year":"2015","journal-title":"Sensors"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/j.apenergy.2014.08.028","article-title":"Parameters affecting scalable underwater compressed air energy storage","volume":"134","author":"Cheung","year":"2014","journal-title":"Appl. Energy"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1049\/iet-spr.2013.0501","article-title":"Heterogeneous Bayesian compressive sensing for sparse signal recovery","volume":"8","author":"Huang","year":"2014","journal-title":"IET Signal Process."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"5059","DOI":"10.1109\/TSP.2014.2343947","article-title":"OMP based joint sparsity pattern recovery under communication constraints","volume":"62","author":"Wimalajeewa","year":"2014","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/8\/2568\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:16:48Z","timestamp":1760195808000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/8\/2568"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,6]]},"references-count":36,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2018,8]]}},"alternative-id":["s18082568"],"URL":"https:\/\/doi.org\/10.3390\/s18082568","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2018,8,6]]}}}