{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:20:51Z","timestamp":1760242851604,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2016,8,19]],"date-time":"2016-08-19T00:00:00Z","timestamp":1471564800000},"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":["61402126","61073041","61073043","61370083"],"award-info":[{"award-number":["61402126","61073041","61073043","61370083"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["HEUCFJ160601"],"award-info":[{"award-number":["HEUCFJ160601"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundamental Research Funds of Shandong University","award":["2016HW003"],"award-info":[{"award-number":["2016HW003"]}]},{"name":"The National Key Technology R&amp;D Program of the Ministry of Science and Technology","award":["2012BAH81F02"],"award-info":[{"award-number":["2012BAH81F02"]}]},{"name":"The Youth Foundation of Heilongjiang Province of China","award":["QC2016083"],"award-info":[{"award-number":["QC2016083"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, we consider the problem of reconstructing the temporal and spatial profile of some physical phenomena monitored by large-scale Wireless Sensor Networks (WSNs) in an energy efficient manner. Compressive sensing is one of the popular choices to reduce the energy consumption of the data collection in WSNs. The existing solutions only consider sparsity of sensors\u2019 data from either temporal or spatial dimensions. In this paper, we propose a novel data collection strategy, CS2-collector, for WSNs based on the theory of Two Dimensional Compressive Sensing (2DCS). It exploits both temporal and spatial sparsity, i.e., 2D-sparsity of WSNs and achieves significant gain on the tradeoff between the compression ratio and reconstruction accuracy as the numerical simulations and evaluations on different types of sensors\u2019 data. More intuitively, with the same given energy budget, CS2-collector provides significantly more accurate reconstruction of the profile of the physical phenomena that are temporal-spatially sparse.<\/jats:p>","DOI":"10.3390\/s16081318","type":"journal-article","created":{"date-parts":[[2016,8,19]],"date-time":"2016-08-19T09:58:27Z","timestamp":1471600707000},"page":"1318","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["CS2-Collector: A New Approach for Data Collection in Wireless Sensor Networks Based on Two-Dimensional Compressive Sensing"],"prefix":"10.3390","volume":"16","author":[{"given":"Yong","family":"Wang","sequence":"first","affiliation":[{"name":"College of Computer Science and Technology, Harbin Engineering University, Harbin 150001, China"}]},{"given":"Zhuoshi","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, Harbin Engineering University, Harbin 150001, China"}]},{"given":"Jianpei","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, Harbin Engineering University, Harbin 150001, China"}]},{"given":"Feng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Shandong University, Jinan 250100, China"}]},{"given":"Hongkai","family":"Wen","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Oxford, Oxford OX1 3QD, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1385-1480","authenticated-orcid":false,"given":"Yiran","family":"Shen","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, Harbin Engineering University, Harbin 150001, China"}]}],"member":"1968","published-online":{"date-parts":[[2016,8,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Taneja, J., Jeong, J., and Culler, D. (2008, January 22\u201324). Design, Modeling, and Capacity Planning for Micro-solar Power Sensor Networks. Proceedings of the 7th International Conference on Information Processing in Sensor Networks, St. Louis, MO, USA.","DOI":"10.1109\/IPSN.2008.67"},{"key":"ref_2","first-page":"100","article-title":"Distributed inference in wireless sensor networks","volume":"370","author":"Veeravalli","year":"2012","journal-title":"Philos. Trans. R. Soc. Lond. A Math. Phys. Eng. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"16766","DOI":"10.3390\/s140916766","article-title":"WSNs data acquisition by combining hierarchical routing method and compressive sensing","volume":"14","author":"Zou","year":"2014","journal-title":"Sensors"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1109\/MSP.2007.4286571","article-title":"Compressive sensing","volume":"24","author":"Baraniuk","year":"2007","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/MSP.2007.914731","article-title":"An introduction to compressive sampling","volume":"25","author":"Wakin","year":"2008","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1109\/TII.2011.2173500","article-title":"Distributed Compressive Sampling for Lifetime Optimization in Dense Wireless Sensor Networks","volume":"8","author":"Caione","year":"2012","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Shen, Y., Hu, W., Rana, R., and Chou, C.T. (2011, January 6\u20139). Non-uniform compressive sensing in wireless sensor networks: Feasibility and application. Processdings of the Seventh International Conference on Intelligent Sensors, Sensor Networks and Information, Adelaide, SA, USA.","DOI":"10.1109\/ISSNIP.2011.6146546"},{"key":"ref_8","first-page":"2120","article-title":"Nonuniform compressive sensing for heterogeneous wireless sensor networks","volume":"13","author":"Shen","year":"2013","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_9","unstructured":"Cand\u00e8s, E.J. (2006, January 22\u201330). Compressive sampling. Proceedings of the International Congress of Mathematicians, Madrid, Spain."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1109\/TIT.2005.862083","article-title":"Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information","volume":"52","author":"Candes","year":"2006","journal-title":"IEEE Trans. Inform. Theory"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Boche, H., Calderbank, R., Kutyniok, G., and Vyb\u00edral, J. (2015). Compressed Sensing and Its Applications, Springer International Publishing.","DOI":"10.1007\/978-3-319-16042-9"},{"key":"ref_12","unstructured":"Jin, Y., and Rao, B.D. (2008, January 6\u201311). Performance limits of matching pursuit algorithms. Processdings of the 2008 IEEE International Symposium on Information Theory, Toronto, ON, Canada."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1109\/JSTSP.2007.910281","article-title":"Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems","volume":"1","author":"Figueiredo","year":"2008","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Quer, G., Masiero, R., Munaretto, D., and Rossi, M. (2009). On the interplay between routing and signal representation for Compressive Sensing in wireless sensor networks. Inform. Theory Appl. Workshop.","DOI":"10.1109\/ITA.2009.5044947"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3728","DOI":"10.1109\/TWC.2010.092810.100063","article-title":"Efficient Measurement Generation and Pervasive Sparsity for Compressive Data Gathering","volume":"9","author":"Luo","year":"2010","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Mahmudimanesh, M., Khelil, A., and Suri, N. (2010, January 7\u20139). Reordering for Better Compressibility: Efficient Spatial Sampling in Wireless Sensor Networks. Proceedings of the 2010 IEEE International Conference on Sensor Networks, Ubiquitous, and Trustworthy Computing, Newport Beach, CA, USA.","DOI":"10.1109\/SUTC.2010.30"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Xiong, J., and Tang, Q. (2014). 1-bit compressive data gathering for wireless sensor networks. J. Sens., 2014.","DOI":"10.1155\/2014\/805423"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Yu, Z., and Hoyos, S. (2009, January 4\u20135). Digitally assisted Analog Compressive Sensing. Proceedings of the 2009 IEEE Dallas Circuits and Systems Workshop, Richardson, TX, USA.","DOI":"10.1109\/DCAS.2009.5505732"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Baheti, P.K., and Garudadri, H. (2009, January 3\u20135). An Ultra Low Power Pulse Oximeter Sensor Based on Compressed Sensing. Proceedings of the 2009 Sixth International Workshop on Wearable and Implantable Body Sensor Networks, Berkeley, CA, USA.","DOI":"10.1109\/BSN.2009.32"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Rana, R., Hu, W., and Chou, C.T. (2010, January 17\u201319). Energy-Aware Sparse Approximation Technique (EAST) for Rechargeable Wireless Sensor Networks. Proceedings of the 7th European conference on Wireless Sensor Networks, Coimbra, Portugal.","DOI":"10.1007\/978-3-642-11917-0_20"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Charbiwala, Z., Kim, Y., Zahedi, S., Friedman, J., and Srivastava, M.B. (2009, January 19\u201321). Energy efficient sampling for event detection in wireless sensor networks. Proceedings of the 2009 ACM\/IEEE international symposium on Low power electronics and design, San Fancisco, CA, USA.","DOI":"10.1145\/1594233.1594339"},{"key":"ref_22","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_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.comnet.2015.04.003","article-title":"An effective dynamic spectrum access algorithm for multi-hop cognitive wireless networks","volume":"84","author":"Jiang","year":"2015","journal-title":"Comput. Netw."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3533","DOI":"10.1016\/j.comnet.2011.06.027","article-title":"Joint time\u2013frequency sparse estimation of large-scale network traffic","volume":"55","author":"Jiang","year":"2011","journal-title":"Comput. Netw."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Mahmudimanesh, M., Khelil, A., and Suri, N. (2012, January 8\u201311). Balanced spatio-temporal compressive sensing for multi-hop wireless sensor networks. Proceedings of the 2012 IEEE 9th International Conference on Mobile Ad-Hoc and Sensor Systems, Las Vegas, NV, USA.","DOI":"10.1109\/MASS.2012.6502539"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Xiang, L., Luo, J., Deng, C., Vasilakos, A.V., and Lin, W. (2012, January 18\u201321). DECA: Recovering fields of physical quantities from incomplete sensory data. Proceedings of the 9th Annual IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks, Seoul, Korea.","DOI":"10.1109\/SECON.2012.6275775"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Kong, L., Xia, M., Liu, X.Y., Wu, M.Y., and Liu, X. (2013, January 14\u201319). Data loss and reconstruction in sensor networks. Proceedings of the 2013 IEEE INFOCOM, Turin, Italy.","DOI":"10.1109\/INFCOM.2013.6566962"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"23137","DOI":"10.3390\/s141223137","article-title":"Correlated spatio-temporal data collection in wireless sensor networks based on low rank matrix approximation and optimized node sampling","volume":"14","author":"Piao","year":"2014","journal-title":"Sensors"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"850","DOI":"10.1109\/TWC.2012.121412.120148","article-title":"STCDG: An efficient data gathering algorithm based on matrix completion for wireless sensor networks","volume":"12","author":"Cheng","year":"2013","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Ahmed, S.H., Bouk, S.H., Javaid, N., and Sasase, I. (2012, January 17\u201319). Combined human, antenna orientation in elevation direction and ground effect on RSSI in wireless sensor networks. Proceedings of the 2012 10th International Conference on Frontiers of Information Technology, Islamabad, Pakistan.","DOI":"10.1109\/FIT.2012.17"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Ahmed, S.H., Bouk, S.H., Javaid, N., and Sasase, I. (2012, January 13\u201315). RF propagation analysis of MICAz Mote\u2019s antenna with ground effect. Proceedings of the 15th International Multitopic Conference, Islamabad, Pakistan.","DOI":"10.1109\/INMIC.2012.6511469"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1109\/TMC.2015.2418775","article-title":"Real-Time and Robust Compressive Background Subtraction for Embedded Camera Networks","volume":"15","author":"Shen","year":"2016","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Shen, Y., Hu, W., Liu, J., Yang, M., Wei, B., and Chou, C.T. (2012, January 6\u20139). Efficient background subtraction for real-time tracking in embedded camera networks. Proceedings of the 10th ACM Conference on Embedded Network Sensor Systems, Toronto, ON, Canada.","DOI":"10.1145\/2426656.2426686"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Wei, B., Yang, M., Shen, Y., Rana, R., Chou, C.T., and Hu, W. (2013, January 11\u201315). Real-time classification via sparse representation in acoustic sensor networks. Proceedings of the 11th ACM Conference on Embedded Networked Sensor Systems, Roma, Italy.","DOI":"10.1145\/2517351.2517357"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Ranieri, J., Rovatti, R., and Setti, G. (June, January 30). Compressive Sensing of Localized Signals: Application to Analog-to- Information Conversion. Proceedings of the 2010 IEEE International Symposium on Circuits and Systems, Paris, France.","DOI":"10.1109\/ISCAS.2010.5537820"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1016\/j.crma.2008.03.014","article-title":"The restricted isometry property and its implications for compressed sensing","volume":"346","author":"Candes","year":"2008","journal-title":"Comptes Rendus Math."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2182","DOI":"10.1109\/TSP.2011.2112650","article-title":"Sensitivity to Basis Mismatch in Compressed Sensing","volume":"59","author":"Chi","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Mahrous, H., and Ward, R. (2016). Block Sparse Compressed Sensing of Electroencephalogram (EEG) Signals by Exploiting Linear and Non-Linear Dependencies. Sensors, 16.","DOI":"10.3390\/s16020201"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/8\/1318\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:28:46Z","timestamp":1760210926000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/8\/1318"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,8,19]]},"references-count":38,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2016,8]]}},"alternative-id":["s16081318"],"URL":"https:\/\/doi.org\/10.3390\/s16081318","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2016,8,19]]}}}