{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:31:35Z","timestamp":1760239895278,"version":"build-2065373602"},"reference-count":53,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,1,11]],"date-time":"2019-01-11T00:00:00Z","timestamp":1547164800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>We consider a Wireless Sensor Network (WSN) monitoring environmental data. Compressive Sensing (CS) is explored to reduce the number of coefficients to transmit and consequently save the energy of sensor nodes. Each sensor node collects N samples of environmental data, these are CS coded to transmit     M &lt; N     values to a sink node. The M CS coefficients are uniformly quantized and entropy coded. We investigate the rate-distortion performance of this approach even under CS coefficient losses. The results show the robustness of the CS coding framework against packet loss. We devise a simple strategy to successively approximate\/quantize CS coefficients, allowing for an efficient incremental transmission of CS coded data. Tests show that the proposed successive approximation scheme provides rate allocation adaptivity and flexibility with a minimum rate-distortion performance penalty.<\/jats:p>","DOI":"10.3390\/s19020266","type":"journal-article","created":{"date-parts":[[2019,1,11]],"date-time":"2019-01-11T04:10:16Z","timestamp":1547179816000},"page":"266","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Rate-Distortion Performance and Incremental Transmission Scheme of Compressive Sensed Measurements in Wireless Sensor Networks"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7221-7466","authenticated-orcid":false,"given":"Felipe","family":"Da Rocha Henriques","sequence":"first","affiliation":[{"name":"Coordena\u00e7\u00e3o de Telecomunica\u00e7\u00f5es\u2014CEFET\/RJ\u2014Campus Petr\u00f3polis, Petr\u00f3polis 25620-003, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7404-9371","authenticated-orcid":false,"given":"Lisandro","family":"Lovisolo","sequence":"additional","affiliation":[{"name":"PROSAICO\u2013DETEL\/PEL\u2013FEN, Universidade do Estado do Rio de Janeiro, Rio de Janeiro 20559-900, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7755-6988","authenticated-orcid":false,"given":"Eduardo Ant\u00f4nio","family":"Barros da Silva","sequence":"additional","affiliation":[{"name":"PEE\/COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro 21941-901, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/S1389-1286(01)00302-4","article-title":"Wireless Sensor Networks: A Survey","volume":"38","author":"Akyildiz","year":"2002","journal-title":"Comput. Netw."},{"key":"ref_2","first-page":"35","article-title":"Energy-efficient Communication Methods in Wireless Sensor Networks: A Critical Review","volume":"39","author":"Sachan","year":"2012","journal-title":"Int. J. Comput. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","article-title":"Compressed Sensing","volume":"52","author":"Donoho","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_4","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":"Romberg","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/j.procs.2013.09.028","article-title":"A Distributed Compressive Sensing Technique for Data Gathering in Wireless Sensor Networks","volume":"21","author":"Masorum","year":"2013","journal-title":"Procedia Comput. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Chen, W., Rodrigues, M.R.D., and Wassel, I.J. (2011, January 5\u20139). Distributed Compressive Sensing Reconstruction Via Common Support Discovery. Proceedings of the IEEE International Conference on Communications, Kyoto, Japan.","DOI":"10.1109\/icc.2011.5962798"},{"key":"ref_7","unstructured":"Lab wsn, I.B. (2019, January 09). Intel Lab Data. Available online: http:\/\/db.csail.mit.edu\/labdata\/labdata.html."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2314","DOI":"10.1109\/TSP.2016.2521608","article-title":"Cost\u2014Aware Activity Sheduling for Compressive Sleeping Wireless Sensor Networks","volume":"64","author":"Chen","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.comnet.2016.06.029","article-title":"CCS: Energy-efficient data collection in clustered wireless sensor networks utilizing block-wise compressive sensing","volume":"106","author":"Nguyen","year":"2016","journal-title":"Comput. Netw."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1109\/TSP.2009.2027773","article-title":"Bayesian Compressive Sensing Via Belief Propagation","volume":"58","author":"Baron","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.adhoc.2016.10.009","article-title":"Compressive sensing based random walk routing in wireless sensor networks","volume":"54","author":"Nguyen","year":"2017","journal-title":"Ad Hoc Netw."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2082","DOI":"10.1109\/TIT.2012.2234823","article-title":"Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors","volume":"59","author":"Jacques","year":"2013","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Schulz, A., Velho, L., and da Silva, E.A.B. (2009, January 7\u201310). On the Empirical Rate-Distortion Performance of Compressive Sensing. Proceedings of the 16th IEEE Conference on Image Processing, Cairo, Egypt.","DOI":"10.1109\/ICIP.2009.5414390"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1857","DOI":"10.1109\/TCOMM.2011.051711.100204","article-title":"Information Theoretical and Algorithmic Approaches to Quantized Compressive Sensing","volume":"59","author":"Dai","year":"2011","journal-title":"IEEE Trans. Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"805423","DOI":"10.1155\/2014\/805423","article-title":"1-Bit Compressive Data Gathering for Wireless Sensor Networks","volume":"2014","author":"Xiong","year":"2014","journal-title":"J. Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1207","DOI":"10.1002\/cpa.20124","article-title":"Stable signal recovery from incomplete and inaccurate measurements","volume":"59","author":"Romberg","year":"2006","journal-title":"Commun. Pure Appl. Math."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2230","DOI":"10.1109\/TIT.2009.2016006","article-title":"Subspace Pursuit for Compressive Sensing Signal Reconstruction","volume":"55","author":"Dai","year":"2009","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2980","DOI":"10.1109\/TIP.2012.2188810","article-title":"Binned Progressive Quantization for Compressive Sensing","volume":"21","author":"Wang","year":"2012","journal-title":"IEEE Trans. Image Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.isprsjprs.2013.12.003","article-title":"UL-Isomap based nonlinear dimensionality reduction for hyperspectral imagery classification","volume":"89","author":"Sun","year":"2014","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_20","unstructured":"Silva, V.D., and Tenenbaum, J.B. (2003). Global versus local methods in nonlinear dimensionality reduction. Advances in Neural Information Processing Systems 15, MIT Press."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1109\/JSTARS.2013.2238890","article-title":"Nonlinear Dimensionality Reduction via the ENH-LTSA Method for Hyperspectral Image Classification","volume":"7","author":"Sun","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Liu, J., Cheung, Y.M., and Yin, H. (2003). Nonlinear Dimension Reduction via Local Tangent Space Alignment. Intelligent Data Engineering and Automated Learning, Springer.","DOI":"10.1007\/b11717"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2560","DOI":"10.1016\/j.comcom.2007.05.046","article-title":"Reliable bursty convergecast in wireless sensor networks","volume":"30","author":"Zhang","year":"2007","journal-title":"Comput. Commun."},{"key":"ref_24","unstructured":"Wu, L., Yu, K., Du, T., and Wang, Z. (2014, January 9\u201311). Efficient Information Transmission under Lossy WSNs Using Compressive Sensing. Proceedings of the IEEE 9th Conference on Industrial Electronics and Applications, Hangzhou, China."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Lindberg, C., Amat, A.G.I., and Wymeersch, H. (2014, January 8\u201312). Distributed Compressed Sensing for Sensor Networks with Packet Erasures. Proceedings of the IEEE Global Communications Conference, Austin, TX, USA.","DOI":"10.1109\/GLOCOM.2014.7036777"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.adhoc.2014.06.003","article-title":"Improving Response Time in Time Critical Visual Sensor Network Applications","volume":"23","author":"Felemban","year":"2014","journal-title":"Ad Hoc Netw."},{"key":"ref_27","unstructured":"Da Silva, E.A.B., and Craizer, M. (1998, January 7). Generalized bit-planes for Embedded Codes. Proceedings of the International Conference on Image Processing, Chicago, IL, USA."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3833","DOI":"10.1109\/TSP.2014.2324992","article-title":"FIR Filter Design Based on Successive Approximation of Vectors","volume":"62","author":"Lovisolo","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.dsp.2014.01.006","article-title":"On the Design of Maximally Incoherent Sensing Matrices for Compressed Sensing and its Extension for Biorthogonal Bases Case","volume":"27","author":"Lovisolo","year":"2014","journal-title":"Digit. Signal Process."},{"key":"ref_30","unstructured":"Cand\u00e8s, E., and Romberg, J. (2019, January 09). L1\u2013magic. Available online: http:\/\/www.l1--magic.org."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.dsp.2012.03.003","article-title":"A* Orthogonal Matching Pursuit: Best-First Search for Compressed Sensing Signal Recovery","volume":"22","author":"Karahanoglu","year":"2012","journal-title":"Digit. Signal Process."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","article-title":"Regression Shrinkage and Selection via the LASSO","volume":"58","author":"Tibshirani","year":"1996","journal-title":"J. R. Statist."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Boyd, S., and Vandenberghe, L. (2004). Convex Optimization, Cambridge University Press.","DOI":"10.1017\/CBO9780511804441"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1049\/iet-wss.2011.0009","article-title":"Energy-efficient signal acquisition in wireless sensor networks: A compressive sensing framework","volume":"2","author":"Chen","year":"2012","journal-title":"IET Wirel. Sens. Syst."},{"key":"ref_35","unstructured":"Pati, Y.C., Rezaiifar, R., and Krishnaprasad, P.S. (1993, January 1\u20133). Orthogonal Matching Pursuit: Recursive Function Approximation with Applications to Wavelet Decomposition. Proceedings of the 27th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA."},{"key":"ref_36","first-page":"99","article-title":"Incremental Heuristic Search in AI","volume":"25","author":"Koenig","year":"2004","journal-title":"Ai Mag."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Lee, D., and Choi, J. (2014, January 27\u201330). Low complexity sensing for big spatio-temporal data. Proceedings of the 2014 IEEE International Conference on Big Data (Big Data), Washington, DC, USA.","DOI":"10.1109\/BigData.2014.7004248"},{"key":"ref_38","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_39","unstructured":"Van den Berg, E., and Friedlander, M.P. (2019, January 09). SPGL1: A Solver for Large-Scale Sparse Reconstruction. Available online: http:\/\/www.cs.ubc.ca\/labs\/scl\/spgl1."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1006\/acha.2000.0313","article-title":"Noiselets","volume":"10","author":"Coifman","year":"2001","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1140","DOI":"10.1109\/76.954501","article-title":"Low-Complexity and Low-Memory Entropy Coder for Image Compression","volume":"11","author":"Zhao","year":"2001","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1109\/79.733495","article-title":"Rate-distortion methods for image and video compression","volume":"15","author":"Ortega","year":"1998","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"744","DOI":"10.1109\/JSSC.2011.2179451","article-title":"Design and analysis of a hardware-efficient compressed sensing architecture for data compression in wireless sensors","volume":"47","author":"Chen","year":"2012","journal-title":"IEEE J. Solid-State Circuits"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/MCS.2003.1200240","article-title":"How Does Control Timing Affect Performance? Analysis and Simulation of Timing using Jitterbug and TrueTime","volume":"23","author":"Cervin","year":"2003","journal-title":"IEEE Control Syst. Mag."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1655","DOI":"10.1016\/j.comcom.2006.12.020","article-title":"Wireless Sensor Networks: A Survey on the State of Art and the 802.15.4 and ZigBee Standards","volume":"30","author":"Baronti","year":"2007","journal-title":"Comput. Commun."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1186\/s13638-016-0662-9","article-title":"DECA: Distributed energy conservation algorithm for process reconstruction with bounded relative error in wireless sensor networks","volume":"2016","author":"Henriques","year":"2016","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1006\/acha.2000.0340","article-title":"Quantized Frames Expansions with Erasures","volume":"10","author":"Goyal","year":"2001","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1109\/TSP.2007.908963","article-title":"Causal Compensation for Erasures in Frame Representations","volume":"56","author":"Boufounos","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_49","first-page":"697153","article-title":"A Mac Protocol Implementation for Wireless Sensor Network","volume":"2015","author":"Bhar","year":"2015","journal-title":"J. Comput. Netw. Commun."},{"key":"ref_50","first-page":"336","article-title":"Energy Efficient Routing in Zigbee Wireless Sensor Network\u2014A Review","volume":"4","author":"Malav","year":"2015","journal-title":"Int. J. Adv. Res. Comput. Commun. Eng."},{"key":"ref_51","unstructured":"Bjontegaard, G. (2001). Calculation of Average PSNR Differences between RD\u2014Curves. Tech. Rep. Vceg\u2014M33, Available online: https:\/\/www.researchgate.net\/publication\/244455155_Calculation_of_average_PSNR_differences_between_RD-Curves."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1016\/j.jvcir.2013.11.008","article-title":"Calculation of average coding efficiency based on subjective quality scores","volume":"25","author":"Hanhart","year":"2014","journal-title":"J. Vis. Commun. Image Represent."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1016\/j.acha.2011.02.002","article-title":"Democracy in Action: Quantization, Saturation and Compressive Sensing","volume":"31","author":"Laska","year":"2011","journal-title":"Appl. Comput. Harmon. Anal."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/2\/266\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:25:13Z","timestamp":1760185513000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/2\/266"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,11]]},"references-count":53,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,1]]}},"alternative-id":["s19020266"],"URL":"https:\/\/doi.org\/10.3390\/s19020266","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,1,11]]}}}