{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T08:40:42Z","timestamp":1772613642213,"version":"3.50.1"},"reference-count":54,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2018,10,12]],"date-time":"2018-10-12T00:00:00Z","timestamp":1539302400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput &amp; Applic"],"published-print":{"date-parts":[[2020,4]]},"DOI":"10.1007\/s00521-018-3812-7","type":"journal-article","created":{"date-parts":[[2018,10,12]],"date-time":"2018-10-12T18:07:47Z","timestamp":1539367667000},"page":"2705-2724","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Compressive sensing MRI reconstruction using empirical wavelet transform and grey wolf optimizer"],"prefix":"10.1007","volume":"32","author":[{"given":"Mohamed","family":"Ragab","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Osama A.","family":"Omer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohamed","family":"Abdel-Nasser","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,10,12]]},"reference":[{"key":"3812_CR1","doi-asserted-by":"crossref","unstructured":"Cheng J, Zhao M, Lin M, Chiu B (2017) AWM: Adaptive Weight Matting for medical image segmentation. In: Medical imaging 2017: image processing, vol 10133. International Society for Optics and Photonics, p. 101332P","DOI":"10.1117\/12.2254774"},{"key":"3812_CR2","doi-asserted-by":"crossref","unstructured":"Lin M et al (2017) Prostate lesion detection and localization based on locality alignment discriminant analysis. In: Medical imaging 2017: computer-aided diagnosis, vol 10134. International Society for Optics and Photonics, p 101344A","DOI":"10.1117\/12.2255621"},{"issue":"6","key":"3812_CR3","doi-asserted-by":"publisher","first-page":"823","DOI":"10.1002\/mrm.1910030602","volume":"3","author":"J Hennig","year":"1986","unstructured":"Hennig J, Nauerth A, Friedburg H (1986) RARE imaging: a fast imaging method for clinical MR. Magn Reson Med 3(6):823\u2013833","journal-title":"Magn Reson Med"},{"key":"3812_CR4","doi-asserted-by":"crossref","unstructured":"Gibby WA (2000) Faster MRI. In Neuroimaging: clinical and physical principles, no. 494, p 227","DOI":"10.1007\/978-1-4612-1152-5_8"},{"issue":"3","key":"3812_CR5","doi-asserted-by":"publisher","first-page":"L55","DOI":"10.1088\/0022-3719\/10\/3\/004","volume":"10","author":"P Mansfield","year":"1977","unstructured":"Mansfield P (1977) Multi-planar image formation using NMR spin echoes. J Phys C Solid State Phys 10(3):L55","journal-title":"J Phys C Solid State Phys"},{"issue":"2","key":"3812_CR6","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1148\/radiology.161.2.3763926","volume":"161","author":"DA Feinberg","year":"1986","unstructured":"Feinberg DA, Hale JD, Watts JC, Kaufman L, Mark A (1986) Halving MR imaging time by conjugation: demonstration at 3.5 kG. Radiology 161(2):527\u2013531","journal-title":"Radiology"},{"issue":"4","key":"3812_CR7","doi-asserted-by":"publisher","first-page":"638","DOI":"10.1002\/mrm.1241","volume":"46","author":"KP Pruessmann","year":"2001","unstructured":"Pruessmann KP, Weiger M, B\u00f6rnert P, Boesiger P (2001) Advances in sensitivity encoding with arbitrary k-space trajectories. Magn Reson Med 46(4):638\u2013651","journal-title":"Magn Reson Med"},{"issue":"6","key":"3812_CR8","doi-asserted-by":"publisher","first-page":"1202","DOI":"10.1002\/mrm.10171","volume":"47","author":"MA Griswold","year":"2002","unstructured":"Griswold MA et al (2002) Generalized autocalibrating partially parallel acquisitions (GRAPPA). Magn Reson Med 47(6):1202\u20131210","journal-title":"Magn Reson Med"},{"issue":"4","key":"3812_CR9","doi-asserted-by":"publisher","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","volume":"52","author":"DL Donoho","year":"2006","unstructured":"Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52(4):1289\u20131306","journal-title":"IEEE Trans Inf Theory"},{"issue":"2","key":"3812_CR10","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1109\/TIT.2005.862083","volume":"52","author":"EJ Cand\u00e8s","year":"2006","unstructured":"Cand\u00e8s EJ, Romberg J, Tao T (2006) Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory 52(2):489\u2013509","journal-title":"IEEE Trans Inf Theory"},{"issue":"6","key":"3812_CR11","doi-asserted-by":"publisher","first-page":"1182","DOI":"10.1002\/mrm.21391","volume":"58","author":"M Lustig","year":"2007","unstructured":"Lustig M, Donoho D, Pauly JM (2007) Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn Reson Med 58(6):1182\u20131195","journal-title":"Magn Reson Med"},{"key":"3812_CR12","unstructured":"Ma S, Yin W, Zhang Y, Chakraborty A (2008) An efficient algorithm for compressed MR imaging using total variation and wavelets. In: IEEE conference on computer vision and pattern recognition. CVPR 2008. IEEE, pp 1\u20138"},{"issue":"2","key":"3812_CR13","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1109\/JSTSP.2010.2042333","volume":"4","author":"J Yang","year":"2010","unstructured":"Yang J, Zhang Y, Yin W (2010) A fast alternating direction method for TVL1-L2 signal reconstruction from partial Fourier data. IEEE J Sel Top Signal Process 4(2):288\u2013297","journal-title":"IEEE J Sel Top Signal Process"},{"issue":"5","key":"3812_CR14","doi-asserted-by":"publisher","first-page":"670","DOI":"10.1016\/j.media.2011.06.001","volume":"15","author":"J Huang","year":"2011","unstructured":"Huang J, Zhang S, Metaxas D (2011) Efficient MR image reconstruction for compressed MR imaging. Med Image Anal 15(5):670\u2013679","journal-title":"Med Image Anal"},{"issue":"1","key":"3812_CR15","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1137\/080716542","volume":"2","author":"A Beck","year":"2009","unstructured":"Beck A, Teboulle M (2009) A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J Imaging Sci 2(1):183\u2013202","journal-title":"SIAM J Imaging Sci"},{"key":"3812_CR16","unstructured":"Chen C, Huang J (2012) Compressive sensing MRI with wavelet tree sparsity. In: Advances in neural information processing systems, pp 1115\u20131123"},{"issue":"3","key":"3812_CR17","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1006\/acha.2000.0343","volume":"10","author":"N Kingsbury","year":"2001","unstructured":"Kingsbury N (2001) Complex wavelets for shift invariant analysis and filtering of signals. Appl Comput Harmon Anal 10(3):234\u2013253","journal-title":"Appl Comput Harmon Anal"},{"issue":"1760","key":"3812_CR18","doi-asserted-by":"publisher","first-page":"2543","DOI":"10.1098\/rsta.1999.0447","volume":"357","author":"N Kingsbury","year":"1999","unstructured":"Kingsbury N (1999) Image processing with complex wavelets. Philos Trans R Soc Lond A Math Phys Eng Sci 357(1760):2543\u20132560","journal-title":"Philos Trans R Soc Lond A Math Phys Eng Sci"},{"key":"3812_CR19","doi-asserted-by":"crossref","unstructured":"Ragab M, Omer OA, Hussien HS (2017) Compressive sensing MRI using dual tree complex wavelet transform with wavelet tree sparsity. In: 34th National Radio Science Conference (NRSC). IEEE, pp 481\u2013486","DOI":"10.1109\/NRSC.2017.7893519"},{"key":"3812_CR20","doi-asserted-by":"crossref","unstructured":"Liu RW, Shi L, Simon C, Wang D (2017) Hybrid regularization for compressed sensing MRI: Exploiting shearlet transform and group-sparsity total variation. In: 20th international conference on information fusion (fusion). IEEE, pp 1\u20138","DOI":"10.23919\/ICIF.2017.8009783"},{"issue":"4","key":"3812_CR21","doi-asserted-by":"publisher","first-page":"816","DOI":"10.1109\/TBME.2016.2578930","volume":"64","author":"Y Yang","year":"2017","unstructured":"Yang Y et al (2017) Pseudo-polar Fourier transform-based compressed sensing MRI. IEEE Trans Biomed Eng 64(4):816\u2013825","journal-title":"IEEE Trans Biomed Eng"},{"issue":"16","key":"3812_CR22","doi-asserted-by":"publisher","first-page":"3999","DOI":"10.1109\/TSP.2013.2265222","volume":"61","author":"J Gilles","year":"2013","unstructured":"Gilles J (2013) Empirical wavelet transform. IEEE Trans Signal Process 61(16):3999\u20134010","journal-title":"IEEE Trans Signal Process"},{"issue":"12","key":"3812_CR23","doi-asserted-by":"publisher","first-page":"3861","DOI":"10.1109\/JSEN.2017.2694970","volume":"17","author":"VN Varghees","year":"2017","unstructured":"Varghees VN, Ramachandran KI (2017) Effective heart sound segmentation and murmur classification using empirical wavelet transform and instantaneous phase for electronic stethoscope. IEEE Sens J 17(12):3861\u20133872","journal-title":"IEEE Sens J"},{"issue":"3","key":"3812_CR24","doi-asserted-by":"publisher","first-page":"803","DOI":"10.1109\/JBHI.2016.2544961","volume":"21","author":"S Maheshwari","year":"2017","unstructured":"Maheshwari S, Pachori RB, Acharya UR (2017) Automated diagnosis of glaucoma using empirical wavelet transform and correntropy features extracted from fundus images. IEEE J Biomed Health Inform 21(3):803\u2013813","journal-title":"IEEE J Biomed Health Inform"},{"key":"3812_CR25","doi-asserted-by":"crossref","unstructured":"Jambholkar T, Gurve D, Sharma PB (2015) Application of Empirical Wavelet Transform (EWT) on images to explore Brain Tumor. In: 2015 international conference on signal processing, computing and control (ISPCC), pp 200\u2013204","DOI":"10.1109\/ISPCC.2015.7375025"},{"key":"3812_CR26","unstructured":"Singh O, Sunkaria RK (2015) Onset detection in arterial blood pressure pulses using Empirical Wavelet Transform. In: 2015 2nd international conference on computing for sustainable global development (INDIACom), pp 1612\u20131615"},{"key":"3812_CR27","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.advengsoft.2013.12.007","volume":"69","author":"S Mirjalili","year":"2014","unstructured":"Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46\u201361","journal-title":"Adv Eng Softw"},{"key":"3812_CR28","unstructured":"Faris H, Aljarah I, Al-Betar MA, Mirjalili S (2017) Grey wolf optimizer: a review of recent variants and applications. In: Neural computing and applications, pp 1\u201323"},{"key":"3812_CR29","doi-asserted-by":"crossref","unstructured":"Das KR, Das D, Das J (2015) Optimal tuning of PID controller using GWO algorithm for speed control in DC motor. In: 2015 international conference on soft computing techniques and implementations (ICSCTI). IEEE, pp 108\u2013112","DOI":"10.1109\/ICSCTI.2015.7489575"},{"issue":"4","key":"3812_CR30","first-page":"373","volume":"4","author":"A Madadi","year":"2014","unstructured":"Madadi A, Motlagh MM (2014) Optimal control of DC motor using grey wolf optimizer algorithm. Tech J Eng Appl Sci 4(4):373\u2013379","journal-title":"Tech J Eng Appl Sci"},{"key":"3812_CR31","doi-asserted-by":"crossref","unstructured":"Gupta P, Kumar V, Rana K, Mishra P (2015) Comparative study of some optimization techniques applied to jacketed CSTR control. In: 2015 4th international conference on reliability, Infocom technologies and optimization (ICRITO) (trends and future directions). IEEE, pp 1\u20136","DOI":"10.1109\/ICRITO.2015.7359368"},{"key":"3812_CR32","doi-asserted-by":"publisher","DOI":"10.1155\/2015\/120975","author":"S-X LI","year":"2015","unstructured":"Li S-X, Wang J-S (2015) Dynamic modeling of steam condenser and design of pi controller based on grey wolf optimizer. Math Probl Eng. \nhttps:\/\/doi.org\/10.1155\/2015\/120975","journal-title":"Math Probl Eng"},{"issue":"1","key":"3812_CR33","doi-asserted-by":"publisher","first-page":"778","DOI":"10.1016\/j.ifacol.2016.03.151","volume":"49","author":"S Yadav","year":"2016","unstructured":"Yadav S, Verma S, Nagar S (2016) Optimized PID controller for magnetic levitation system. IFAC-PapersOnLine 49(1):778\u2013782","journal-title":"IFAC-PapersOnLine"},{"key":"3812_CR34","unstructured":"Tsai P-W, Dao T-K (2016) Robot path planning optimization based on multiobjective grey wolf optimizer. In: International conference on genetic and evolutionary computing. Springer, pp 166\u2013173"},{"key":"3812_CR35","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1016\/j.advengsoft.2016.05.015","volume":"99","author":"S Zhang","year":"2016","unstructured":"Zhang S, Zhou Y, Li Z, Pan W (2016) Grey wolf optimizer for unmanned combat aerial vehicle path planning. Adv Eng Softw 99:121\u2013136","journal-title":"Adv Eng Softw"},{"key":"3812_CR36","doi-asserted-by":"crossref","unstructured":"Korayem L, Khorsid M, Kassem S (2015) Using grey wolf algorithm to solve the capacitated vehicle routing problem. In: IOP conference series: materials science and engineering, vol 83, no 1. IOP Publishing, p 012014","DOI":"10.1088\/1757-899X\/83\/1\/012014"},{"key":"3812_CR37","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/9512741","author":"Q Li","year":"2017","unstructured":"Li Q et al (2017) An enhanced grey wolf optimization based feature selection wrapped kernel extreme learning machine for medical diagnosis. Comput Math Methods Med. \nhttps:\/\/doi.org\/10.1155\/2017\/9512741","journal-title":"Comput Math Methods Med"},{"key":"3812_CR38","doi-asserted-by":"crossref","unstructured":"Jayapriya J, Arock M (2015) A parallel GWO technique for aligning multiple molecular sequences. In: 2015 international conference on advances in computing, communications and informatics (ICACCI). IEEE, pp 210\u2013215","DOI":"10.1109\/ICACCI.2015.7275611"},{"key":"3812_CR39","unstructured":"Mostafa A et al (2016) A hybrid grey wolf based segmentation with statistical image for ct liver images. In: International conference on advanced intelligent systems and informatics. Springer, pp 846\u2013855"},{"key":"3812_CR40","doi-asserted-by":"publisher","first-page":"853","DOI":"10.1016\/j.ijepes.2015.06.005","volume":"73","author":"Y Sharma","year":"2015","unstructured":"Sharma Y, Saikia LC (2015) Automatic generation control of a multi-area ST\u2013Thermal power system using Grey Wolf Optimizer algorithm based classical controllers. Int J Electr Power Energy Syst 73:853\u2013862","journal-title":"Int J Electr Power Energy Syst"},{"issue":"4","key":"3812_CR41","first-page":"360","volume":"4","author":"P Rathee","year":"2015","unstructured":"Rathee P, Garg R, Meena S (2015) Using grey wolf optimizer for image registration. Int J Adv Res Sci Eng 4(4):360\u2013364","journal-title":"Int J Adv Res Sci Eng"},{"issue":"1","key":"3812_CR42","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/S0021-9045(03)00083-2","volume":"123","author":"L Borup","year":"2003","unstructured":"Borup L, Nielsen M (2003) Approximation with brushlet systems. J Approx Theory 123(1):25\u201351","journal-title":"J Approx Theory"},{"issue":"2","key":"3812_CR43","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1006\/acha.1997.0208","volume":"4","author":"FG Meyer","year":"1997","unstructured":"Meyer FG, Coifman RR (1997) Brushlets: a tool for directional image analysis and image compression. Appl Comput Harmon Anal 4(2):147\u2013187","journal-title":"Appl Comput Harmon Anal"},{"issue":"3","key":"3812_CR44","doi-asserted-by":"publisher","first-page":"992","DOI":"10.1137\/040619454","volume":"4","author":"E Pennec Le","year":"2005","unstructured":"Le Pennec E, Mallat S (2005) Bandelet image approximation and compression. Multiscale Model Simul 4(3):992\u20131039","journal-title":"Multiscale Model Simul"},{"issue":"4","key":"3812_CR45","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1109\/TIP.2005.843753","volume":"14","author":"E Pennec Le","year":"2005","unstructured":"Le Pennec E, Mallat S (2005) Sparse geometric image representations with bandelets. IEEE Trans Image Process 14(4):423\u2013438","journal-title":"IEEE Trans Image Process"},{"issue":"2","key":"3812_CR46","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1016\/j.acha.2008.03.004","volume":"26","author":"S Mallat","year":"2009","unstructured":"Mallat S (2009) Geometrical grouplets. Appl Comput Harmon Anal 26(2):161\u2013180","journal-title":"Appl Comput Harmon Anal"},{"key":"3812_CR47","doi-asserted-by":"crossref","unstructured":"Huang NE et al (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. In: Proceedings of the Royal Society of London A: mathematical, physical and engineering sciences, vol 454, no 1971. The Royal Society, pp 903\u2013995","DOI":"10.1098\/rspa.1998.0193"},{"issue":"1","key":"3812_CR48","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1112\/plms\/s3-7.1.113","volume":"3","author":"TM Flett","year":"1957","unstructured":"Flett TM (1957) On an extension of absolute summability and some theorems of Littlewood and Paley. Proc Lond Math Soc 3(1):113\u2013141","journal-title":"Proc Lond Math Soc"},{"key":"3812_CR49","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/978-0-387-09432-8","volume-title":"Classical fourier analysis","author":"L Grafakos","year":"2008","unstructured":"Grafakos L (2008) Classical fourier analysis, 2nd edn. Springer, New York, p 161. \nhttps:\/\/doi.org\/10.1007\/978-0-387-09432-8","edition":"2"},{"issue":"2","key":"3812_CR50","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/j.acha.2005.11.003","volume":"21","author":"A Averbuch","year":"2006","unstructured":"Averbuch A, Coifman RR, Donoho DL, Elad M, Israeli M (2006) Fast and accurate polar Fourier transform. Appl Comput Harmon Anal 21(2):145\u2013167","journal-title":"Appl Comput Harmon Anal"},{"issue":"1","key":"3812_CR51","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1137\/130923774","volume":"7","author":"J Gilles","year":"2014","unstructured":"Gilles J, Tran G, Osher S (2014) 2D empirical transforms. Wavelets, ridgelets, and curvelets revisited. SIAM J Imaging Sci 7(1):157\u2013186","journal-title":"SIAM J Imaging Sci"},{"issue":"4","key":"3812_CR52","doi-asserted-by":"publisher","first-page":"600","DOI":"10.1109\/TIP.2003.819861","volume":"13","author":"Z Wang","year":"2004","unstructured":"Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13(4):600\u2013612","journal-title":"IEEE Trans Image Process"},{"key":"3812_CR53","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.advengsoft.2016.01.008","volume":"95","author":"S Mirjalili","year":"2016","unstructured":"Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51\u201367","journal-title":"Adv Eng Softw"},{"key":"3812_CR54","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1016\/j.advengsoft.2017.07.002","volume":"114","author":"S Mirjalili","year":"2017","unstructured":"Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp Swarm Algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163\u2013191","journal-title":"Adv Eng Softw"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-018-3812-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-018-3812-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-018-3812-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,3,31]],"date-time":"2020-03-31T00:08:42Z","timestamp":1585613322000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-018-3812-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,12]]},"references-count":54,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2020,4]]}},"alternative-id":["3812"],"URL":"https:\/\/doi.org\/10.1007\/s00521-018-3812-7","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,12]]},"assertion":[{"value":"26 September 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 October 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 October 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that they have no conflict of interest, and the manuscript is approved by all authors for publication.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}