{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T00:18:45Z","timestamp":1759882725566,"version":"build-2065373602"},"reference-count":40,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2015,8,1]],"date-time":"2015-08-01T00:00:00Z","timestamp":1438387200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2015,8,1]],"date-time":"2015-08-01T00:00:00Z","timestamp":1438387200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2019,8,1]],"date-time":"2019-08-01T00:00:00Z","timestamp":1564617600000},"content-version":"vor","delay-in-days":1461,"URL":"http:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"funder":[{"DOI":"10.13039\/100002418","name":"Intel","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100002418","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100003132","name":"Institute for the Promotion of Innovation through Science and Technology in Flanders","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003132","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2015,8]]},"DOI":"10.1016\/j.cam.2014.12.044","type":"journal-article","created":{"date-parts":[[2015,1,14]],"date-time":"2015-01-14T14:41:10Z","timestamp":1421246470000},"page":"1-16","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":2,"special_numbering":"C","title":["A multi-level preconditioned Krylov method for the efficient solution of algebraic tomographic reconstruction problems"],"prefix":"10.1016","volume":"283","author":[{"given":"Siegfried","family":"Cools","sequence":"first","affiliation":[]},{"given":"Pieter","family":"Ghysels","sequence":"additional","affiliation":[]},{"given":"Wim","family":"van Aarle","sequence":"additional","affiliation":[]},{"given":"Jan","family":"Sijbers","sequence":"additional","affiliation":[]},{"given":"Wim","family":"Vanroose","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"2","key":"10.1016\/j.cam.2014.12.044_br000005","doi-asserted-by":"crossref","first-page":"R41","DOI":"10.1088\/0266-5611\/15\/2\/022","article-title":"Optical tomography in medical imaging","volume":"15","author":"Arridge","year":"1999","journal-title":"Inverse Problems"},{"issue":"7","key":"10.1016\/j.cam.2014.12.044_br000010","doi-asserted-by":"crossref","first-page":"918","DOI":"10.1109\/TMI.2008.923696","article-title":"Computational analysis and improvement of SIRT","volume":"27","author":"Gregor","year":"2008","journal-title":"IEEE Trans. Med. Imaging"},{"issue":"1","key":"10.1016\/j.cam.2014.12.044_br000015","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/nla.499","article-title":"Recent computational developments in Krylov subspace methods for linear systems","volume":"14","author":"Simoncini","year":"2007","journal-title":"Numer. Linear Algebra Appl."},{"issue":"1","key":"10.1016\/j.cam.2014.12.044_br000020","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1137\/080716542","article-title":"A fast iterative shrinkage-thresholding algorithm for linear inverse problems","volume":"2","author":"Beck","year":"2009","journal-title":"SIAM J. Imag. Sci."},{"issue":"9","key":"10.1016\/j.cam.2014.12.044_br000025","doi-asserted-by":"crossref","first-page":"2542","DOI":"10.1109\/TIP.2011.2131661","article-title":"DART: a practical reconstruction algorithm for discrete tomography","volume":"20","author":"Batenburg","year":"2011","journal-title":"IEEE Trans. Image Process."},{"issue":"12","key":"10.1016\/j.cam.2014.12.044_br000030","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/0266-5611\/25\/12\/123009","article-title":"Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction?","volume":"25","author":"Pan","year":"2009","journal-title":"Inverse Problems"},{"key":"10.1016\/j.cam.2014.12.044_br000035","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1016\/j.jsb.2011.07.017","article-title":"Performance improvements for iterative electron tomography reconstruction using graphics processing units (GPUs)","volume":"176","author":"Palenstijn","year":"2011","journal-title":"J. Struct. Biol."},{"key":"10.1016\/j.cam.2014.12.044_br000040","unstructured":"W. van Aarle, P. Ghysels, J. Sijbers, W. Vanroose, Memory access optimization for iterative tomography on many-core architectures, in: Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine, 2012, pp. 369\u2013372."},{"issue":"6","key":"10.1016\/j.cam.2014.12.044_br000045","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1088\/0266-5611\/9\/6\/007","article-title":"Multigrid solution of a linearized, regularized least-squares problem in electrical impedance tomography","volume":"9","author":"McCormick","year":"1993","journal-title":"Inverse Problems"},{"issue":"1","key":"10.1016\/j.cam.2014.12.044_br000050","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1137\/0917014","article-title":"Multilevel image reconstruction with natural pixels","volume":"17","author":"Henson","year":"1996","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"10.1016\/j.cam.2014.12.044_br000055","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1109\/TIP.2004.837555","article-title":"A general framework for nonlinear multigrid inversion","volume":"14","author":"Oh","year":"2005","journal-title":"IEEE Trans. Image Process."},{"key":"10.1016\/j.cam.2014.12.044_br000060","unstructured":"H. K\u00f6stler, C. Popa, M. Pr\u00fcmmer, U. R\u00fcde, Towards an algebraic multigrid method for tomographic reconstruction\u2014improving convergence of ART, in: Proceedings of the European Conference on Computational Fluid Dynamics ECCOMAS CFD."},{"issue":"3","key":"10.1016\/j.cam.2014.12.044_br000065","first-page":"559","article-title":"The speed of convergence of one iterative process","volume":"4","author":"Fedorenko","year":"1964","journal-title":"Zh. Vychisl. Mat. Mat. Fiz."},{"issue":"138","key":"10.1016\/j.cam.2014.12.044_br000070","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1090\/S0025-5718-1977-0431719-X","article-title":"Multi-level adaptive solutions to boundary-value problems","volume":"31","author":"Brandt","year":"1977","journal-title":"Math. Comp."},{"issue":"4","key":"10.1016\/j.cam.2014.12.044_br000075","doi-asserted-by":"crossref","first-page":"1291","DOI":"10.1137\/S1064827501357190","article-title":"A multigrid method enhanced by Krylov subspace iteration for discrete Helmholtz equations","volume":"23","author":"Elman","year":"2002","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.cam.2014.12.044_br000080","doi-asserted-by":"crossref","first-page":"3417","DOI":"10.1137\/080731657","article-title":"Algebraic multilevel Krylov methods","volume":"31","author":"Erlangga","year":"2009","journal-title":"SIAM J. Sci. Comput."},{"year":"2000","series-title":"A Multigrid Tutorial","author":"Briggs","key":"10.1016\/j.cam.2014.12.044_br000085"},{"key":"10.1016\/j.cam.2014.12.044_br000090","series-title":"Multigrid Methods","first-page":"1","article-title":"Multigrid methods: fundamental algorithms, model problem analysis and applications","volume":"vol. 960","author":"St\u00fcben","year":"1982"},{"year":"2001","series-title":"Multigrid","author":"Trottenberg","key":"10.1016\/j.cam.2014.12.044_br000095"},{"year":"1985","series-title":"Multi-grid Methods and Applications. Vol. 4","author":"Hackbusch","key":"10.1016\/j.cam.2014.12.044_br000100"},{"issue":"6","key":"10.1016\/j.cam.2014.12.044_br000105","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1109\/83.388081","article-title":"Multiresolution tomographic reconstruction using wavelets","volume":"4","author":"Delaney","year":"1995","journal-title":"IEEE Trans. Image Process."},{"issue":"1","key":"10.1016\/j.cam.2014.12.044_br000110","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1109\/42.481444","article-title":"A wavelet-based method for multiscale tomographic reconstruction","volume":"15","author":"Bhatia","year":"1996","journal-title":"IEEE Trans. Med. Imaging"},{"issue":"4","key":"10.1016\/j.cam.2014.12.044_br000115","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1007\/BF01462238","article-title":"The Hierarchical basis multigrid method","volume":"52","author":"Bank","year":"1988","journal-title":"Numer. Math."},{"key":"10.1016\/j.cam.2014.12.044_br000120","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0962492900002610","article-title":"Hierarchical bases and the finite element method","volume":"5","author":"Bank","year":"1996","journal-title":"Acta Numer."},{"issue":"3","key":"10.1016\/j.cam.2014.12.044_br000125","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1109\/TMI.1982.4307572","article-title":"An improved algorithm for reprojecting rays through pixel images","volume":"1","author":"Joseph","year":"1982","journal-title":"IEEE Trans. Med. Imaging"},{"year":"1986","series-title":"The Mathematics of Computerized Tomography","author":"Natterer","key":"10.1016\/j.cam.2014.12.044_br000130"},{"year":"2001","series-title":"Principles of Computerized Tomographic Imaging, Vol. 33","author":"Kak","key":"10.1016\/j.cam.2014.12.044_br000135"},{"issue":"2","key":"10.1016\/j.cam.2014.12.044_br000140","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1137\/0913035","article-title":"Bi-CGStab: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems","volume":"13","author":"Van der Vorst","year":"1992","journal-title":"SIAM J. Sci. Stat. Comput."},{"issue":"2","key":"10.1016\/j.cam.2014.12.044_br000145","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1134\/S1995423912020127","article-title":"Two-level preconditioned Krylov subspace methods for the solution of three-dimensional heterogeneous Helmholtz problems in seismics","volume":"5","author":"Calandra","year":"2012","journal-title":"Numer. Anal. Appl."},{"issue":"2","key":"10.1016\/j.cam.2014.12.044_br000150","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1002\/nla.1806","article-title":"Analyzing the wave number dependency of the convergence rate of a multigrid preconditioned Krylov method for the Helmholtz equation with an absorbing layer","volume":"19","author":"Reps","year":"2012","journal-title":"Numer. Linear Algebra Appl."},{"issue":"4","key":"10.1016\/j.cam.2014.12.044_br000155","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1002\/nla.1881","article-title":"Local Fourier analysis of the complex shifted Laplacian preconditioner for Helmholtz problems","volume":"20","author":"Cools","year":"2013","journal-title":"Numer. Linear Algebra Appl."},{"issue":"3","key":"10.1016\/j.cam.2014.12.044_br000160","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/BF01456326","article-title":"Zur theorie der orthogonalen funktionensysteme","volume":"69","author":"Haar","year":"1910","journal-title":"Math. Ann."},{"issue":"7","key":"10.1016\/j.cam.2014.12.044_br000165","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1002\/cpa.3160410705","article-title":"Orthonormal bases of compactly supported wavelets","volume":"41","author":"Daubechies","year":"1988","journal-title":"Comm. Pure Appl. Math."},{"issue":"6","key":"10.1016\/j.cam.2014.12.044_br000170","doi-asserted-by":"crossref","first-page":"596","DOI":"10.1109\/TMI.2002.800607","article-title":"Krylov subspace iterative techniques: on the detection of brain activity with electrical impedance tomography","volume":"21","author":"Polydorides","year":"2002","journal-title":"IEEE Trans. Med. Imaging"},{"issue":"4","key":"10.1016\/j.cam.2014.12.044_br000175","doi-asserted-by":"crossref","first-page":"582","DOI":"10.1137\/S1064827599353014","article-title":"Fourier analysis of GMRES(m) preconditioned by multigrid","volume":"22","author":"Wienands","year":"2000","journal-title":"SIAM J. Sci. Comput."},{"year":"1995","series-title":"Numerical Methods for the Solution of Ill-Posed Problems. Vol. 328","author":"Tikhonov","key":"10.1016\/j.cam.2014.12.044_br000180"},{"issue":"1","key":"10.1016\/j.cam.2014.12.044_br000185","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1137\/S0895479897326432","article-title":"Tikhonov regularization and total least squares","volume":"21","author":"Golub","year":"1999","journal-title":"SIAM J. Matrix Anal. Appl."},{"year":"2010","series-title":"Discrete Inverse Problems: Insight and Algorithms. Vol. 7","author":"Hansen","key":"10.1016\/j.cam.2014.12.044_br000190"},{"year":"1996","series-title":"Regularization of Inverse Problems. Vol. 375","author":"Engl","key":"10.1016\/j.cam.2014.12.044_br000195"},{"year":"2012","series-title":"Linear and Nonlinear Inverse Problems with Practical Applications. Vol. 10","author":"Siltanen","key":"10.1016\/j.cam.2014.12.044_br000200"}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042715000096?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042715000096?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T10:57:04Z","timestamp":1759834624000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042715000096"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,8]]},"references-count":40,"alternative-id":["S0377042715000096"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2014.12.044","relation":{},"ISSN":["0377-0427"],"issn-type":[{"type":"print","value":"0377-0427"}],"subject":[],"published":{"date-parts":[[2015,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A multi-level preconditioned Krylov method for the efficient solution of algebraic tomographic reconstruction problems","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational and Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cam.2014.12.044","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 2015 Elsevier B.V. Published by Elsevier B.V. All rights reserved.","name":"copyright","label":"Copyright"}]}}