{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,22]],"date-time":"2025-02-22T00:45:19Z","timestamp":1740185119454,"version":"3.37.3"},"reference-count":42,"publisher":"Oxford University Press (OUP)","issue":"11","license":[{"start":{"date-parts":[[2019,10,16]],"date-time":"2019-10-16T00:00:00Z","timestamp":1571184000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2017YFE0103900","2017YFA0504702"],"award-info":[{"award-number":["2017YFE0103900","2017YFA0504702"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research","award":["FCC\/1\/1976-18-01","FCC\/1\/1976-23-01","FCC\/1\/1976-25-01","FCC\/1\/1976-26-01","FCS\/1\/4102-02-01","FCS\/1\/4102-02-01"],"award-info":[{"award-number":["FCC\/1\/1976-18-01","FCC\/1\/1976-23-01","FCC\/1\/1976-25-01","FCC\/1\/1976-26-01","FCS\/1\/4102-02-01","FCS\/1\/4102-02-01"]}]},{"name":"NSFC projects Grant","award":["U1611263","U1611261","61932018","61672493"],"award-info":[{"award-number":["U1611263","U1611261","61932018","61672493"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,7,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:sec>\n                  <jats:title>Motivation<\/jats:title>\n                  <jats:p>Electron tomography (ET) offers a unique capacity to image biological structures in situ. However, the resolution of ET reconstructed tomograms is not comparable to that of the single-particle cryo-EM. If many copies of the object of interest are present in the tomograms, their structures can be reconstructed in the tomogram, picked, aligned and averaged to increase the signal-to-noise ratio and improve the resolution, which is known as the subtomogram averaging. To date, the resolution improvement of the subtomogram averaging is still limited because each reconstructed subtomogram is of low reconstruction quality due to the missing wedge issue.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Results<\/jats:title>\n                  <jats:p>In this article, we propose a novel computational model, the constrained reconstruction model (CRM), to better recover the information from the multiple subtomograms and compensate for the missing wedge issue in each of them. CRM is supposed to produce a refined reconstruction in the final turn of subtomogram averaging after alignment, instead of directly taking the average. We first formulate the averaging method and our CRM as linear systems, and prove that the solution space of CRM is no larger, and in practice much smaller, than that of the averaging method. We then propose a sparse Kaczmarz algorithm to solve the formulated CRM, and further extend the solution to the simultaneous algebraic reconstruction technique (SART). Experimental results demonstrate that CRM can significantly alleviate the missing wedge issue and improve the final reconstruction quality. In addition, our model is robust to the number of images in each tilt series, the tilt range and the noise level.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Availability and implementation<\/jats:title>\n                  <jats:p>The codes of CRM-SIRT and CRM-SART are available at https:\/\/github.com\/icthrm\/CRM.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Supplementary information<\/jats:title>\n                  <jats:p>Supplementary data are available at Bioinformatics online.<\/jats:p>\n               <\/jats:sec>","DOI":"10.1093\/bioinformatics\/btz787","type":"journal-article","created":{"date-parts":[[2019,10,14]],"date-time":"2019-10-14T19:29:26Z","timestamp":1571081366000},"page":"1616-1626","source":"Crossref","is-referenced-by-count":3,"title":["A novel constrained reconstruction model towards high-resolution subtomogram averaging"],"prefix":"10.1093","volume":"37","author":[{"given":"Renmin","family":"Han","sequence":"first","affiliation":[{"name":"Computational Bioscience Research Center (CBRC), Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division , King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia"}]},{"given":"Lun","family":"Li","sequence":"additional","affiliation":[{"name":"High Performance Computer Research Center, Institute of Computing Technology , Chinese Academy of Sciences, 100190 Beijing, China"},{"name":"University of Chinese Academy of Sciences , Beijing, China"}]},{"given":"Peng","family":"Yang","sequence":"additional","affiliation":[{"name":"Computational Bioscience Research Center (CBRC), Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division , King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia"}]},{"given":"Fa","family":"Zhang","sequence":"additional","affiliation":[{"name":"High Performance Computer Research Center, Institute of Computing Technology , Chinese Academy of Sciences, 100190 Beijing, China"}]},{"given":"Xin","family":"Gao","sequence":"additional","affiliation":[{"name":"Computational Bioscience Research Center (CBRC), Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division , King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia"}]}],"member":"286","published-online":{"date-parts":[[2019,10,16]]},"reference":[{"key":"2023051709453423300_btz787-B1","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1177\/016173468400600107","article-title":"Simultaneous algebraic reconstruction technique (SART): a superior implementation of the art algorithm","volume":"6","author":"Andersen","year":"1984","journal-title":"Ultrason. Imaging"},{"key":"2023051709453423300_btz787-B2","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1109\/42.20361","article-title":"Algebraic reconstruction in CT from limited views","volume":"8","author":"Andersen","year":"1989","journal-title":"IEEE Trans. Med. Imaging"},{"key":"2023051709453423300_btz787-B3","doi-asserted-by":"crossref","first-page":"2003","DOI":"10.1016\/j.str.2012.10.016","article-title":"Protein secondary structure determination by constrained single-particle cryo-electron tomography","volume":"20","author":"Bartesaghi","year":"2012","journal-title":"Structure"},{"key":"2023051709453423300_btz787-B4","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.ejmp.2012.01.003","article-title":"Iterative reconstruction methods in X-ray CT","volume":"28","author":"Beister","year":"2012","journal-title":"Phys. Med"},{"key":"2023051709453423300_btz787-B5","doi-asserted-by":"crossref","first-page":"2054.","DOI":"10.1038\/nprot.2016.124","article-title":"Resolving macromolecular structures from electron cryo-tomography data using subtomogram averaging in RELION","volume":"11","author":"Bharat","year":"2016","journal-title":"Nat. Protoc"},{"key":"2023051709453423300_btz787-B6","doi-asserted-by":"crossref","first-page":"1743","DOI":"10.1016\/j.str.2015.06.026","article-title":"Advances in single-particle electron cryomicroscopy structure determination applied to sub-tomogram averaging","volume":"23","author":"Bharat","year":"2015","journal-title":"Structure"},{"key":"2023051709453423300_btz787-B7","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/j.sbi.2013.02.003","article-title":"Structural biology in situ: the potential of subtomogram averaging","volume":"23","author":"Briggs","year":"2013","journal-title":"Curr. Opin. Struct. Biol"},{"key":"2023051709453423300_btz787-B8","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/978-1-4757-2163-8_6","article-title":"The fidelity of 3D reconstructions from incomplete data and the use of restoration methods","author":"Carazo","year":"1992","journal-title":"Electron Tomography"},{"key":"2023051709453423300_btz787-B9","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/j.jsb.2013.12.001","article-title":"Iterative reconstruction of cryo-electron tomograms using nonuniform fast Fourier transforms","volume":"185","author":"Chen","year":"2014","journal-title":"J. Struct. Biol"},{"key":"2023051709453423300_btz787-B10","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1038\/217130a0","article-title":"Reconstruction of three dimensional structures from electron micrographs","volume":"217","author":"De Rosier","year":"1968","journal-title":"Nature"},{"key":"2023051709453423300_btz787-B11","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/j.jsb.2016.04.004","article-title":"ICON: 3D reconstruction with \u2018missing-information\u2019 restoration in biological electron tomography","volume":"195","author":"Deng","year":"2016","journal-title":"J. Struct. Biol"},{"key":"2023051709453423300_btz787-B12","doi-asserted-by":"crossref","first-page":"4729","DOI":"10.1073\/pnas.0409178102","article-title":"Retrovirus envelope protein complex structure in situ studied by cryo-electron tomography","volume":"102","author":"F\u00f6rster","year":"2005","journal-title":"Proc. Natl. Acad. Sci"},{"key":"2023051709453423300_btz787-B13","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-69008-7","volume-title":"Electron Tomography: Methods for Three-Dimensional Visualization of Structures in the Cell","author":"Frank","year":"2006"},{"key":"2023051709453423300_btz787-B14","doi-asserted-by":"crossref","first-page":"219","DOI":"10.2514\/3.6561","article-title":"Condition of finite element matrices generated from nonuniform meshes","volume":"10","author":"Fried","year":"1972","journal-title":"AIAA J"},{"key":"2023051709453423300_btz787-B15","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/s41048-017-0040-0","article-title":"The advent of structural biology in situ by single particle cryo-electron tomography","volume":"3","author":"Galaz-Montoya","year":"2017","journal-title":"Biophys. Rep"},{"key":"2023051709453423300_btz787-B16","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/0022-5193(72)90180-4","article-title":"Iterative methods for the three-dimensional reconstruction of an object from projections","volume":"36","author":"Gilbert","year":"1972","journal-title":"J. Theor. Biol"},{"key":"2023051709453423300_btz787-B17","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1016\/0022-5193(70)90109-8","article-title":"Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography","volume":"29","author":"Gordon","year":"1970","journal-title":"J. Theor. Biol"},{"key":"2023051709453423300_btz787-B18","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.jsb.2017.07.008","article-title":"Autom: a novel automatic platform for electron tomography reconstruction","volume":"199","author":"Han","year":"2017","journal-title":"J. Struct. Biol"},{"key":"2023051709453423300_btz787-B19","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1093\/bioinformatics\/bty620","article-title":"AuTom-dualx: a toolkit for fully automatic fiducial marker-based alignment of dual-axis tilt series with simultaneous reconstruction","volume":"35","author":"Han","year":"2019","journal-title":"Bioinformatics"},{"key":"2023051709453423300_btz787-B20","doi-asserted-by":"crossref","first-page":"1089","DOI":"10.1002\/mp.12102","article-title":"Estimating 4D-CBCT from prior information and extremely limited angle projections using structural PCA and weighted free-form deformation for lung radiotherapy","volume":"44","author":"Harris","year":"2017","journal-title":"Med. Phys"},{"key":"2023051709453423300_btz787-B21","doi-asserted-by":"crossref","first-page":"1437","DOI":"10.1126\/science.aai9127","article-title":"Translational termination without a stop codon","volume":"354","author":"James","year":"2016","journal-title":"Science"},{"key":"2023051709453423300_btz787-B22","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1109\/TIP.2003.815295","article-title":"Convergence of the simultaneous algebraic reconstruction technique (SART","volume":"12","author":"Jiang","year":"2003","journal-title":"IEEE Trans. Image Process"},{"key":"2023051709453423300_btz787-B23","first-page":"355","article-title":"Angen\u00e4herte aufl\u00f6sung von systemen linearer gleichungen","volume":"35","author":"Kaczmarz","year":"1937","journal-title":"Bull. Int. Acad. Polon. Sci. Lett"},{"key":"2023051709453423300_btz787-B24","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.jsb.2014.02.004","article-title":"A simple Fourier filter for suppression of the missing wedge ray artefacts in single-axis electron tomographic reconstructions","volume":"186","author":"Kovacik","year":"2014","journal-title":"J. Struct. Biol"},{"key":"2023051709453423300_btz787-B25","doi-asserted-by":"crossref","first-page":"63.","DOI":"10.1038\/nmeth.2727","article-title":"Quantifying the local resolution of cryo-EM density maps","volume":"11","author":"Kucukelbir","year":"2014","journal-title":"Nat. Methods"},{"key":"2023051709453423300_btz787-B26","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.jsb.2014.09.010","article-title":"Super-sampling SART with ordered subsets","volume":"188","author":"Kunz","year":"2014","journal-title":"J. Struct. Biol"},{"key":"2023051709453423300_btz787-B27","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1111\/jmi.12313","article-title":"Missing wedge computed tomography by iterative algorithm DIRECTT","volume":"261","author":"Kupsch","year":"2016","journal-title":"J. Microsc"},{"key":"2023051709453423300_btz787-B28","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.ultramic.2013.03.019","article-title":"Compressed sensing electron tomography","volume":"131","author":"Leary","year":"2013","journal-title":"Ultramicroscopy"},{"key":"2023051709453423300_btz787-B29","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1364\/JOSAA.21.000499","article-title":"Gridding-based direct Fourier inversion of the three-dimensional ray transform","volume":"21","author":"Penczek","year":"2004","journal-title":"J. Opt. Soc. Am. A Opt. Image Sci. Vis"},{"key":"2023051709453423300_btz787-B30","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1097\/RLI.ob013e3181dzfeec","article-title":"Reducing abdominal CT radiation dose with adaptive statistical iterative reconstruction technique","volume":"45","author":"Prakash","year":"2010","journal-title":"Invest. Radiol"},{"key":"2023051709453423300_btz787-B31","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1016\/j.jsb.2012.09.006","article-title":"RELION: implementation of a Bayesian approach to cryo-EM structure determination","volume":"180","author":"Scheres","year":"2012","journal-title":"J. Struct. Biol"},{"key":"2023051709453423300_btz787-B32","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.jsb.2007.09.018","article-title":"Methods for aligning and for averaging 3D volumes with missing data","volume":"161","author":"Schmid","year":"2008","journal-title":"J. Struct. Biol"},{"key":"2023051709453423300_btz787-B33","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/TNS.1974.6499235","article-title":"The Fourier reconstruction of a head section","volume":"21","author":"Shepp","year":"1974","journal-title":"IEEE Trans. Nucl. Sci"},{"key":"2023051709453423300_btz787-B34","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1002\/jmri.1880080145","article-title":"Rapid tip tracking with MRI by a limited projection reconstruction technique","volume":"8","author":"Shimizu","year":"1998","journal-title":"J. Magn. Reson. Imaging"},{"key":"2023051709453423300_btz787-B35","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.jsb.2006.05.009","article-title":"EMAN2: an extensible image processing suite for electron microscopy","volume":"157","author":"Tang","year":"2007","journal-title":"J. Struct. Biol"},{"key":"2023051709453423300_btz787-B36","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.jsb.2013.05.008","article-title":"Image formation modeling in cryo-electron microscopy","volume":"183","author":"Vulovi\u0107","year":"2013","journal-title":"J. Struct. Biol"},{"key":"2023051709453423300_btz787-B37","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1118\/1.1543934","article-title":"Tomographic mammography using a limited number of low-dose cone-beam projection images","volume":"30","author":"Wu","year":"2003","journal-title":"Med. Phys"},{"key":"2023051709453423300_btz787-B38","doi-asserted-by":"crossref","first-page":"S18.","DOI":"10.1186\/1752-0509-6-S1-S18","article-title":"High precision alignment of cryo-electron subtomograms through gradient-based parallel optimization","volume":"6","author":"Xu","year":"2012","journal-title":"BMC Syst. Biol"},{"key":"2023051709453423300_btz787-B39","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/j.jsb.2012.02.014","article-title":"High-throughput subtomogram alignment and classification by Fourier space constrained fast volumetric matching","volume":"178","author":"Xu","year":"2012","journal-title":"J. Struct. Biol"},{"key":"2023051709453423300_btz787-B40","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1007\/s13238-017-0465-8","article-title":"A binding-block ion selective mechanism revealed by a Na\/K selective channel","volume":"9","author":"Yu","year":"2018","journal-title":"Protein Cell"},{"key":"2023051709453423300_btz787-B41","doi-asserted-by":"crossref","first-page":"i227","DOI":"10.1093\/bioinformatics\/bty267","article-title":"An integration of fast alignment and maximum-likelihood methods for electron subtomogram averaging and classification","volume":"34","author":"Zhao","year":"2018","journal-title":"Bioinformatics"},{"key":"2023051709453423300_btz787-B42","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1016\/j.energy.2004.09.005","article-title":"Ultrasonic computerized tomography (CT) for temperature measurements with limited projection data based on extrapolated filtered back projection (FBP) method","volume":"30","author":"Zhu","year":"2005","journal-title":"Energy"}],"container-title":["Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/bioinformatics\/advance-article-pdf\/doi\/10.1093\/bioinformatics\/btz787\/31077304\/btz787.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/37\/11\/1616\/50361165\/btz787.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/37\/11\/1616\/50361165\/btz787.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,17]],"date-time":"2023-05-17T10:29:24Z","timestamp":1684319364000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article\/37\/11\/1616\/5588412"}},"subtitle":[],"editor":[{"given":"Janet","family":"Kelso","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2019,10,16]]},"references-count":42,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2021,7,12]]}},"URL":"https:\/\/doi.org\/10.1093\/bioinformatics\/btz787","relation":{},"ISSN":["1367-4803","1367-4811"],"issn-type":[{"type":"print","value":"1367-4803"},{"type":"electronic","value":"1367-4811"}],"subject":[],"published-other":{"date-parts":[[2021,6,1]]},"published":{"date-parts":[[2019,10,16]]}}}