Implementation of the computer tomography parallel algorithms with the incomplete set of data

Computer tomography has a wide field of applicability; however, most of its applications assume that the data, obtained from the scans of the examined object, satisfy the expectations regarding their amount and quality. Unfortunately, sometimes such expected data cannot be achieved. Then we deal wit...

Full description

Saved in:

Bibliographic Details
Published in:	PeerJ. Computer science Vol. 7; p. e339
Main Author:	Pleszczynski, Mariusz
Format:	Journal Article
Language:	English
Published:	United States PeerJ. Ltd 24.02.2021 PeerJ, Inc PeerJ Inc
Subjects:	Algebra Algorithms Analysis Artificial Intelligence Big Data Coal Computed tomography Computer Aided Design Computer tomography Computer Vision Energy Incomplete set of data Linear equations Optimization Theory and Computation Parallel algorithms Reconstruction Scientific Computing and Simulation Signal and data processing Tomography Big Data Incomplete set of data Computer tomography Parallel algorithms Signal and data processing
ISSN:	2376-5992, 2376-5992
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	Computer tomography has a wide field of applicability; however, most of its applications assume that the data, obtained from the scans of the examined object, satisfy the expectations regarding their amount and quality. Unfortunately, sometimes such expected data cannot be achieved. Then we deal with the incomplete set of data. In the paper we consider an unusual case of such situation, which may occur when the access to the examined object is difficult. The previous research, conducted by the author, showed that the CT algorithms can be used successfully in this case as well, but the time of reconstruction is problematic. One of possibilities to reduce the time of reconstruction consists in executing the parallel calculations. In the analyzed approach the system of linear equations is divided into blocks, such that each block is operated by a different thread. Such investigations were performed only theoretically till now. In the current paper the usefulness of the parallel-block approach, proposed by the author, is examined. The conducted research has shown that also for an incomplete data set in the analyzed algorithm it is possible to select optimal values of the reconstruction parameters. We can also obtain (for a given number of pixels) a reconstruction with a given maximum error. The paper indicates the differences between the classical and the examined problem of CT. The obtained results confirm that the real implementation of the parallel algorithm is also convergent, which means it is useful.
AbstractList	Computer tomography has a wide field of applicability; however, most of its applications assume that the data, obtained from the scans of the examined object, satisfy the expectations regarding their amount and quality. Unfortunately, sometimes such expected data cannot be achieved. Then we deal with the incomplete set of data. In the paper we consider an unusual case of such situation, which may occur when the access to the examined object is difficult. The previous research, conducted by the author, showed that the CT algorithms can be used successfully in this case as well, but the time of reconstruction is problematic. One of possibilities to reduce the time of reconstruction consists in executing the parallel calculations. In the analyzed approach the system of linear equations is divided into blocks, such that each block is operated by a different thread. Such investigations were performed only theoretically till now. In the current paper the usefulness of the parallel-block approach, proposed by the author, is examined. The conducted research has shown that also for an incomplete data set in the analyzed algorithm it is possible to select optimal values of the reconstruction parameters. We can also obtain (for a given number of pixels) a reconstruction with a given maximum error. The paper indicates the differences between the classical and the examined problem of CT. The obtained results confirm that the real implementation of the parallel algorithm is also convergent, which means it is useful. Computer tomography has a wide field of applicability; however, most of its applications assume that the data, obtained from the scans of the examined object, satisfy the expectations regarding their amount and quality. Unfortunately, sometimes such expected data cannot be achieved. Then we deal with the incomplete set of data. In the paper we consider an unusual case of such situation, which may occur when the access to the examined object is difficult. The previous research, conducted by the author, showed that the CT algorithms can be used successfully in this case as well, but the time of reconstruction is problematic. One of possibilities to reduce the time of reconstruction consists in executing the parallel calculations. In the analyzed approach the system of linear equations is divided into blocks, such that each block is operated by a different thread. Such investigations were performed only theoretically till now. In the current paper the usefulness of the parallel-block approach, proposed by the author, is examined. The conducted research has shown that also for an incomplete data set in the analyzed algorithm it is possible to select optimal values of the reconstruction parameters. We can also obtain (for a given number of pixels) a reconstruction with a given maximum error. The paper indicates the differences between the classical and the examined problem of CT. The obtained results confirm that the real implementation of the parallel algorithm is also convergent, which means it is useful.Computer tomography has a wide field of applicability; however, most of its applications assume that the data, obtained from the scans of the examined object, satisfy the expectations regarding their amount and quality. Unfortunately, sometimes such expected data cannot be achieved. Then we deal with the incomplete set of data. In the paper we consider an unusual case of such situation, which may occur when the access to the examined object is difficult. The previous research, conducted by the author, showed that the CT algorithms can be used successfully in this case as well, but the time of reconstruction is problematic. One of possibilities to reduce the time of reconstruction consists in executing the parallel calculations. In the analyzed approach the system of linear equations is divided into blocks, such that each block is operated by a different thread. Such investigations were performed only theoretically till now. In the current paper the usefulness of the parallel-block approach, proposed by the author, is examined. The conducted research has shown that also for an incomplete data set in the analyzed algorithm it is possible to select optimal values of the reconstruction parameters. We can also obtain (for a given number of pixels) a reconstruction with a given maximum error. The paper indicates the differences between the classical and the examined problem of CT. The obtained results confirm that the real implementation of the parallel algorithm is also convergent, which means it is useful.
ArticleNumber	e339
Audience	Academic
Author	Pleszczyński, Mariusz
Author_xml	– sequence: 1 fullname: Pleszczynski, Mariusz
BackLink	https://www.ncbi.nlm.nih.gov/pubmed/33816990$$D View this record in MEDLINE/PubMed
BookMark	eNptkktv1DAUhSNUREvpjjWKxAYkZoidh-0NUlUVGKkSEo8lsm6c64xHThxsB9p_j2emlE7VZGHr5jvH8dF5nh2NbsQse0mKJWOEvZ8Q_WahwrIsxZPshJasWdRC0KN7--PsLIRNURSkJukRz7LjsuSkEaI4yX6uhsnigGOEaNyYO53HNebKDdMc0efRDa73MK1v8gk8WIs2B9s7b-J6CPmftOwEZtxKLEbMA8atTQcRXmRPNdiAZ7frafbj4-X3i8-Lqy-fVhfnVwtVMxEXihJGO1GKutKEtB3htGsFUAE1lMg4VlooogmoosKupqC15m1VMdZyLIUqT7PV3rdzsJGTNwP4G-nAyN3A-V6Cj0ZZlE1FaaUK3mpFK1YxaKHtdNcWJaOADSSvD3uvaW4H7FSKJt37wPTwy2jWsne_JRO1aCqRDN7cGnj3a8YQ5WCCQmthRDcHSeuCc9HUgiX09QN042Y_pqgkrQRlvCkI-U_1kC5gRu3SuWprKs-bmnJWMs4TtXyESm-Hg1GpNtqk-YHg7YEgMRGvYw9zCHL17esh--p-KHdp_CtSAt7tAeVdCB71HUIKua2q3FVVqpA024zoA1yZfQPTTxv7uOgv-Z3uvA
CitedBy_id	crossref_primary_10_3390_asi8020031 crossref_primary_10_3390_s22197297 crossref_primary_10_62486_latia2025304 crossref_primary_10_1088_1361_6420_ad5583 crossref_primary_10_3390_pr10030462 crossref_primary_10_3390_sym14112256 crossref_primary_10_3390_e27050534 crossref_primary_10_1016_j_apradiso_2022_110510 crossref_primary_10_3390_s23063214
Cites_doi	10.1088/0266-5611/25/11/115011 10.1177/016173468400600107 10.1007/BF01580425 10.1007/978-3-663-01409-6 10.1007/BF01436376 10.1109/TMI.2003.812253 10.3390/en13153774 10.1137/130920642 10.1109/42.845179 10.1016/j.jpdc.2015.12.002 10.1016/0022-5193(72)90180-4 10.1137/050639399 10.1088/0031-9155/41/9/012 10.1016/j.cam.2017.08.015 10.1016/S1063-5203(03)00030-7 10.1007/s10665-014-9699-0 10.3390/app10124296 10.1109/PROC.1983.12597 10.1007/BF01215050 10.1117/12.60852 10.1109/42.20361 10.1007/BF02242277 10.1137/18M1166407 10.1137/0515047 10.3390/a13050129 10.3390/rs12142306 10.1016/0022-5193(70)90109-8 10.1137/040609458 10.3390/medicina56080373
ContentType	Journal Article
Copyright	2021 Pleszczyński. COPYRIGHT 2021 PeerJ. Ltd. 2021 Pleszczyński. This is an open access article distributed under the terms of the Creative Commons Attribution License: https://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Computer Science) and either DOI or URL of the article must be cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. 2021 Pleszczyński 2021 Pleszczyński
Copyright_xml	– notice: 2021 Pleszczyński. – notice: COPYRIGHT 2021 PeerJ. Ltd. – notice: 2021 Pleszczyński. This is an open access article distributed under the terms of the Creative Commons Attribution License: https://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Computer Science) and either DOI or URL of the article must be cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. – notice: 2021 Pleszczyński 2021 Pleszczyński
DBID	AAYXX CITATION NPM ISR 3V. 7XB 8AL 8FE 8FG 8FK ABUWG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO GNUQQ HCIFZ JQ2 K7- M0N P5Z P62 PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PRINS Q9U 7X8 5PM DOA
DOI	10.7717/peerj-cs.339
DatabaseName	CrossRef PubMed Gale In Context: Science ProQuest Central (Corporate) ProQuest Central (purchase pre-March 2016) Computing Database (Alumni Edition) ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central Technology Collection ProQuest One Community College ProQuest Central Korea ProQuest Central Student SciTech Premium Collection ProQuest Computer Science Collection Computer Science Database Computing Database ProQuest advanced technologies & aerospace journals ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic (New) Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China ProQuest Central Basic MEDLINE - Academic PubMed Central (Full Participant titles) DOAJ Directory of Open Access Journals
DatabaseTitle	CrossRef PubMed Publicly Available Content Database Computer Science Database ProQuest Central Student Technology Collection ProQuest One Academic Middle East (New) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Central Korea ProQuest Central (New) Advanced Technologies & Aerospace Collection ProQuest Computing ProQuest Central Basic ProQuest Computing (Alumni Edition) ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection Advanced Technologies & Aerospace Database ProQuest One Academic UKI Edition ProQuest One Academic ProQuest One Academic (New) ProQuest Central (Alumni) MEDLINE - Academic
DatabaseTitleList	CrossRef PubMed MEDLINE - Academic Publicly Available Content Database
Database_xml	– sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website – sequence: 2 dbid: NPM name: PubMed url: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed sourceTypes: Index Database – sequence: 3 dbid: PIMPY name: Publicly Available Content Database url: http://search.proquest.com/publiccontent sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Computer Science
EISSN	2376-5992
ExternalDocumentID	oai_doaj_org_article_64224c08bfc24747ababdfdb0372ae6a PMC7959649 A652873788 33816990 10_7717_peerj_cs_339
Genre	Journal Article
GroupedDBID	53G 5VS 8FE 8FG AAFWJ AAYXX ABUWG ADBBV AFFHD AFKRA AFPKN ALMA_UNASSIGNED_HOLDINGS ARAPS AZQEC BCNDV BENPR BGLVJ BPHCQ CCPQU CITATION DWQXO FRP GNUQQ GROUPED_DOAJ H13 HCIFZ IAO ICD IEA ISR ITC K6V K7- M~E OK1 P62 PHGZM PHGZT PIMPY PQGLB PQQKQ PROAC RPM 3V. ARCSS M0N NPM 7XB 8AL 8FK JQ2 PKEHL PQEST PQUKI PRINS Q9U 7X8 PUEGO 5PM
ID	FETCH-LOGICAL-c579t-c2172d93954f11bd182db9a29a5a3e78e4f9c1f1ac04ed52afff8b4477b8e39c3
IEDL.DBID	K7-
ISICitedReferencesCount	10
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000621362800001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	2376-5992
IngestDate	Fri Oct 03 12:53:38 EDT 2025 Tue Nov 04 02:01:22 EST 2025 Thu Sep 04 16:00:31 EDT 2025 Thu Nov 20 10:41:39 EST 2025 Tue Nov 11 10:26:54 EST 2025 Tue Nov 04 17:20:10 EST 2025 Thu Nov 13 15:08:23 EST 2025 Thu Jan 02 22:57:15 EST 2025 Tue Nov 18 19:56:20 EST 2025 Sat Nov 29 02:15:13 EST 2025
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Keywords	Big Data Incomplete set of data Computer tomography Parallel algorithms Signal and data processing
Language	English
License	https://creativecommons.org/licenses/by/4.0 2021 Pleszczyński. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Computer Science) and either DOI or URL of the article must be cited.
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c579t-c2172d93954f11bd182db9a29a5a3e78e4f9c1f1ac04ed52afff8b4477b8e39c3
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23
OpenAccessLink	https://www.proquest.com/docview/2492786011?pq-origsite=%requestingapplication%
PMID	33816990
PQID	2492786011
PQPubID	2045934
PageCount	e339
ParticipantIDs	doaj_primary_oai_doaj_org_article_64224c08bfc24747ababdfdb0372ae6a pubmedcentral_primary_oai_pubmedcentral_nih_gov_7959649 proquest_miscellaneous_2508896597 proquest_journals_2492786011 gale_infotracmisc_A652873788 gale_infotracacademiconefile_A652873788 gale_incontextgauss_ISR_A652873788 pubmed_primary_33816990 crossref_primary_10_7717_peerj_cs_339 crossref_citationtrail_10_7717_peerj_cs_339
PublicationCentury	2000
PublicationDate	2021-02-24
PublicationDateYYYYMMDD	2021-02-24
PublicationDate_xml	– month: 02 year: 2021 text: 2021-02-24 day: 24
PublicationDecade	2020
PublicationPlace	United States
PublicationPlace_xml	– name: United States – name: San Diego – name: San Diego, USA
PublicationTitle	PeerJ. Computer science
PublicationTitleAlternate	PeerJ Comput Sci
PublicationYear	2021
Publisher	PeerJ. Ltd PeerJ, Inc PeerJ Inc
Publisher_xml	– name: PeerJ. Ltd – name: PeerJ, Inc – name: PeerJ Inc
References	Gilbert (10.7717/peerj-cs.339/ref-9) 1972; 36 Gordon (10.7717/peerj-cs.339/ref-12) 1970; 29 Hetmaniok (10.7717/peerj-cs.339/ref-15) 2017 Louis (10.7717/peerj-cs.339/ref-22) 1984b; 15 Radon (10.7717/peerj-cs.339/ref-25) 1917; 69 Lewitt (10.7717/peerj-cs.339/ref-20) 1983; 71 Yao (10.7717/peerj-cs.339/ref-32) 2020; 12 Andersen (10.7717/peerj-cs.339/ref-1) 1989; 8 Hounsfield (10.7717/peerj-cs.339/ref-16) 1972 Tanabe (10.7717/peerj-cs.339/ref-27) 1971; 17 Andersen (10.7717/peerj-cs.339/ref-2) 1984; 6 Kamath (10.7717/peerj-cs.339/ref-19) 2016; 89 Waldén (10.7717/peerj-cs.339/ref-31) 2000; 19 Censor (10.7717/peerj-cs.339/ref-4) 2008; 30 Jiang (10.7717/peerj-cs.339/ref-17) 2003; 22 Gordon (10.7717/peerj-cs.339/ref-11) 2005; 27 Torun (10.7717/peerj-cs.339/ref-28) 2018; 6 Donegani (10.7717/peerj-cs.339/ref-6) 2020; 56 Drummond (10.7717/peerj-cs.339/ref-7) 2015; 93 Elfving (10.7717/peerj-cs.339/ref-8) 2009; 25 Herman (10.7717/peerj-cs.339/ref-14) 1975; 8 Gong (10.7717/peerj-cs.339/ref-10) 2020; 13 Zhang (10.7717/peerj-cs.339/ref-33) 2018; 340 Malczewski (10.7717/peerj-cs.339/ref-23) 2020; 13 Kaczmarz (10.7717/peerj-cs.339/ref-18) 1937; 15 Sørensen (10.7717/peerj-cs.339/ref-26) 2014; 36 Guan (10.7717/peerj-cs.339/ref-13) 1996; 41 Cozzolino (10.7717/peerj-cs.339/ref-5) 2020; 10 Natterer (10.7717/peerj-cs.339/ref-24) 1986 Verhoeven (10.7717/peerj-cs.339/ref-30) 1993; 32 Averbuch (10.7717/peerj-cs.339/ref-3) 2003; 15 Louis (10.7717/peerj-cs.339/ref-21) 1984a; 185 Trummer (10.7717/peerj-cs.339/ref-29) 1984; 33
References_xml	– volume: 25 start-page: 115011 issue: 11 year: 2009 ident: 10.7717/peerj-cs.339/ref-8 article-title: Properties of a class of block-iterative methods publication-title: Inverse Problems doi: 10.1088/0266-5611/25/11/115011 – volume: 6 start-page: 81 issue: 1 year: 1984 ident: 10.7717/peerj-cs.339/ref-2 article-title: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the art algorithm publication-title: Ultrasonic Imaging doi: 10.1177/016173468400600107 – volume: 8 start-page: 1 issue: 1 year: 1975 ident: 10.7717/peerj-cs.339/ref-14 article-title: A relaxation method for reconstructing objects from noisy x-rays publication-title: Mathematical Programming doi: 10.1007/BF01580425 – volume: 69 start-page: 262 year: 1917 ident: 10.7717/peerj-cs.339/ref-25 article-title: Über die bestimmung von funktionen durch ihre integalwerte längs gewisser mannigfaltigkeiten publication-title: Berichte Sächsische Akademie der Wissenschaften – volume-title: The mathematics of computerized tomography year: 1986 ident: 10.7717/peerj-cs.339/ref-24 doi: 10.1007/978-3-663-01409-6 – volume: 17 start-page: 203 issue: 3 year: 1971 ident: 10.7717/peerj-cs.339/ref-27 article-title: Projection method for solving a singular system of linear equations and its applications publication-title: Numerische Mathematik doi: 10.1007/BF01436376 – volume: 22 start-page: 569 issue: 5 year: 2003 ident: 10.7717/peerj-cs.339/ref-17 article-title: Convergence studies on iterative algorithms for image reconstruction publication-title: IEEE Transactions on Medical Imaging doi: 10.1109/TMI.2003.812253 – volume: 13 start-page: 3774 issue: 15 year: 2020 ident: 10.7717/peerj-cs.339/ref-10 article-title: Geometrical and topological analysis of pore space in sandstones based on x-ray computed tomography publication-title: Energies doi: 10.3390/en13153774 – volume: 36 start-page: 524 issue: 5 year: 2014 ident: 10.7717/peerj-cs.339/ref-26 article-title: Multicore performance of block algebraic iterative reconstruction methods publication-title: SIAM Journal on Scientific Computing doi: 10.1137/130920642 – volume: 19 start-page: 211 issue: 3 year: 2000 ident: 10.7717/peerj-cs.339/ref-31 article-title: Analysis of the direct Fourier method for computer tomography publication-title: IEEE Transactions in Medical Imaging doi: 10.1109/42.845179 – start-page: 39 volume-title: Selected Problems on Experimental Mathematics year: 2017 ident: 10.7717/peerj-cs.339/ref-15 article-title: Examination of stability of the computer tomography algorithms in case of the incomplete information for the objects with non-transparent elements – volume: 89 start-page: 50 issue: 3–4 year: 2016 ident: 10.7717/peerj-cs.339/ref-19 article-title: Distributed travel-time seismic tomography in large-scale sensor networks publication-title: Journal of Parallel and Distributed Computing doi: 10.1016/j.jpdc.2015.12.002 – volume: 36 start-page: 105 issue: 1 year: 1972 ident: 10.7717/peerj-cs.339/ref-9 article-title: Iterative methods for the three-dimensional reconstruction of an object from projections publication-title: Journal of Theoretical Biology doi: 10.1016/0022-5193(72)90180-4 – volume: 30 start-page: 473 issue: 1 year: 2008 ident: 10.7717/peerj-cs.339/ref-4 article-title: On diagonally relaxed orthogonal projection methods publication-title: SIAM Journal on Scientific Computing doi: 10.1137/050639399 – volume: 41 start-page: 1727 issue: 9 year: 1996 ident: 10.7717/peerj-cs.339/ref-13 article-title: Computed tomography using algebraic reconstruction techniques with different projection access schemes: a comparison study under practical situation publication-title: Physics in Medicine and Biology doi: 10.1088/0031-9155/41/9/012 – volume: 340 start-page: 731 issue: 2 year: 2018 ident: 10.7717/peerj-cs.339/ref-33 article-title: Block row projection method based on m-matrix splitting publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/j.cam.2017.08.015 – volume: 15 start-page: 33 issue: 1 year: 2003 ident: 10.7717/peerj-cs.339/ref-3 article-title: 3D Fourier based discrete radon transform publication-title: Applied and Computational Harmonic Analysis doi: 10.1016/S1063-5203(03)00030-7 – volume: 93 start-page: 21 issue: 1 year: 2015 ident: 10.7717/peerj-cs.339/ref-7 article-title: Partitioning strategies for the block cimmino algorithm publication-title: Journal of Engineering Mathematics doi: 10.1007/s10665-014-9699-0 – volume: 10 start-page: 4296 issue: 12 year: 2020 ident: 10.7717/peerj-cs.339/ref-5 article-title: Non-destructive techniques for building evaluation in urban areas: the case study of the redesigning project of Eleftheria square (Nicosia, Cyprus) publication-title: Applied Sciences doi: 10.3390/app10124296 – volume: 71 start-page: 390 issue: 3 year: 1983 ident: 10.7717/peerj-cs.339/ref-20 article-title: Reconstruction algorithms: transform methods publication-title: Proceedings of the IEEE doi: 10.1109/PROC.1983.12597 – volume: 185 start-page: 429 issue: 3 year: 1984a ident: 10.7717/peerj-cs.339/ref-21 article-title: Nonuniqueness in inverse radon problems: the frequency distribution of the ghosts publication-title: Mathematische Zeitschrift doi: 10.1007/BF01215050 – volume: 32 start-page: 410 issue: 2 year: 1993 ident: 10.7717/peerj-cs.339/ref-30 article-title: Multiplicative algebraic computed tomography algorithms for the reconstruction of multidirectional interferometric data publication-title: Optical Engineering doi: 10.1117/12.60852 – volume: 8 start-page: 50 issue: 1 year: 1989 ident: 10.7717/peerj-cs.339/ref-1 article-title: Algebraic reconstruction in CT from limited views publication-title: IEEE Transactions in Medical Imaging doi: 10.1109/42.20361 – volume: 33 start-page: 349 issue: 3–4 year: 1984 ident: 10.7717/peerj-cs.339/ref-29 article-title: A note on the art of relaxation publication-title: Computing doi: 10.1007/BF02242277 – year: 1972 ident: 10.7717/peerj-cs.339/ref-16 article-title: A method of and apparatus for examination of a body by radiation such as x-ray or gamma radiation – volume: 6 start-page: 827 issue: 6 year: 2018 ident: 10.7717/peerj-cs.339/ref-28 article-title: A novel partitioning method for accelerating the block cimmino algorithm publication-title: SIAM Journal on Scientific Computing doi: 10.1137/18M1166407 – volume: 15 start-page: 2346 issue: 3 year: 1984b ident: 10.7717/peerj-cs.339/ref-22 article-title: Orthogonal function series expansions and the null space of the radon transform publication-title: SIAM Journal of Mathematical Analysis doi: 10.1137/0515047 – volume: 13 start-page: 129 issue: 5 year: 2020 ident: 10.7717/peerj-cs.339/ref-23 article-title: Image resolution enhancement of highly compressively sensed CT/PET signals publication-title: Algorithms doi: 10.3390/a13050129 – volume: 12 start-page: 2306 issue: 14 year: 2020 ident: 10.7717/peerj-cs.339/ref-32 article-title: A new GNSS-derived water vapor tomography method based on optimized voxel for large GNSS network publication-title: Remote Sens doi: 10.3390/rs12142306 – volume: 29 start-page: 471 issue: 3 year: 1970 ident: 10.7717/peerj-cs.339/ref-12 article-title: Algebraic reconstruction techniques (art) for three-dimensional electron microscopy and x-ray photography publication-title: Journal of Theoretical Biology doi: 10.1016/0022-5193(70)90109-8 – volume: 27 start-page: 1092 issue: 3 year: 2005 ident: 10.7717/peerj-cs.339/ref-11 article-title: Component-averaged row projections: a robust, block-parallel scheme for sparse linear systems publication-title: SIAM Journal on Scientific Computing doi: 10.1137/040609458 – volume: 15 start-page: 355 year: 1937 ident: 10.7717/peerj-cs.339/ref-18 article-title: Angenäherte auflösung von systemen lineare gleichungen publication-title: International Academy of Political Science Letter – volume: 56 start-page: 373 issue: 8 year: 2020 ident: 10.7717/peerj-cs.339/ref-6 article-title: Positron emission tomography-based response to target and immunotherapies in oncology publication-title: Medicina doi: 10.3390/medicina56080373
SSID	ssj0001511119
Score	2.210476
Snippet	Computer tomography has a wide field of applicability; however, most of its applications assume that the data, obtained from the scans of the examined object,...
SourceID	doaj pubmedcentral proquest gale pubmed crossref
SourceType	Open Website Open Access Repository Aggregation Database Index Database Enrichment Source
StartPage	e339
SubjectTerms	Algebra Algorithms Analysis Artificial Intelligence Big Data Coal Computed tomography Computer Aided Design Computer tomography Computer Vision Energy Incomplete set of data Linear equations Optimization Theory and Computation Parallel algorithms Reconstruction Scientific Computing and Simulation Signal and data processing Tomography
SummonAdditionalLinks	– databaseName: DOAJ Directory of Open Access Journals dbid: DOA link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1bi9UwEA6y-OCL90t1lSiKD1K3adOmeVzFRUEW8QL7IiHX3bP0tMtpj7_fmTbn0CLii6_NJKQzk-SbdvINIS9rOEUBxhYpQCKfcqFZWjvmIFTRVWasF2KqWvJZnJ7WZ2fyy6zUF-aETfTAk-KOAB_n3Ga1CTbngH210cYFZ7JC5NpXIzQC1DMLpqb7wbgVyCnTXUDIcnTl_eYytf3bAuuCz86gkar_zw15diItsyVnx8_JbXIz4kZ6PM33Drnm27vk1q4mA41L9B75OdL9ruONopZ2gQLEo3YnOHTrSFJNkfW7aXxDdXPebVbDxbqn-Fl27ICkDTjS4GnvBxwGc0nvkx8nH76__5jGEgqpLYUcUov1p5wsZMkDY8ZBNOGM1LnUpS68qD0P0rLAtM24d2WuQwi14VwIU_tC2uIBOWi71j8iVJfBwPbocgGG0FyazMm6cswKU7BQ5Ql5s1OqspFfHMtcNAriDDSBGk2gbK_ABAl5tZe-mng1_iL3Du2zl0E27PEB-IiKPqL-5SMJeYHWVai6FhNqzvW279Wnb1_VcVVCzIik-gl5HYVCB_O2Ot5PgLdHiqyF5OFCEhakXTbvnEjFDaFXSMwoaoh-WUKe75uxJya5tb7bggyCZSR4FAl5OPnc_r0L_MELyCEhYuGNC8UsW9rVxUgXjtXkKy4f_w9NPiE3ckzqwTv9_JAcDJutf0qu21_Dqt88G9fgbxKWPD8 priority: 102 providerName: Directory of Open Access Journals
Title	Implementation of the computer tomography parallel algorithms with the incomplete set of data
URI	https://www.ncbi.nlm.nih.gov/pubmed/33816990 https://www.proquest.com/docview/2492786011 https://www.proquest.com/docview/2508896597 https://pubmed.ncbi.nlm.nih.gov/PMC7959649 https://doaj.org/article/64224c08bfc24747ababdfdb0372ae6a
Volume	7
WOSCitedRecordID	wos000621362800001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 2376-5992 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001511119 issn: 2376-5992 databaseCode: DOA dateStart: 20150101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources customDbUrl: eissn: 2376-5992 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001511119 issn: 2376-5992 databaseCode: M~E dateStart: 20150101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 2376-5992 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001511119 issn: 2376-5992 databaseCode: K7- dateStart: 20150527 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest advanced technologies & aerospace journals customDbUrl: eissn: 2376-5992 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001511119 issn: 2376-5992 databaseCode: P5Z dateStart: 20150527 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 2376-5992 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001511119 issn: 2376-5992 databaseCode: BENPR dateStart: 20150527 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Publicly Available Content Database customDbUrl: eissn: 2376-5992 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001511119 issn: 2376-5992 databaseCode: PIMPY dateStart: 20150527 isFulltext: true titleUrlDefault: http://search.proquest.com/publiccontent providerName: ProQuest
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3db9MwELfYxgMvjG8CowoIxAMKq_Pl-AltqBMTrKoGSAUJWf7shtqkNCmP_O3cpW7XCMELL3mIz4njO5_vLuffEfK8gF0UzNgkApPIRimTNCoMNeCqyLyvtGVsVbXkAxsOi_GYj3zArfZplWud2CpqU2mMkR8ish0rwH2gb-Y_IqwahX9XfQmNHbJH45iinL9n0VWMJUOFwFf57gwcl8O5tYvvka5fJ1gdfGsnagH7_1TLW_tSN2dyaxM62f_f4d8iN735GR6t5OU2uWbLO2R_Xdoh9Cv9LvnWogbP_MGkMqxcCJZiqNeETTXzWNchgodPp3YayukE3thczOoQo7ttB8R-wCc1Nqxtg4_BlNR75PPJ4NPbd5GvxBDpjPEm0ljGyvCEZ6mjVBlwSoziMuYyk4llhU0d19RRqfupNVksnXOFSlPGVGETrpP7ZLesSvuQhDJzCrSsiZmOU5ly1Te8yA3VTCXU5XFAXq25IrSHKcdqGVMB7gryULQ8FLoWwMOAvNhQz1fwHH-hO0YGb2gQVLu9US0mwq9RAa5YnOp-oRwMDdwsqaQyzqh-wmJpcxmQZygeAqeuxLyciVzWtTj9eC6O8gxcT8TmD8hLT-QqGLeW_pgDfD0ibXUoDzqUsK51t3ktScLrlVpciVFAnm6asSfmypW2WgIN2tyIE8kC8mAltJvvTvA_MRggAWEdce5MTLelvLxoUcexKH2e8kf_HtZjciPGrB889J8ekN1msbRPyHX9s7msFz2yw8ZFj-wdD4aj814b_-i1SxauZ78GcB1lX6F9dHo2-vIbigZQTQ
linkProvider	ProQuest
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1bb9MwFLbGQIIXxp3AgICYeEBhTeLE8QNC4zKtaqkQbNJekPG1G2qT0qQg_hS_kXPSpGuE4G0PvMYnlu0cn4tz_H2EPM3Ai0IYGwcQEtmAMhkGmQkNpCoy7SltGVuylgzZaJQdH_MPG-RXexcGyypbm1gbalNoPCPfRWQ7lkH6EL6afQuQNQr_rrYUGku1GNifPyBlK1_238L33Ymi_XeHbw6ChlUg0AnjVaCRksnwmCfUhaEyEGAbxWXEZSJjyzJLHdehC6XuUWuSSDrnMkUpYyqzMdcx9HuBXKRxxhCrf8CCszOdBA0QX9bXM0iUdmfWzr8GunwRIxv5muerCQL-dANrfrBbo7nm9Pa3_rflukauNuG1v7fcD9fJhs1vkK2WusJvLNlN8rlGRZ42F69yv3A-RMK-bgWrYtpgefsIjj6Z2IkvJ2OYYXUyLX08va5fQGwL7Kmyfmkr7AZLbm-Ro3OZ5G2ymRe5vUt8mTgFXsRETEdUUq56hmepCTVTcejSyCPPWy0QuoFhRzaQiYB0DHVG1DojdClAZzyys5KeLeFH_iL3GhVqJYOg4fWDYj4WjQ0SkGpGVPcy5WBokEZKJZVxRvViFkmbSo88QXUUuHQ51h2N5aIsRf_TR7GXJpBaI_eAR541Qq6AcWvZXOOA2SOSWEdyuyMJdkt3m1vNFY3dLMWZ2nrk8aoZ38RawNwWC5DBnAJxMJlH7iw3yWreMf4HhwDLI6yzfToL023JT09qVHXGE55Sfu_fw3pELh8cvh-KYX80uE-uRFjhhAAHdJtsVvOFfUAu6e_VaTl_WJsGn3w57831G8iip4Y
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Jb9NAFB6VghAXyo6hgEFUHJBJvI7ngFChRESpoopF6gUNs6ZFjh1iB8Rf49fxnpc0FoJbD1wzzyPP5K3jN99HyNMUoiiksaEHKZHxIip8L9W-hlJFJEOpDKUNa8khnU7T42N2tEV-dXdhsK2y84m1o9aFwjPyASLb0RTKB39g27aIo4PRq8U3Dxmk8EtrR6fRqMjE_PwB5Vv5cnwA__VeEIzefnzzzmsZBjwVU1Z5CumZNAtZHFnflxqSbS2ZCJiIRWhoaiLLlG99oYaR0XEgrLWpjCJKZWpCpkKY9wK5CFE4RhubUO_sfCdGZ8SaXnsKRdNgYczyq6fKFyEyk29EwZos4M-QsBET-_2aGwFwtPM_b901crVNu939xk6uky2T3yA7HaWF23q4m-RzjZY8by9k5W5hXciQXdUJVsW8xfh2ETQ9y0zmimwGK6xO5qWLp9r1A4h5gTNVxi1NhdNgK-4t8ulcFnmbbOdFbu4SV8RWQnTRAVVBJCImh5qlifYVlaFvk8AhzzuN4KqFZ0eWkIxDmYb6w2v94arkoD8O2VtLLxpYkr_IvUblWssgmHj9Q7Gc8dY3cShBg0gNU2nh1aC8FFJIbbUchjQQJhEOeYKqyXHrctSemViVJR9_eM_3kxhKbuQkcMizVsgW8N5KtNc7YPWIMNaT3O1Jgj9T_eFOi3nrT0t-psIOebwexiexRzA3xQpksNZAfEzqkDuNwazXHeL3cUi8HEJ7ptTbmP5IfnpSo61TFrMkYvf-_VqPyGWwKX44nk7ukysBNj4h7kG0S7ar5co8IJfU9-q0XD6svYRLvpy3bf0GpQ-wQA
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Implementation+of+the+computer+tomography+parallel+algorithms+with+the+incomplete+set+of+data&rft.jtitle=PeerJ.+Computer+science&rft.au=Pleszczy%C5%84ski%2C+Mariusz&rft.date=2021-02-24&rft.pub=PeerJ%2C+Inc&rft.eissn=2376-5992&rft_id=info:doi/10.7717%2Fpeerj-cs.339&rft.externalDBID=HAS_PDF_LINK
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2376-5992&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2376-5992&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2376-5992&client=summon