Simultaneous algebraic reconstruction technique information
Algorithm in computerised tomography
Simultaneous algebraic reconstruction technique (SART) is a computerized tomography (CT) imaging algorithm useful in cases when the projection data is limited; it was proposed by Anders Andersen and Avinash Kak in 1984.[1]
It generates a good reconstruction in just one iteration and it is superior to standard algebraic reconstruction technique (ART).
As a measure of its popularity, researchers have proposed various extensions to
SART: OS-SART, FA-SART, VW-OS-SART,[2] SARTF, etc. Researchers have also studied how SART can best be implemented on different parallel processing architectures. SART and its proposed extensions are used in emission CT in nuclear medicine, dynamic CT,[3] and holographic tomography, and other reconstruction applications.[4] Convergence
of the SART algorithm was theoretically established in 2004 by Jiang and Wang.[5] Further convergence analysis was done by Yan.[6]
An application of SART to ionosphere was presented by Hobiger et al.[7] Their method does not use matrix algebra and therefore it can be implemented in a low-level programming language. Its convergence speed is significantly higher than that of classical SART. A discrete version of SART called DART was developed by Batenburg and Sijbers.[8]
^Andersen, A.; Kak, A. (1984). "Simultaneous Algebraic Reconstruction Technique (SART): A Superior Implementation of ART". Ultrasonic Imaging. 6 (1): 81–94. doi:10.1016/0161-7346(84)90008-7. PMID 6548059.
^Pan, Jinxiao; Zhou, Tie; Han, Yan; Jiang, Ming (2006). "Variable Weighted Ordered Subset Image Reconstruction Algorithm". International Journal of Biomedical Imaging. 2006: 1–7. doi:10.1155/IJBI/2006/10398. PMC 2324020. PMID 23165012.
^Zang, G.; Idoughi, R.; Tao, R.; Lubineau, G.; Wonka, P.; Heidrich, W. (2018). "Space-time Tomography for Continuously Deforming Objects". ACM Transactions on Graphics. 37 (4): 1–14. doi:10.1145/3197517.3201298. hdl:10754/628902. S2CID 5064003.
^Byrne, C. A unified treatment of some iterative algorithms in signal processing and image reconstruction. Inverse Problems 20 103 (2004)
^Jiang, M.; Wang, G. (2003). "Convergence of the simultaneous algebraic reconstruction technique (SART)". IEEE Transactions on Image Processing. 12 (8): 957–961. Bibcode:2003ITIP...12..957J. doi:10.1109/tip.2003.815295. PMID 18237969. S2CID 16267223.
image reconstruction. Inverse Problems 20 103 (2004) Jiang, M. and Ge Wang, "Convergence of the simultaneousalgebraicreconstructiontechnique (SART)"...
good geometrical interpretation) it is called an algebraic error. Therefore, compared with algebraic error, we prefer to minimize a geometric error for...
formulae. Topological combinatorics concerns the use of techniques from topology and algebraic topology/combinatorial topology in combinatorics. Design...
expense, for example the multiple line-of-sight simultaneous multiplicative algebraicreconstructiontechnique (MLOS-SMART) which takes advantage of the sparsity...
of algebraic surfaces and algebraic varieties defined on number fields and their field extensions. Connes embedding problem in Von Neumann algebra theory...
and iterative algorithms for reconstruction. Currently, algorithms such as the real-space algebraicreconstructiontechnique (ART) and the fast Fourier...
sometimes synchronized to make events at points far apart appear simultaneous or near-simultaneous from a certain perspective. Timekeeping technologies such...
computational number theory and algebra. Work in this field is often distinguished by its emphasis on mathematical technique and rigor. While logical inference...
fluxomics have been described as "COBRA" methods, for constraint based reconstruction and analysis. A number of software tools and environments have been...
on arithmetic and advanced algebra for astronomical uses, they were also the first to develop negative numbers, algebraic geometry, and the usage of decimals...
notably line reconstruction and preprocessing, but these are rare. The main phases of the front end include the following: Line reconstruction converts the...
approximation and smoothness Universal differential equation — differential–algebraic equation whose solutions can approximate any continuous function Fekete...
be algebraic numbers. If the circle could be squared using only compass and straightedge, then π {\displaystyle \pi } would have to be an algebraic number...
sequence comparison and reconstruction of ancestral genome sequences. Zhang L. 1991. Conjugacy in special monoids. Journal of Algebra 143: 487-497. Ma B,...
(1997). Linear Algebra, Geodesy, and GPS. Wellesley-Cambridge Press. pp. 507–508. ISBN 978-0961408862. Lange, Antti (2001). "Simultaneous Statistical Calibration...
LORAN. Later mathematicians introduced algebraic methods, which transform a geometric problem into algebraic equations. These methods were simplified...
algorithm to merge the two arrays Cliques Bron–Kerbosch algorithm: a technique for finding maximal cliques in an undirected graph MaxCliqueDyn maximum...
manner more closely resembling Hegel's philosophy. Lacan often used an algebraic symbology for his concepts: the big other (l'Autre) is designated A, and...
are kept at the National Archaeological Museum, Athens, along with reconstructions and replicas, to demonstrate how it may have looked and worked. In...
this is not the only technique available: the original EMI scanner solved the tomographic reconstruction problem by linear algebra, but this approach was...
inducing a different order of operations. For example: in the usual order of algebraic operations, 4 × 3 + 2 equals 14, since the multiplication is done before...
Global Information