(45-6) 14 * << * >> * Русский * English * Содержание * Все выпуски

X-ray tomography: the way from layer-by-layer radiography to computed tomography
V.L. Arlazarov 1,2, D.P. Nikolaev 1,3, V.V. Arlazarov 1,2, M.V. Chukalina 1,3

Smart Engines Service LLC, 121205, Moscow, Russia, Nobelya str.7,

FRC "Computer Science and Control" RAS Institute for Systems Analysis,
117312, Moscow, Russia, pr. 60-letiya Oktyabrya 9

Institute for Information Transmission Problems (Kharkevich Institute) RAS,
127051, Moscow, Russia, Bolshoy Karetny per. 19, build. 1

 PDF, 1569 kB

DOI: 10.18287/2412-6179-CO-898

Страницы: 897-906.

Язык статьи: English.

The methods of X-ray computed tomography allow us to study the internal morphological structure of objects in a non-destructive way. The evolution of these methods is similar in many respects to the evolution of photography, where complex optics were replaced by mobile phone cameras, and the computers built into the phone took over the functions of high-quality image generation. X-ray tomography originated as a method of hardware non-invasive imaging of a certain internal cross-section of the human body. Today, thanks to the advanced reconstruction algorithms, a method makes it possible to reconstruct a digital 3D image of an object with a submicron resolution. In this article, we will analyze the tasks that the software part of the tomographic complex has to solve in addition to managing the process of data collection. The issues that are still considered open are also discussed. The relationship between the spatial resolution of the method, sensitivity and the radiation load is reviewed. An innovative approach to the organization of tomographic imaging, called “reconstruction with monitoring”, is described. This approach makes it possible to reduce the radiation load on the object by at least 2 – 3 times. In this work, we show that when X-ray computed tomography moves towards increasing the spatial resolution and reducing the radiation load, the software part of the method becomes increasingly important.

Ключевые слова:
computer tomography, data size, radiation load, monitored reconstruction.

This work was supported by Russian Foundation for Basic Research (Projects No.18-29-26033, 18-29-26020).

Arlazarov VL, Nikolaev DP, Arlazarov VV, Chukalina MV. X-ray tomography: the way from layer-by-layer radiography to computed tomography. Computer Optics 2021; 45(6): 897-906. DOI: 10.18287/2412-6179-CO-898.


  1. Friedland GW, Thurber BD. The birth of CT. Am J of Ro-entgenol 1996; 167(6): 1365-1370. DOI: 10.2214/ajr.167.6.8956560.
  2. Bulatov K, Chukalina M, Buzmakov A, NikolaevD, Arla-zarov V. Monitored reconstruction: Computed to-mography as an anytime algorithm. IEEE Access 2020; 8: 110759-110774. DOI: 10.1109/ACCESS.2020.3002019.
  3. Rabinovich AM. Tomography for pulmonary tuberculosis [In Russian]. Leningrad: "Medgiz" Publisher; 1963.
  4. Radon J. Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten. Berichte Sächsische Akademie der Wissenschaften Leipzig 1917; 29: 262-277.
  5. Grossman G. Tomographie I (Rontgenographische Darstellung von Korperschnitten). Fortschr a d Geb d Röntgenstr 1935; 51: 61-80.
  6. Grossman G. Tomographie II (Theoretisches über Tomographie). Fortschr a d Geb d Röntgenstr 1935; 51: 191-208.
  7. Grossman G. Praktische Voraussetzungen für die Tomographie. Fortschr a d Geb d Röntgenstr 1935; 52(H): 44.
  8. Chaoul H. Ueber die Tomographie und insbesondoreihreAnwendung in der Lungendiagnostik. Fortschr a d Geb d Röntgenstr 1935; 51: 342-356.
  9. Korenblum BI, Tetelbaum SI, Tyutin AA. About one scheme of tomography [In Russian]. Izvestiya VUZov MVO: Radiofizika 1958; 1(3): 13-19.
  10. Gustschin A. Translation: About one scheme of tomography. arXiv Preprint arXiv:2004.03750v1 2020. Source: <https://arxiv.org/abs/2004.03750>.
  11. Cormack AM. Representation of a function by its line integrals, with some radiological applications. J Appl Phys 1963; 34(9): 2722-2727. DOI: 10.1063/1.1729798.
  12. Cormack AM. Representation of a function by its line integrals, with some radiological applications. II. J Appl Phys 1964; 35(10): 2908-2913. DOI: 10.1063/1.1713127.
  13. Cormack AM. Reconstruction of densities from their projections, with applications in radiological physics. Phys Med Biol 1973; 18(2): 195-207. DOI: 10.1088/0031-9155/18/2/003.
  14. Alexander RE, Gunderman RE. EMI and the first CT scanner. J Am Coll Radiol 2010; 7(10): 778-781. DOI: 10.1016/j.jacr.2010.06.003.
  15. Mitchell W. Playing leap-frog with elephants: EMI Ltd. and the CT scanner competition in the 1970's. Ann Arbor: University of Michigan Ross Business School; 1989. Source: <http://www-2.rotman.utoronto.ca/william.mitchell/Bio/TeachingMaterials/0Cases/emi/emi_2005a.pdf>.
  16. Vanshtein BК. About finding the structure of objects by projections [In Russian]. Kristallographia 1970; 15(5): 894-902.
  17. Vanshtein BК. Three-dimensional electron microscopy of biological macromolecules. Sov Phys Usp 1973; 109(3): 455-497. DOI: 10.1070/PU1973v016n02ABEH005164.
  18. Vasilieva EYu, Maiorov A. Application of computer tomography for fuel rod control [In Russian]. Atomnaya Energia 1979; 46(6): 403-406.
  19. Rubashov IB, Timonov AA, RapkinYuI, DorofeevYuV, Pestryakov AV. Tomograph [In Russia]. ussr Inventor’s certificate SU 928277 of May 15, 1982, Russian Bull of Inventions N18, 1982.
  20. Rubashov IB, Timonov AA, Pestryakov AV. Abaut computer tomography [In Russian]. Doklady Academii Nauk SSSR 1980; 258(4): 846-850.
  21. Topal E, Liao Zh, Löffler M, Gluch J, Zhang J, Feng X, Zschech E. Multi-scale X-ray tomography and machine learning algorithms to study MoNi4 electrocatalysts anchored on MoO2 cuboids aligned on Ni foam. BMC Ma-ter 2020; 2: 5. DOI: 10.1186/s42833-020-00011-0.
  22. Du M, Nashed YoSG, Kandel S, Gürsoy D, Jacobsen C. Three dimensions, two microscopes, one code: Automatic differentiation for X-ray nanotomography beyond the depth of focus limit. Sci Adv 2020; 6(13): eaay3700. DOI: 10.1126/sciadv.aay3700.
  23. Lemelle L, Simionovici A, Colin P, Knott G, Bohic S, . Cloetens B., Schneider B. Nano-imaging trace elements at organelle levels in substantia nigra overexpressing α-synuclein to model Parkinson’s disease. Commun Biol 2020; 3: 364. DOI: 10.1038/s42003-020-1084-0.
  24. Nguyen TT, Villanova J, Su Z, Tucoulou R, Fleutot B, Delobel B, Delacourt C, Demortière A. 3D Quantification of microstructural properties of LiNi0.5Mn0.3Co0.2O2 high-energy density electrodes by X-Ray holographic nano-tomography. Adv Energy Mater 2021; 11: 2003529. DOI: 10.1002/aenm.202003529.
  25. Taffel S. Google’s lens: computational photography and platform capitalism. Media, Culture & Society 2020; 43(2): 0163443720939449. DOI: 10.1177/0163443720939449.
  26. Nikonorov AV, Petrov MV, Bibikov SA, Kutikova VV, Morozov AA, Kazanskiy NL. Image restoration in diffractive optical systems using deep learning and deconvolution. Computer Optics 2017; 41(6): 875-887. DOI: 10.18287/2412-6179-2017-41-6-875-887.
  27. Yoon D-H, Han Y. Parallel power flow computation trends and applications: A review focusing on GPU. Energies 2020; 13(9): 2147. DOI: 10.3390/en13092147.
  28. Draelos R, Dov D, Mazurowski M, Lo J, Henao R, Rubin G, Carin L. Machine-learning-based multiple abnormality prediction with large-scale chest computed tomography volumes. Med Image Anal 2021; 67: 101857. DOI: 10.1016/j.media.2020.101857.
  29. Zhao X, Hu J, Zhang P. GPU-based 3D cone-beam CT image reconstruction for large data volume. Int J Biomed Imaging 2009; 2009: 149079. DOI: 10.1155/2009/149079.
  30. Chukalina МV, Ingacheva AI, Buzmakov AV, Terekhin AP, Shikina Yu. Algebraic reconstruction in case of limited GPU memory in the task of computed tomography [In Russian]. Sensornye Systemy 2019; 33(2): 166-172. DOI: 10.1134/S0235009219020021.
  31. Karhula SS, Finnilä MAJ, Rytky SJO, Cooper DM, Thevenot J, Valkealahti M, Pritzker KPH, Heapea M, Joukaainen A, Lehenkari P, Kroger H, Korhonen RK, Nieminen HJ, Saarakkala S. Quantifying subresolution 3D morphology of bone with clinical computed tomography. Ann Biomed Eng 2020; 48: 595-605. DOI: 10.1007/s10439-019-02374-2.
  32. Janssens N, Huysmans M, SwennenR. Computed tomography 3D super-resolution with generative adversarial neural networks: Implications on unsaturated and two-phase fluid flow. Materials 2020; 13(6): 1397. DOI: 10.3390/ma13061397.
  33. Milanfar P, ed. Super-resolution imaging. Boca Raton, London, New York: CRC Press; 2011.
  34. Smal P, Gouze P, Rodriguez O. An automatic segmentation algorithm for retrieving sub-resolution porosity from X-ray tomography images. J Pet Sci Eng 2018; 166: 198-207. DOI: 10.1016/j.petrol.2018.02.062.
  35. Bukreeva I, Asadchikov V, Buzmakov A, Chukalina M, Ingacheva A, Korolev N, Bravin A, Mittone A, Biell G, Sierra G, Brun F, Massimi L, Fratini M, Cedola A. High resolution 3D visualization of the spinal cord in a post-mortem murine model. Biomed Opt Express 2020; 11(4): 2235-2253. DOI: 10.1364/BOE.386837.
  36. Natterer F. The mathematics of computerized tomography. Stuttgart: John Wi1ey & Sons Ltd, B G Teubner; 1986.
  37. Ramachandrah GN, Lakshminarayanan AV. Three-dimensional reconstruction from radiographs and electron micrographs: application of convolutions instead of Fourier transforms. Proc Nat Acad Sci U S A 1971; 68(9): 2236-2240. DOI: 10.1073/pnas.68.9.2236.
  38. Shepp L, Logan BF. The Fourier reconstruction of a head section. IEEE Trans Nucl Sci 1974; NS-21: 21-43.
  39. Gordon R, Bender R, German GT. Algebraic Reconstruction Techniques (ART) for three-dimensional electron microscopy and X-Ray photography. J Theor Biol 1970; 29: 471-481.
  40. Gordon R. A tutorial on ART (algebraic reconstruction techniques). IEEE Trans Nucl Sci 1974; 21(3): 78-93. DOI: 10.1109/TNS.1974.6499238.
  41. Ambrose J, Hounsfield GN. Computerized transverse axial tomography. Br J Radiol 1973; 46(542): 148-149.
  42. Tikhonov AN. About ill-posed problems and regularization technique [In Russian]. Doklady Akademii Nauk SSSR 1963, 151(3): 501-504.
  43. Kuyumchyan A, Isoyan A, Shulakov E, Aristov V, Kondratenkov V, Snigirev A, Snigireva I, Souvorov A, Tama-saku K, Yabashi M, Ishikawa T, Trouni K. High-efficiency and low-absorption Fresnel compound zone plates for hard X-ray focusing. Proc SPIE 2002: 4783: 92-96. DOI: 10.1117/12.450480.
  44. Loffelmann V, Mlynar J, Imrisek M, Mazon D,Jardin A, Weinzettl V, Hron M. Minimum Fisher Tikhonov regularization adapted to real-time tomography. Fusion Sci Technol 2016; 69(2): 505-513. DOI: 10.13182/FST15-180.
  45. Webber JW, Quinto ET, Miller EL. A joint reconstruction and lambda tomography regularization technique for energy-resolved X-ray imaging. Inverse Probl 2020; 36: 074002.
  46. Kaczmarz S. Angenäherte auflösung von systemen linearer gleichungen. Bull Int Acad Pol Sci Lett 1937; 35: 355-357.
  47. Andersen AH, Kak AC. Simultaneous Algebraic Reconstruction (SART): a superior implementation of ART algorithm. Ultrason Imaging 1984; 6: 81-94.
  48. Gilbert P. Iterative methods for three dimensional re-construction of an object from projections. J Theor Biol 1972; 36: 105-117.
  49. Gorobets AV, Neiman-Zade MI, Okunev SK, Kalyakin AA, Soukov SA. Performance of Elbrus-8C processor in supercomputer CFD simulations. Math Models Comput Simul 2019; 11(6): 914-923. DOI: 10.1134/S2070048219060073.
  50. Sedrak M, Sabelman E, Pezeshkian P, Duncan J, Bernstein I, Bruce D, Tse V, Khandhar S, Call E, Heit G, Alaminos-Bouza A. Biplanar X-ray methods for stereo-tactic intraoperative localization in deep brain stimulation surgery. Oper Neurosurg 2020; 19(3): 302-312. DOI: 10.1093/ons/opz397.
  51. Ueberschaer M, Vettermann F, Forbrig R, Unterrainer M, Siller S, Biczok A, Thorsteinsdottir J, Cyran C, Bartenstein P, Tonn J, Albert N, Schichor C, Grade S. Simpson grade revisited – Intraoperative estimation of the extent of resection in meningiomas versus postoperative somatostatin receptor positron emission tomography. computed tomography and magnetic resonance imaging. Neurosurgery 2021; 88(1): 140-146. DOI: 10.1093/neuros/nyaa333.
  52. Qadeer SMA, Filomena S, Lamei RH, Paul F, Roshan H. Configurational diffusion transport of water and oil in dual continuum shales. Sci Rep 2021; 11(2152): 18. DOI: 10.1038/s41598-021-81004-1.
  53. Singh N, Kumar S, Udawatta RP, Anderson SH, Jonge LW, Katuwal S. X-ray micro-computed tomography characterized soil pore network as influenced by long-term application of manure and fertilizer. Geoderma 2021; 385: 114872. DOI: 10.1016/j.geoderma.2020.114872.
  54. Ziesche RF,Arlt T, Finegan DP, Heenan T, Tengattini A, Baum D, Kardjilov N, Marketter H, Manke I, Kockelmann W, Brett D, Shearing P. 4D imaging of lithium-batteries using correlative neutron and X-ray tomography with a virtual unrolling technique. Nat Commun 2020; 11: 777. DOI: 10.1038/s41467-019-13943-3.
  55. Creveling PJ, Fisher J, LeBaron N, Czabaj MW. 4D Imaging of ceramic matrix composites during polymer infiltration and pyrolysis. Acta Materialia 2020; 201: 547-560. DOI: 10.1016/j.actamat.2020.10.036.
  56. Khokhriakov I, Lottermoser L, Gehrke R, Kracht T, Wintersberger E, Kopmann A, Vogelgesang M, Beckmann F. Integrated control system environment for high-throughput tomography. Proc SPIE 2014; 9212: 921217. DOI: 10.1117/12.2060975.
  57. Sarkissian HD, Lucka F, Eijnatten M, Colacicco G, Coban SB, Batenburg KJ. A cone-beam X-ray computed tomography data collection designed for machine learning. Sci Data 2019; 6: 215. DOI: 10.1038/s41597-019-0235-y.
  58. De Carlo F, Gürsoy D, Ching, DJ,Batenburg KJ, Ludwig W, Mancini L, Marone F, Mokso R, Pelt DM, Sijbers J, RiversM. TomoBank: a tomographic data repository for computational X-ray science. Meas Sci Technol 2018; 29: 034004. DOI: 10.1088/1361-6501/aa9c19.
  59. Cristofaro M, Busi R, Rizzi E, Piselli P, Pianura P, Petrone A, Fusco N, Di F, Schinina S. Image quality and radiation dose reduction in chest CT in pulmonary infection. Radiol Med 2020; 125(5): 451. DOI: 10.1007/s11547-020-0113.
  60. Villarraga-Gómez H, Smith ST. Effect of the number of projections on dimensional measurements with X-ray computed tomography. Precis Eng 2020; 66: 445-456. DOI: 10.1016/j.precisioneng.2020.08.006.
  61. Müller P. Estimation of measurement uncertainties in X-ray computed tomography metrology using the substitution method. CIRP J Manuf Sci Technol 2014; 7(3): 222-232. DOI: 10.1016/j.cirpj.2014.04.002.
  62. Hansen HN, Carneiro K, Haitjema H, De Chiffre L. Dimensional micro and nano metrology. Annals of the CIRP 2006; 55(2): 721-743. DOI: 10.1016/j.cirp.2006.10.005.
  63. Fernandes T, Oliveira M, Castro R, Araujo B, Viamonte B, Cunha R. Bowel wall thickening at CT: simplifying the diagnosis. Insights into Imaging 2014; 5: 195-208. DOI 10.1007/s13244-013-0308-y.
  64. Kruth JP, Bartscher M, Carmignato S, Schmitt R, De Chiffre L, Weckenmann A. Computed tomography for dimensional metrology. CIRP Annals 2011; 60(2): 821-842. DOI: 10.1016/j.cirp.2011.05.006.
  65. Gómez AML, Santana PS, Mourão AP. Dosimetry study in head and neck of anthropomorphic phantoms in computed tomography scans. SciMedicine J 2020; 2(1): 38-43. DOI: 10.28991/SciMedJ-2020-0201-6.
  66. Sara U, Akter M, Uddin MS. Image quality assessment through FSIM, SSIM, MSE and PSNR. J Comput Commun 2019; 7(3): 8-18. DOI: 10.4236/jcc.2019.73002.
  67. Martin CJ, Sharp PF, Sutton DG. Measurement of image quality in diagnostic radiology. Appl Radiat Isot 1999; 50: 21-38. DOI: 10.1016/s0969-8043(98)00022-0.
  68. Gori C, Rossi F, Stecco A, Villari N, Zatelli G. Dose evaluation and quality criteria in dental radiology. Radiat Prot Dosimetry 2000; 90(1-2): 225-227. DOI: 10.1093/oxfordjournals.rpd.a033125.
  69. Guo L, Zhang J, Kong D, Shan W, Duan L. WITHDRAWN: Lung nodule image quality assessment under iterative model reconstruction. Future Gener Comput Syst 2021; February: online. DOI: 10.1016/j.future.2021.02.004.

© 2009, IPSI RAS
Россия, 443001, Самара, ул. Молодогвардейская, 151; электронная почта: journal@computeroptics.ru; тел: +7 (846) 242-41-24 (ответственный секретарь), +7 (846) 332-56-22 (технический редактор), факс: +7 (846) 332-56-20