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Volume 36 #1

Contents

  1. An overview of the visual acuity assessment. 2. Theoretical and clinical requirements to the optotypes and chart designs
  2. Assessment of peripheral visual acuity in various conditions of testing
  3. The expression and function of components of signaling cascades of taste, olfactory, and phototransduction in mammalian pancreas beta-cells
  4. Recognition of projectively transformed planar figures. XVI The octet of projectively stable vertices of the oval and new methods for its reference description using the octet
  5. Heteroscedasticity correction to improve tomographic reconstruction with an algebraic approach

Heteroscedasticity correction to improve tomographic reconstruction with an algebraic approach

© 2022 М. V. Chukalinaa,b, А. S. Ingachevab,c, А. V. Buzmakova,b, I. V. Yakimchukd, I. A. Varfolomeevd, P. A. Kulagine, D. P. Nikolaevb,c

aFSRC Cristallograhy and photonics, 119333 Moscow, Leninskii prospect, 59, Russia
bСмарт Энджинс Сервис, 117312 Moscow, pr. 60-letiya Oktyabrya, 9, Russia
cInstitute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), 127051 Moscow, Bolshoi karetnii., 19, Russia
dMoscow Research Center Schlumberger, 125171 Moscow, Leningradskoe shosse,16 А, str. 3, Russia
eMoscow Institute of Physics and Technology, 141701 Moscow Region, Dolgoprudny, Institutskiy per. 9, Russia

Received 20 Oct 2021

Computed tomography is a non-destructive method of artificial intelligence, makes it possible to reconstruct the internal morphological structure of the objects from a set of projections collected at different angles. The object is probed by X-rays, which are attenuated as they pass through the object. Attenuated radiation is collected by a position- sensitive detector. This is a stochastic process. The signal formation model has based on the Poisson distribution. The exposure time is an important parameter of the measuring system and, along with the absorbing properties of the sample itself, determines the probabilistic characteristics of the collected data. As shorter the exposure time as greater the variance of the collected data, i.e. the values are heteroscedastic. Heteroscedasticity generates distortions in the reconstructed images that interfere with the correct interpretation of the results. In this paper, we propose a reconstruction method based on the algebraic approach. The main idea of the method is to add a “confidence” matrix to the system of linear algebraic equations to be solved. The matrix is calculated based on the results of the analysis of the variance of the collected signals. The step of the gradient optimization method used to solve the equations system is written out. The results of experiments on synthetic data show an increase in the accuracy of reconstruction when taking into account heteroscedasticity.

Key words: X-ray tomography, artificial intelligence method, tomographic reconstruction, heteroscedasticity

DOI: 10.31857/S0235009222010036

Cite: Chukalina М. V., Ingacheva А. S., Buzmakov А. V., Yakimchuk I. V., Varfolomeev I. A., Kulagin P. A., Nikolaev D. P. Uchet geteroskedastichnosti v izmeryaemykh tomograficheskikh proektsiyakh pri realizatsii algebraicheskogo podkhoda v tomograficheskoi rekonstruktsii [Heteroscedasticity correction to improve tomographic reconstruction with an algebraic approach]. Sensornye sistemy [Sensory systems]. 2022. V. 36(1). P. 90–98 (in Russian). doi: 10.31857/S0235009222010036

References:

  • Gladilin S., Kotov A., Nikolaev D., Usilin S. Postroenie ustojchivyh priznakov detekcii i klassifikacii ob''ektov, ne obladajushhih harakternymi jarkostnymi kontrastami [Construction of stable signs of detection and classification of objects that do not have characteristic brightness contrasts]. ITiVS [Journal of Information Technologies and Computing Systems]. 2014. № 1. P. 53–60 (in Russian)
  • Kodnyanko V.А. Binary Scanning Search (Biscan) for Conditional Minimization of Weakly Unimodal Functions. Bulletin of the South Ural State University, Series “Computational Mathematics and Software Engineer ing”. 2018. V. 7 (4). P. 59–66 (in Russian) https://doi.org/10.14529/cmse180404
  • Agulleiro J.I., Fernandez J.J. Fast tomographic reconstruction on multicore computers. Bioinformatics. 2011. V. 27 (4). P. 582–583. https://doi.org/10.1093/bioinformatics/btq692
  • Arlazarov V.L., Nikolaev D.P., Arlazarov V.V., Chukalina M.V. X-ray tomography: the way from layer-by-layer radiography to computed tomography. Computer Optics. 2021. V. 45 (6). Р. 897–906.
  • Balasubramani V., Montresor S., Tu H-Y., Huang C-H., Picart P., Cheng C-J. Influence of noise-reduction techniques in sparse-data sample rotation tomographic imaging. Applied Optics. 2021. V. 60. P. B81–B87. https://doi.org/10.1364/AO.415284
  • Bulatov K., Chukalina M., Buzmakov A., Nikolaev D., Arlazarov V. V. Monitored reconstruction: computed tomography as an anytime algorithm. IEEE Access. 2020. V. 8. P. 110759–110774. https://doi.org/10.1109/ACCESS.2020.3002019
  • Gilbert P. Iterative methods for the three-dimensional reconstruction of an object from projections. J. Theoretical Biology. 1972. V. 36 (1). P. 105–117.
  • Grigoriev M., Khafizov A., Kokhan V., Asadchikov V. Robust technique for representative volume element identification in noisy microtomography images of porous materials based on pores morphology and their spatial distribution. Proc. SPIE, Thirteenth International Conference on Machine Vision. 2021. V. 11605. P. 1–10. https://doi.org/10.1117/12.2586785
  • Inoue H. Efficient tomographic reconstruction for commodity processors with limited memory bandwidth. 13th International Symposium on Biomedical Imaging (ISBI). 2016. P. 747–750. https://doi.org/10.1109/ISBI.2016.7493374
  • Kak A.C., Slaney M. Principles of Computerized Tomographic Imaging. NY. IEEE Press, 1988. 329 p.
  • Konovalenko I.A., Smagina A.A., Nikolaev D.P., Nikolaev P.P. ProLab: A Perceptually Uniform Projective Color Coordinate System. IEEE Access. 2021. V. 9. P. 133023–133042. https://doi.org/10.1109/ACCESS.2021.3115425
  • Lasio G.M., Whiting B.R., Williamson J.F. Statistical reconstruction for x-ray computed tomography using energy-integrating detectors. Physics in Medicine & Biology. 2007. V. 52. (8). P. 2247–2266.
  • Pietsch P., Wood V. X-Ray tomography for lithium ion battery research: a practical guide. Annual Review of Materials Research. 2017. V. 47. P. 451–479. https://doi.org/10.1146/annurev-matsci-070616-123957
  • Sartini S., Frizzi J., Borselli M., Sarcoli E., Granai C., Gealli V., Cevenini G., Guazzi G., Bruni F., Gonelli S., Postorelly M. Which method is best for an early accurate diagnosis of acute heart failure? Comparison between lung ultrasound, chest X-ray and NT pro-BNP performance: a prospective study. Internal and Emergency Medicine. 2017. V. 12. P. 861–869. https://doi.org/10.1007/s11739-016-1498-3
  • Shepelev D.A., Bozhkova V.P., Ershov E.I., Nikolaev D.P. Simulating shot noise of color underwater images. Computer Optics. 2020. V. 44 (4). P. 671–679. https://doi.org/10.18287/2412-6179-CO-754
  • Withers P.J., Bouman C., Carmignato S., Cnudde V., Grimaldi D., Hagen C.K., Meire E., Manley M., Du Plessis A., Stock S.R. X-ray computed tomography. Nature Reviews Methods Primers. 2021. V. 1. (18). P. 1–21. https://doi.org/10.1038/s43586-021-00015-4
  • Zschech E., Löffler M., Krüger P., Gluch J., Kutukova K., Zgłobicka, I., Silomon J., Rosenkranz R., Standke Y., Topal E. Laboratory computed X-ray tomography – a nondestructive technique for 3D microstructure analyis of materials. Practical Metallography. 2018. V. 55 (8). P. 539–555. https://doi.org/10.3139/147.110537