IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v71y2018i1d10.1007_s10589-017-9961-2.html
   My bibliography  Save this article

Reconstruction of 3D X-ray CT images from reduced sampling by a scaled gradient projection algorithm

Author

Listed:
  • E. Loli Piccolomini

    (University of Bologna)

  • V. L. Coli

    (University of Modena and Reggio Emilia)

  • E. Morotti

    (University of Padova)

  • L. Zanni

    (University of Modena and Reggio Emilia)

Abstract

We propose a scaled gradient projection algorithm for the reconstruction of 3D X-ray tomographic images from limited data. The problem arises from the discretization of an ill-posed integral problem and, due to the incompleteness of the data, has infinite possible solutions. Hence, by following a regularization approach, we formulate the reconstruction problem as the nonnegatively constrained minimization of an objective function given by the sum of a fit-to-data term and a smoothed differentiable Total Variation function. The problem is challenging for its very large size and because a good reconstruction is required in a very short time. For these reasons, we propose to use a gradient projection method, accelerated by exploiting a scaling strategy for defining gradient-based descent directions and generalized Barzilai–Borwein rules for the choice of the step-lengths. The numerical results on a 3D phantom are very promising since they show the ability of the scaling strategy to accelerate the convergence in the first iterations.

Suggested Citation

  • E. Loli Piccolomini & V. L. Coli & E. Morotti & L. Zanni, 2018. "Reconstruction of 3D X-ray CT images from reduced sampling by a scaled gradient projection algorithm," Computational Optimization and Applications, Springer, vol. 71(1), pages 171-191, September.
  • Handle: RePEc:spr:coopap:v:71:y:2018:i:1:d:10.1007_s10589-017-9961-2
    DOI: 10.1007/s10589-017-9961-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-017-9961-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10589-017-9961-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. NESTEROV, Yurii, 2013. "Gradient methods for minimizing composite functions," LIDAM Reprints CORE 2510, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Roberta De Asmundis & Daniela di Serafino & William Hager & Gerardo Toraldo & Hongchao Zhang, 2014. "An efficient gradient method using the Yuan steplength," Computational Optimization and Applications, Springer, vol. 59(3), pages 541-563, December.
    3. di Serafino, Daniela & Ruggiero, Valeria & Toraldo, Gerardo & Zanni, Luca, 2018. "On the steplength selection in gradient methods for unconstrained optimization," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 176-195.
    4. Clóvis Gonzaga & Ruana Schneider, 2016. "On the steepest descent algorithm for quadratic functions," Computational Optimization and Applications, Springer, vol. 63(2), pages 523-542, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yakui Huang & Yu-Hong Dai & Xin-Wei Liu & Hongchao Zhang, 2022. "On the acceleration of the Barzilai–Borwein method," Computational Optimization and Applications, Springer, vol. 81(3), pages 717-740, April.
    2. Crisci, Serena & Ruggiero, Valeria & Zanni, Luca, 2019. "Steplength selection in gradient projection methods for box-constrained quadratic programs," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 312-327.
    3. Yu-Hong Dai & Yakui Huang & Xin-Wei Liu, 2019. "A family of spectral gradient methods for optimization," Computational Optimization and Applications, Springer, vol. 74(1), pages 43-65, September.
    4. Serena Crisci & Federica Porta & Valeria Ruggiero & Luca Zanni, 2023. "Hybrid limited memory gradient projection methods for box-constrained optimization problems," Computational Optimization and Applications, Springer, vol. 84(1), pages 151-189, January.
    5. Corsaro, Stefania & De Simone, Valentina & Marino, Zelda, 2021. "Split Bregman iteration for multi-period mean variance portfolio optimization," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    6. di Serafino, Daniela & Ruggiero, Valeria & Toraldo, Gerardo & Zanni, Luca, 2018. "On the steplength selection in gradient methods for unconstrained optimization," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 176-195.
    7. Hugo Lara & Rafael Aleixo & Harry Oviedo, 2024. "Delayed Weighted Gradient Method with simultaneous step-sizes for strongly convex optimization," Computational Optimization and Applications, Springer, vol. 89(1), pages 151-182, September.
    8. Harry Fernando Oviedo Leon, 2019. "A delayed weighted gradient method for strictly convex quadratic minimization," Computational Optimization and Applications, Springer, vol. 74(3), pages 729-746, December.
    9. Behzad Azmi & Karl Kunisch, 2020. "Analysis of the Barzilai-Borwein Step-Sizes for Problems in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 819-844, June.
    10. Roberto Andreani & Marcos Raydan, 2021. "Properties of the delayed weighted gradient method," Computational Optimization and Applications, Springer, vol. 78(1), pages 167-180, January.
    11. Bonettini, Silvia & Prato, Marco & Rebegoldi, Simone, 2016. "A cyclic block coordinate descent method with generalized gradient projections," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 288-300.
    12. Masoud Fatemi, 2022. "On initial point selection of the steepest descent algorithm for general quadratic functions," Computational Optimization and Applications, Springer, vol. 82(2), pages 329-360, June.
    13. Ren Jiang & Zhifeng Ji & Wuling Mo & Suhua Wang & Mingjun Zhang & Wei Yin & Zhen Wang & Yaping Lin & Xueke Wang & Umar Ashraf, 2022. "A Novel Method of Deep Learning for Shear Velocity Prediction in a Tight Sandstone Reservoir," Energies, MDPI, vol. 15(19), pages 1-20, September.
    14. Masaru Ito, 2016. "New results on subgradient methods for strongly convex optimization problems with a unified analysis," Computational Optimization and Applications, Springer, vol. 65(1), pages 127-172, September.
    15. TAYLOR, Adrien B. & HENDRICKX, Julien M. & François GLINEUR, 2016. "Exact worst-case performance of first-order methods for composite convex optimization," LIDAM Discussion Papers CORE 2016052, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. Dimitris Bertsimas & Ryan Cory-Wright, 2022. "A Scalable Algorithm for Sparse Portfolio Selection," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1489-1511, May.
    17. Weibin Mo & Yufeng Liu, 2022. "Efficient learning of optimal individualized treatment rules for heteroscedastic or misspecified treatment‐free effect models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 440-472, April.
    18. Liu, Yulan & Bi, Shujun, 2019. "Error bounds for non-polyhedral convex optimization and applications to linear convergence of FDM and PGM," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 418-435.
    19. Sun, Shilin & Wang, Tianyang & Yang, Hongxing & Chu, Fulei, 2022. "Damage identification of wind turbine blades using an adaptive method for compressive beamforming based on the generalized minimax-concave penalty function," Renewable Energy, Elsevier, vol. 181(C), pages 59-70.
    20. Saif Eddin Jabari & Nikolaos M. Freris & Deepthi Mary Dilip, 2020. "Sparse Travel Time Estimation from Streaming Data," Transportation Science, INFORMS, vol. 54(1), pages 1-20, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:71:y:2018:i:1:d:10.1007_s10589-017-9961-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.