Skip to main content
SpringerLink
Log in

Supercomputer Simulations of Ultrasound Tomography Problems of Flat Objects

  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Abstract

This paper is concerned with investigating the capabilities of wave tomography methods via supercomputer numerical simulations on a model problem of imaging the wave velocity structure inside flat solid objects. The problem of reconstructing the velocity structure is formulated as a nonlinear coefficient inverse problem. Iterative algorithms for solving this inverse problem are based on computing the gradient of the residual functional between the experimentally measured wave field and the numerically computed wave field. A tomographic diagnostic method is proposed for imaging flat objects which are accessible only from a single side. The method employs two ultrasonic transducer arrays and takes into account reflections from the flat bottom of the object, assuming that the thickness of the object is known. The use of the reflections from the bottom is a key feature of the method, since it significantly increases the number of sounding angles and allows the transmitted waves to be registered. This study compares the results of solving inverse problems with complete and incomplete data sets. The proposed scalable numerical algorithms can be efficiently parallelized on supercomputers. The computations were performed on 50 CPU cores of the ‘‘Lomonosov-2’’ supercomputer at Lomonosov Moscow State University. Numerical simulations were carried out for various tomographic schemes using the high-performance algorithms and supercomputer software developed in this study. The acoustic and geometric parameters of the simulations correspond to a real experiment on nondestructive testing (NDT) of solids.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

REFERENCES

  1. N. V. Ruiter, M. Zapf, T. Hopp, H. Gemmeke, and K. W. A. van Dongen, ‘‘USCT data challenge,’’ in Medical Imaging 2017: Ultrasonic Imaging and Tomography, Ed. by N. Duric and B. Heyde, Proc. SPIE 10139, 101391N (2017).

  2. N. Vinard, N. K. Martiartu, C. Boehm, I. J. Balic, and A. Fichtner, ‘‘Optimized transducer configuration for ultrasound waveform tomography in breast cancer detection,’’ in Medical Imaging 2018: Ultrasonic Imaging and Tomography, Ed. by N. Duric and B. C. Byram, Proc. SPIE 10580, 105800I (2018).

  3. A. V. Goncharsky, V. A. Kubyshkin, S. Yu. Romanov, and S. Yu. Seryozhnikov, ‘‘Inverse problems of experimental data interpretation in 3D ultrasound tomography,’’ Numer. Methods Program.20, 254–269 (2019).

    Google Scholar 

  4. R. G. Pratt, ‘‘Seismic waveform inversion in the frequency domain, Part 1: Theory and verification in a physical scale model,’’ Geophysics 64, 888–901 (1999).

    Google Scholar 

  5. J. Virieux and S. Operto, ‘‘An overview of full-waveform inversion in exploration geophysics,’’ Geophysics 74, WCC1–WCC26 (2009).

    Google Scholar 

  6. R. Seidl and E. Rank, ‘‘Iterative time reversal based flaw identification,’’ Comput. Math. Appl. 72, 879–892 (2016).

    MathSciNet  MATH  Google Scholar 

  7. M. V. Klibanov, A. E. Kolesov, and D.-L. Nguyen, ‘‘Convexification method for an inverse scattering problem and its performance for experimental backscatter data for buried targets,’’ SIAM J. Imaging Sci. 12, 576–603 (2019).

    MathSciNet  Google Scholar 

  8. A. V. Goncharsky and S. Y. Romanov, ‘‘Supercomputer technologies in inverse problems of ultrasound tomography,’’ Inverse Probl. 29, 075004 (2013).

  9. J. Blitz and G. Simpson, Ultrasonic Methods of Non-Destructive Testing (Springer, London, 1995).

    Google Scholar 

  10. S. Rodriguez, M. Deschamps, M. Castaings, and E. Ducasse, ‘‘Guided wave topological imaging of isotropic plates,’’ Ultrasonics 54, 1880–1890 (2014).

    Google Scholar 

  11. E. Bachmann, X. Jacob, S. Rodriguez, and V. Gibiat, ‘‘Three-dimensional and real-time two-dimensional topological imaging using parallel computing,’’ J. Acoust. Soc. Am. 138, 1796 (2015).

    Google Scholar 

  12. N. Dominguez and V. Gibiat, ‘‘Non-destructive imaging using the time domain topological energy,’’ Ultrasonics 50, 367–372 (2010).

    Google Scholar 

  13. E. Lubeigt, S. Mensah, S. Rakotonarivo, J.-F. Chaix, F. Baqué, and G. Gobillot, ‘‘Topological imaging in bounded elastic media,’’ Ultrasonics 76, 145–153 (2017).

    Google Scholar 

  14. T. E. Hall, S. R. Doctor, L. D. Reid, R. J. Littlefield, and R. W. Gilbert, ‘‘Implementation of real-time ultrasonic SAFT system for inspection of nuclear reactor components,’’ Acoust. Imaging 15, 253–266 (1987).

    Google Scholar 

  15. V. Schmitz, S. Chakhlov, and W. Muller, ‘‘Experiences with synthetic aperture focusing in the field,’’ Ultrasonics 38, 731–738 (2000).

    Google Scholar 

  16. J. A. Jensen, S. I. Nikolov, K. L. Gammelmark, and M. H. Pedersen, ‘‘Synthetic aperture ultrasound imaging,’’ Ultrasonics 44, 5–15 (2006).

    Google Scholar 

  17. E. G. Bazulin, ‘‘Comparison of systems for ultrasonic nondestructive testing using antenna arrays or phased antenna arrays,’’ Russ. J. Nondestruct. 49, 404–423 (2013).

    Google Scholar 

  18. E. G. Bazulin, A. V. Goncharsky, and S. Y. Romanov, ‘‘Solving inverse problems of ultrasound tomography in a nondestructive testing on a supercomputer,’’ in Supercomputing. RuSCDays 2019, Commun. Comput. Inform. Sci. 1129, 392–402 (2019).

    Google Scholar 

  19. E. G. Bazulin, A. V. Goncharsky, S. Yu. Romanov, and S. Yu. Seryozhnikov, ‘‘Inverse problems of ultrasonic tomography in nondestructive testing: Mathematical methods and experiment,’’ Russ. J. Nondestruct. 55, 453–462 (2019).

    Google Scholar 

  20. S. Y. Romanov, ‘‘Supercomputer simulations of nondestructive tomographic imaging with rotating transducers,’’ Supercomput. Front. Innov. 5 (3), 98–102 (2018).

    Google Scholar 

  21. E. G. Bazulin, A. V. Goncharsky, S. Y. Romanov, and S. Y. Seryozhnikov, ‘‘Parallel CPU- and GPU-algorithms for inverse problems in nondestructive testing,’’ Lobachevskii J. Math. 39, 486–493 (2018).

    MathSciNet  MATH  Google Scholar 

  22. A. Goncharsky, S. Romanov, and S. Seryozhnikov, ‘‘Supercomputer technologies in tomographic imaging applications,’’ Supercomput. Front. Innov. 3, 41–66 (2016).

    Google Scholar 

  23. A. V. Goncharsky, S. Yu. Romanov, and S. Yu. Seryozhnikov, ‘‘Comparison of the capabilities of GPU clusters and general-purpose supercomputers for solving 3D inverse problems of ultrasound tomography,’’ J. Parallel Distrib. Comput. 133, 77–92 (2019).

    Google Scholar 

  24. Vl. Voevodin, A. Antonov, D. Nikitenko, P. Shvets, S. Sobolev, I. Sidorov, K. Stefanov, Vad. Voevodin, and S. Zhumatiy, ‘‘Supercomputer Lomonosov-2: Large scale, deep monitoring and fine analytics for the user community,’’ Supercomput. Front. Innov. 6 (2), 4–11 (2019).

    Google Scholar 

  25. A. V. Goncharsky, and S. Y. Romanov, ‘‘A method of solving the coefficient inverse problems of wave tomography,’’ Comput. Math. Appl. 77, 967–980 (2019).

    MathSciNet  MATH  Google Scholar 

  26. A. V. Goncharsky, S. Yu. Romanov, and S. Yu. Seryozhnikov, ‘‘Problems of limited-data wave tomography,’’ Numer. Methods Program. 15, 274–285 (2014).

    MATH  Google Scholar 

  27. F. Natterer, ‘‘Possibilities and limitations of time domain wave equation imaging,’’ in Tomography and Inverse Transport Theory, Vol. 559 of Contemporary Mathematics (Am. Math. Society, Providence, 2011), pp. 151–162.

  28. M. V. Klibanov and A. E. Kolesov, ‘‘Convexification of a 3-D coefficient inverse scattering problem,’’ Comput. Math. Appl. 77, 1681–1702 (2019).

    MathSciNet  MATH  Google Scholar 

  29. M. V. Klibanov, J. Li, and W. Zhang, ‘‘Convexification for the inversion of a time dependent wave front in a heterogeneous medium,’’ SIAM J. Appl. Math. 79, 1722–1747 (2019).

    MathSciNet  MATH  Google Scholar 

  30. A. V. Goncharsky and S. Y. Romanov, ‘‘Iterative methods for solving coefficient inverse problems of wave tomography in models with attenuation,’’ Inverse Probl. 33, 025003 (2017).

  31. A. V. Goncharskii and S. Y. Romanov, ‘‘Two approaches to the solution of coefficient inverse problems for wave equations,’’ Comput. Math. Math. Phys. 52, 245–251 (2012).

    MathSciNet  Google Scholar 

  32. A. V. Goncharsky, S. Y. Romanov, and S. Y. Seryozhnikov, ‘‘Inverse problems of 3D ultrasonic tomography with complete and incomplete range data,’’ Wave Motion 51, 389–404 (2014).

    MathSciNet  MATH  Google Scholar 

  33. A. V. Goncharsky and S. Y. Romanov, ‘‘Inverse problems of ultrasound tomography in models with attenuation,’’ Phys. Med. Biol. 59, 1979–2004 (2014).

    Google Scholar 

  34. A. Goncharsky, S. Romanov, and S. Seryozhnikov, ‘‘A computer simulation study of soft tissue characterization using low-frequency ultrasonic tomography,’’ Ultrasonics 67, 136–150 (2016).

    Google Scholar 

  35. A. V. Goncharsky and S. Yu. Romanov, ‘‘Iterative methods for solving inverse problems of ultrasonic tomography,’’ Numer. Methods Program. 16, 464–475 (2015).

    Google Scholar 

  36. A. V. Goncharsky, S. Y. Romanov, and S. Y. Seryozhnikov, ‘‘Low-frequency three-dimensional ultrasonic tomography,’’ Dokl. Phys. 61, 211–214 (2016).

    Google Scholar 

  37. S. Romanov, ‘‘Optimization of numerical algorithms for solving inverse problems of ultrasonic tomography on a supercompute,’’ in Supercomputing. RuSCDays 2017, Commun. Comput. Inform. Sci. 793, 67–79 (2017).

    Google Scholar 

  38. B. Engquist and A. Majda, ‘‘Absorbing boundary conditions for the numerical simulation of waves,’’ Math. Comput. 31, 629 (1977).

    MathSciNet  MATH  Google Scholar 

  39. D. Givoli and J. B. Keller, ‘‘Non-reflecting boundary conditions for elastic waves,’’ Wave Motion 12, 261–279 (1990).

    MathSciNet  MATH  Google Scholar 

  40. E. G. Bazulin and M. S. Sadykov, ‘‘Determining the speed of longitudinal waves in anisotropic homogeneous welded joint using echo signals measured by two antenna arrays,’’ Russ. J. Nondestruct. 54, 303–315 (2018).

    Google Scholar 

Download references

Funding

The work is carried out according to the research program of Moscow Center of Fundamental and Applied Mathematics. The research is carried out using the equipment of the shared research facilities of HPC computing resources at Lomonosov Moscow State University.

Author information

Authors and Affiliations

  1. Moscow Center of Fundamental and Applied Mathematics, 119991, Moscow, Russia

    S. Y. Romanov

Authors
  1. S. Y. Romanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Y. Romanov.

Additional information

(Submitted by Vl. V. Voevodin)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Romanov, S.Y. Supercomputer Simulations of Ultrasound Tomography Problems of Flat Objects. Lobachevskii J Math 41, 1563–1570 (2020). https://doi.org/10.1134/S199508022008017X

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S199508022008017X

Keywords:

Search

Navigation