Inverse problems of sounding pulse formation in ultrasound tomography: mathematical modeling and experiments


  • A.V. Goncharsky Lomonosov Moscow State University
  • S.Yu. Romanov Lomonosov Moscow State University
  • S.Yu. Seryozhnikov Lomonosov Moscow State University



ultrasound tomography, waveform tomography, inverse problems, supercomputing technologies, regularizing algorithms


This paper is concerned with developing the methods of forming acoustic sounding pulses in ultrasound tomography applications. The inverse problem of forming acoustic sounding pulses is considered in the framework of linear models. This problem is ill-posed and requires the use of regularizing algorithms. Tikhonov’s regularization scheme is used to solve the problem numerically. The developed algorithms are tested on model problems as well as on experimental data. In the experimental setup, the acoustic path includes a digital waveform generator, an amplifier, an ultrasound emitter, a hydrophone with a preamplifier, and an analog-digital converter. The applicability of the linear model and the efficiency of the proposed algorithms are substantiated experimentally.

Author Biographies

A.V. Goncharsky

Lomonosov Moscow State University
• Head of Laboratory

S.Yu. Romanov

Lomonosov Moscow State University
• Leading Researcher

S.Yu. Seryozhnikov


  1. F. Natterer, “Incomplete Data Problems in Wave Equation Imaging,” Inverse Probl. Imag. 4 (4), 685-691 (2010).
  2. L. Beilina and M. V. Klibanov, Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems (Springer, New York, 2012).
  3. A. V. Goncharsky, S. Y. Romanov, and S. Y. Seryozhnikov, “A Computer Simulation Study of Soft Tissue Characterization Using Low-Frequency Ultrasonic Tomography,” Ultrasonics 67, 136-150 (2016).
  4. A. Goncharsky and S. Seryozhnikov, “The Architecture of Specialized GPU Clusters Used for Solving the Inverse Problems of 3D Low-Frequency Ultrasonic Tomography,” in Supercomputing, RuSCDays 2017, Communications in Computer and Information Science (Springer, Cham, 2017), Vol. 793, pp. 363-395.
  5. S. Romanov, “Optimization of Numerical Algorithms for Solving Inverse Problems of Ultrasonic Tomography on a Supercomputer,” in Supercomputing, RuSCDays 2017, Communications in Computer and Information Science (Springer, Cham, 2017), Vol. 793, pp. 67-79.
  6. A. V. Goncharsky, S. Y. Romanov, and S. Y. Seryozhnikov, “Inverse Problems of Layer-by-Layer Ultrasonic Tomography with the Data Measured on a Cylindrical Surface,” Vychisl. Metody Programm. 18, 267-276 (2017).
  7. A. V. Goncharsky and S. Y. Romanov, “Inverse Problems of Ultrasound Tomography in Models with Attenuation,” Phys. Med. Biol. 59 (8), 1979-2004 (2014).
  8. A. V. Goncharsky and S. Y. Romanov, “Iterative Methods for Solving Coefficient Inverse Problems of Wave Tomography in Models with Attenuation,” Inverse Probl. 33 (2) (2017).
    doi 10.1088/1361-6420/33/2/025003
  9. R. G. Pratt, L. Huang, N. Duric, and P. Littrup, “Sound-Speed and Attenuation Imaging of Breast Tissue Using Waveform Tomography of Transmission Ultrasound Data,” in {Proc. SPIE Vol. 6510, Medical Imaging 2007: Physics of Medical Imaging},
    doi 10.1117/12.708789
  10. R. Jiří k, I. Peterlí k, N. Ruiter, et al., “Sound-Speed Image Reconstruction in Sparse-Aperture 3-D Ultrasound Transmission Tomography,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59 (2), 254-264 (2012).
  11. J. Wiskin, D. T. Borup, S. A. Johnson, and M. Berggren, “Non-Linear Inverse Scattering: High Resolution Quantitative Breast Tissue Tomography,” J. Acoust. Soc. Am. 131 (5), 3802-3813 (2012).
  12. V. A. Burov, D. I. Zotov, and O. D. Rumyantseva, “Reconstruction of the Sound Velocity and Absorption Spatial Distributions in Soft Biological Tissue Phantoms from Experimental Ultrasound Tomography Data,” Akust. Zh. 61 (2), 254-273 (2015) [Acoust. Phys. 61 (2), 231-248 (2015)].
  13. A. V. Goncharsky, S. Y. Romanov, and S. Y. Seryozhnikov, Supercomputer Technologies in Development of Diagnostic Tomography Facilities (Politekh. Univ., St. Petersburg, 2016) [in Russian].
  14. A. V. Goncharskii, S. Yu. Romanov, and S. Yu. Seryozhnikov, “Low-Frequency Three-Dimensional Ultrasonic Tomography,” Dokl. Akad. Nauk 468 (3), 268-271 (2016). [Dokl. Phys. 61 (5), 211-214 (2016)].
  15. A. V. Goncharsky and S. Y. Romanov, “Iterative Methods for Solving Inverse Problems of Ultrasonic Tomography,” Vychisl. Metody Programm. 16, 464-475 (2015).
  16. A. N. Tikhonov, “Solution of Incorrectly Formulated Problems and the Regularization Method,” Dokl. Akad. Nauk SSSR 151 (3), 501-504 (1963) [Sov. Math. Dokl. 5 (4), 1035-1038 (1963)].
  17. A. N. Tikhonov, “Regularization of Incorrectly Posed Problems,” Dokl. Akad. Nauk SSSR 153 (1), 49-52 (1963) [Sov. Math. Dokl. 4 (6), 1624-1627 (1963)].
  18. A. N. Tikhonov and A. V. Goncharsky (Eds), Ill-Posed Problems in the Natural Sciences (Mir, Moscow, 1987).
  19. A. V. Goncharsky, S. Yu. Romanov, and S. Yu. Seryozhnikov, “Inverse Problems of 3D Ultrasonic Tomography with Complete and Incomplete Range Data,” Wave Motion 51 (3), 389-404 (2014).
  20. A. V. Goncharsky, S. Y. Romanov, and S. Y. Seryozhnikov, “The Problem of Choosing Initial Approximations in Inverse Problems of Ultrasound Tomography,” Vychisl. Metody Programm. 18, 312-321 (2017).
  21. A. V. Goncharsky, S. Yu. Romanov, and S. Yu. Seryozhnikov, “Problems of Limited-Data Wave Tomography,” Vychisl. Metody Programm. 15, 274-285 (2014).
  22. A. V. Goncharsky, S. Y. Romanov, and S.Y. Seryozhnikov, “Supercomputer Technologies in Tomographic Imaging Applications,” Supercomput. Front. Innov. 3 (1), 41-66 (2016).
  23. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis (Nauka, Moscow, 1976; Dover, New York, 1999).
  24. A. Bakushinsky and A. Goncharsky, Ill-Posed Problems: Theory and Applications (Springer, Dordrecht, 1994).
  25. A. B. Bakushinsky and A. V. Goncharsky, Iterative Methods for Solving Ill-Posed Problems (Nauka, Moscow, 1989) [in Russian].
  26. V. A. Vinokurov, “The Order of Magnitude of the Error in the Computation of a Function with Approximately Defined Argument,” Zh. Vychisl. Mat. Mat. Fiz. 13 (5), 1112-1123 (1973) [USSR Comput. Math. Math. Phys. 13 (5), 17-31 (1973)].
  27. V. A. Morozov, Regular Methods for Solving Ill-Posed Problems (Mosk. Gos. Univ., Moscow, 1974) [in Russian].
  28. V. I. Domarkas and R. J. Kazhys, Piezoelectric Transducers for Measuring Devices (Mintis, Vilnius, 1975) [in Russian].



How to Cite

Гончарский А., Романов С., Серёжников С. Inverse Problems of Sounding Pulse Formation in Ultrasound Tomography: Mathematical Modeling and Experiments // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2018. 19. 150-157. doi 10.26089/NumMet.v19r213



Section 1. Numerical methods and applications

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