Abstract
This paper is concerned with developing efficient methods for solving inverse problems of ultrasonic nondestructive imaging in the framework of a scalar wave model, which describes the propagation, diffraction and refraction of longitudinal ultrasonic waves. The problem of recovering the velocity of a longitudinal wave in a solid is formulated as a coefficient inverse problem, which in this formulation is nonlinear. The proposed scalable numerical algorithms can be efficiently parallelized both on CPU- and GPU-equipped supercomputers. The efficiency of the algorithms is illustrated by applying them to model problems. The computations were performed on the “Lomonosov” supercomputer at Lomonosov Moscow State University.
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References
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 Medical Imaging 2007: Physics of Medical Imaging, Ed. by J. Hsieh and M. J. Flynn (SPIE, San Diego, CA, 2007).
H. Gemmeke, L. Berger, M. Birk, G. Gobel, A. Menshikov, D. Tcherniakhovski, M. Zapf, and N. V. Ruiter, “Hardware setup for the next generation of 3D Ultrasound Computer Tomography,” in Proceedings of the IEEE Nuclear Science Symposuim and Medical Imaging Conference (Inst. Electrical and Electronics Eng. IEEE, 2010).
J. Wiskin, D. Borup, M. Andre, S. Johnson, J. Greenleaf, Y. Parisky, and J. Klock, “Three-dimensional nonlinear inverse scattering: Quantitative transmission algorithms, refraction corrected reflection, scanner design, and clinical results,” J. Acoust. Soc. Am. 133, 3229–3229 (2013).
A. V. Goncharsky and S. Y. Romanov, “Inverse problems of ultrasound tomography in models with attenuation,” Phys.Med. Biol. 59, 1979–2004 (2014).
C. Maierhofer, H.-W. Reinhardt, and G. Dobmann, Non-Destructive Evaluation of Reinforced Concrete Structures: Non-Destructive Testing Methods (Elsevier, 2010).
J. Blitz and G. Simpson, Ultrasonic Methods of Non-destructive Testing (Springer, Netherlands, 1995).
K.-J. Langenberg, R. Marklein, and K. Mayer, Ultrasonic Nondestructive Testing of Materials: Theoretical Foundations (CRC, Boca Raton, FL, 2012).
A. Lechleiter and J. W. Schlasche, “Identifying Laméparameters from time-dependent elastic wave measurements,” Inverse Problems Sci. Eng. 25, 2–26 (2017).
F. Natterer, “Possibilities and limitations of time domain wave equation imaging,” in Tomography and Inverse Transport Theory, Vol. 559 of Contemp. Math. (Am. Math. Society, Providence, 2011), pp. 151–162.
L. Beilina and M. V. Klibanov, Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems (Springer, New York, 2012).
A. V. Goncharsky and S. Y. Romanov, “Supercomputer technologies in inverse problems of ultrasound tomography,” Inverse Probl. 29, 075004 (2013).
A. V. Goncharsky, S. Y. Romanov, and S. Y. Seryozhnikov, “Low-frequency three-dimensional ultrasonic tomography,” Dokl. Phys. 468, 268–271 (2016).
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).
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).
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).
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).
N. Dominguez and V. Gibiat, “Non-destructive imaging using the time domain topological energy method,” Ultrasonics 50, 367–372 (2010).
A. E. Bazulin, E. G. Bazulin, A. K. Vopilkin, S. A. Kokolev, S. Romashkin, and D. S. Tikhonov, “Application of 3D coherent processing in ultrasonic testing,” Russ. J. Nondestruct. 50, 92–108 (2014).
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).
E. G. Bazulin, “On the possibility of using the maximum entropy method in ultrasonic nondestructive testing for scatterer visualization from a set of echo signals,” Acoust. Phys. 59, 210–227 (2013).
V. Voevodin, S. A. Zhumatiy, S. Sobolev, A. Antonov, P. Bryzgalov, D. A. Nikitenko, K. S. Stefanov, and V. V. Voevodin, “Practice of Lomonosov supercomputer,” Open Syst. J., No. 7, 36–39 (2012).
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Bazulin, E.G., Goncharsky, A.V., Romanov, S.Y. et al. Parallel CPU- and GPU-Algorithms for Inverse Problems in Nondestructive Testing. Lobachevskii J Math 39, 486–493 (2018). https://doi.org/10.1134/S1995080218040030
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DOI: https://doi.org/10.1134/S1995080218040030