nach oben

Erschienen in:

2019 | OriginalPaper | Buchkapitel

Supercomputer Simulation Study of the Convergence of Iterative Methods for Solving Inverse Problems of 3D Acoustic Tomography with the Data on a Cylindrical Surface

verfasst von : Sergey Romanov

Erschienen in: Supercomputing

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

This paper is dedicated to developing effective methods of 3D acoustic tomography. The inverse problem of acoustic tomography is formulated as a coefficient inverse problem for a hyperbolic equation where the speed of sound and the absorption factor in three-dimensional space are unknown. Substantial difficulties in solving this inverse problem are due to its nonlinear nature. A method which uses short sounding pulses of two different central frequencies is proposed. The method employs an iterative parallel gradient-based minimization algorithm at the higher frequency with the initial approximation of unknown coefficients obtained by solving the inverse problem at the lower frequency. The efficiency of the proposed method is illustrated via a model problem. In the model problem an easy to implement 3D tomographic scheme is used with the data specified at a cylindrical surface. The developed algorithms can be efficiently parallelized using GPU clusters. Computer simulations show that a GPU cluster capable of performing 3D image reconstruction within reasonable time.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel SL-AV Model: Numerical Weather Prediction at Extra-Massively Parallel Supercomputer

Nächstes Kapitel Supercomputer Technology for Ultrasound Tomographic Image Reconstruction: Mathematical Methods and Experimental Results

Bazulin, E.G., Goncharsky, A.V., Romanov, S.Y., Seryozhnikov, S.Y.: Parallel CPU- and GPU-algorithms for inverse problems in nondestructive testing. Lobachevskii J. Math. 39(4), 486–493 (2018). https://doi.org/10.1134/S1995080218040030MathSciNetCrossRefMATH

Beilina, L., Klibanov, M.V., Kokurin, M.Y.: Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem. J. Math. Sci. 167(3), 279–325 (2010). https://doi.org/10.1007/s10958-010-9921-1MathSciNetCrossRefMATH

Boehm, C., Martiartu, N.K., Vinard, N., Balic, I.J., Fichtner, A.: Time-domain spectral-element ultrasound waveform tomography using a stochastic quasi-newton method. In: Proceedings of SPIE 10580, Medical Imaging 2018: Ultrasonic Imaging and Tomography p. 105800H, March 2018. https://doi.org/10.1117/12.2293299

Goncharsky, A.V., Romanov, S.Y., Seryozhnikov, S.Y.: A computer simulation study of soft tissue characterization using low-frequency ultrasonic tomography. Ultrasonics 67, 136–150 (2016). https://doi.org/10.1016/j.ultras.2016.01.008CrossRef

Goncharsky, A.V., Romanov, S.Y., Seryozhnikov, S.Y.: Supercomputer technologies in tomographic imaging applications. Supercomput. Front. Innov. 3(1), 41–66 (2016). https://doi.org/10.14529/jsfi160103CrossRef

Goncharsky, A.V., Romanov, S.Y., Seryozhnikov, S.Y.: Low-frequency three-dimensional ultrasonic tomography. Doklady Phys. 61(5), 211–214 (2016). https://doi.org/10.1134/s1028335816050086CrossRef

Goncharsky, A.V., Seryozhnikov, S.Y.: The architecture of specialized GPU clusters used for solving the inverse problems of 3D low-frequency ultrasonic tomography. In: Voevodin, V., Sobolev, S. (eds.) RuSCDays 2017. Communications in Computer and Information Science, vol. 793, pp. 363–395. Springer, Cham. (2017). https://doi.org/10.1007/978-3-319-71255-0_29CrossRef

Goncharsky, A.V., Romanov, S.Y.: Supercomputer technologies in inverse problems of ultrasound tomography. Inverse Probl. 29(7), 075004 (2013). https://doi.org/10.1088/0266-5611/29/7/075004MathSciNetCrossRefMATH

Goncharsky, A.V., Romanov, S.Y.: Inverse problems of ultrasound tomography in models with attenuation. Phys. Med. Biol. 59(8), 1979–2004 (2014). https://doi.org/10.1088/0031-9155/59/8/1979CrossRef

10.

Goncharsky, A.V., Romanov, S.Y.: Iterative methods for solving coefficient inverse problems of wave tomography in models with attenuation. Inverse Probl. 33(2), 025003 (2017). https://doi.org/10.1088/1361-6420/33/2/025003MathSciNetCrossRefMATH

11.

Goncharsky, A., Romanov, S., Seryozhnikov, S.: Inverse problems of 3D ultrasonic tomography with complete and incomplete range data. Wave Motion 51(3), 389–404 (2014). https://doi.org/10.1016/j.wavemoti.2013.10.001MathSciNetCrossRef

12.

Jirik, R., et al.: Sound-speed image reconstruction in sparse-aperture 3-D ultrasound transmission tomography. IEEE T. Ultrason. Ferr. 59(2), 254–264 (2012)CrossRef

13.

Klibanov, M.V., Timonov, A.A.: Carleman Estimates for Coefficient Inverse Problems and Numerical Applications. Walter de Gruyter GmbH, january 2004

14.

Kuzhuget, A.V., Beilina, L., Klibanov, M.V., Sullivan, A., Nguyen, L., Fiddy, M.A.: Blind backscattering experimental data collected in the field and an approximately globally convergent inverse algorithm. Inverse Probl. 28(9), 095007 (2012). https://doi.org/10.1088/0266-5611/28/9/095007CrossRefMATH

15.

Mu, S.Y., Chang, H.W.: Dispersion and local-error analysis of compact LFE-27 formulas for obtaining sixth-order accurate numerical solutions of 3D Helmholz equation. Pr. Electromagn. Res. S. 143, 285–314 (2013)CrossRef

16.

Natterer, F.: Possibilities and limitations of time domain wave equation imaging. In: AMS Vol. 559: Tomography and Inverse Transport Theory, pp. 151–162. American Mathematical Society (2011). https://doi.org/10.1090/conm/559

17.

Natterer, F.: Sonic imaging. In: Scherzer, O. (ed.) Handbook of Mathematical Methods in Imaging, pp. 1–23. Springer Nature, New York (2014). https://doi.org/10.1007/978-3-642-27795-5_37-2CrossRef

18.

Romanov, S.: Optimization of numerical algorithms for solving inverse problems of ultrasonic tomography on a supercomputer. In: Voevodin, V., Sobolev, S. (eds.) RuSCDays 2017. Communications in Computer and Information Science, vol. 793, pp. 67–79. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-71255-0_6CrossRef

19.

Sadovnichy, V., Tikhonravov, A., Voevodin, V., Opanasenko, V.: “Lomonosov”: supercomputing at Moscow State University. In: Vetter, J. (ed.) Contemporary High Performance Computing: From Petascale toward Exascale, pp. 283–307. Chapman & Hall/CRC Computational Science, CRC Press, Boca Raton (2013)

20.

Saha, R.K., Sharma, S.K.: Validity of a modified Born approximation for a pulsed plane wave in acoustic scattering problems. Phys. Med. Biol. 50(12), 2823 (2005)CrossRef

21.

Sak, M., et al.: Using speed of sound imaging to characterize breast density. Ultrasound Med. Biol. 43(1), 91–103 (2017)CrossRef

22.

Schmidt, S., Duric, N., Li, C., Roy, O., Huang, Z.F.: Modification of Kirchhoff migration with variable sound speed and attenuation for acoustic imaging of media and application to tomographic imaging of the breast. Med. Phys. 38(2), 998–1007 (2011). https://doi.org/10.1118/1.3539552CrossRef

23.

Wiskin, J.W., Borup, D.T., Iuanow, E., Klock, J., Lenox, M.W.: 3-D nonlinear acoustic inverse scattering: Algorithm and quantitative results. EEE Trans. Ultrason. Ferroelectr. Freq. Control 64(8), 1161–1174 (2017)CrossRef

24.

Zeqiri, B., Baker, C., Alosa, G., Wells, P.N.T., Liang, H.D.: Quantitative ultrasonic computed tomography using phase-insensitive pyroelectric detectors. Phys. Med. Biol. 58(15), 5237 (2013). https://doi.org/10.1088/0031-9155/58/15/5237CrossRef

Titel: Supercomputer Simulation Study of the Convergence of Iterative Methods for Solving Inverse Problems of 3D Acoustic Tomography with the Data on a Cylindrical Surface
verfasst von: Sergey Romanov
Verlag: Springer International Publishing
Buch: Supercomputing
Print ISBN: 978-3-030-05806-7

Electronic ISBN: 978-3-030-05807-4

Copyright-Jahr: 2019
DOI: https://doi.org/10.1007/978-3-030-05807-4_33

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner