Supercomputer technologies in tomographic imaging applications

Alexander V. Goncharsky, Sergey Y. Romanov, Sergey Y. Seryozhnikov


Currently, tomographic imaging is widely used in medical and industrial non-destructive testing applications. X-ray tomography is the prevalent imaging technology. Modern medical X-ray CT scanners provide up to 1 mm spatial resolution. The disadvantage of X-ray tomography is that it cannot be used for regular medical examinations. Early breast cancer diagnosis is one of the most pressing issues in modern healthcare. Ultrasound tomography devices are being developed in USA, Germany and Russia to address this problem. One of the main challenges in ultrasound tomographic imaging is the development of efficient algorithms for solving inverse problems of wave tomography, which are nonlinear three-dimensional coefficient inverse problems for a hyperbolic differential equation. Solving such computationally-expensive problems requires the use of supercomputers.

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Glide-Hurst C.K., Duric N., Littrup P. Volumetric breast density evaluation from ultrasound tomography images // Medical Physics. 2008. 35. 3988-3997. DOI: 10.1118/1.2964092.

Matej S., Fessler J.A., Kazantsev I.G. Iterative tomographic image reconstruction using fourier-based forward and back-projectors IEEE Transactions on Medical Imaging. 2004. Vol. 23. p. 401. DOI: 10.1109/NSSMIC.2002.1239651.

Bazulin A.E., Bazulin E.G., Vopilkin A.K., Kokolev S.A., Romashkin S.V., Tikhonov D.S. Application of 3D coherent processing in ultrasonic testing // Russian journal of nondestructive testing, Vol. 50, No. 2, 2014. pp. 92-108. DOI: 10.1134/S1061830914020028

Levin G.G., Vishnyakov G.N., Minaev V.L., Latushko M.I., Pickalov V.V., Belyakov V.K., Sukhenko E.P., Demyanenko A.V. Shearing interference microscopy for tomography of living cells // Proceedings of SPIE, Vol. 9536, 2015. pp. 95360G. doi: 10.1117/12.2183717

Glinskii B.M., Sobisevich A.L., Khairetdinov M.S. Experience of vibroseismic sounding of complex geological structures (with the Shugo mud volcano as an example) Doklady earth sciences, 2007, Vol. 413, No. 3. pp.397-401. DOI: 10.1134/S1028334X07030178

Digisens 3D tomography software solutions.

Jia X., Yan H., Cervino L., Folkerts M., Jiang S.B. A GPU tool for efficient, accurate, and realistic simulation of cone beam CT projections // Med Phys. 2012 Dec;39 (12):7368-78. doi: 10.1118/1.4766436. DOI: 10.1118/1.4766436.

Wiskin J., Borup D., Johnson S., Berggren M., Robinson D., Smith J., Chen J., Parisky Y., Klock J. Inverse scattering and refraction corrected reflection for breast cancer imaging // Proc. of SPIE Vol. 7629 76290K-1. doi: 10.1117/12.844910.

Gemmeke H., Menshikov A., Tchernikovski D., Berger L., Gobel G., Birk M., Zapf M. and Ruiter N. V. 2010 Hardware setup for the next generation of 3D ultrasound computer tomography Nuclear Science Symposium Conference Record (NSS/MIC) IEEE pp 2449-54. DOI:


Burov V.A., Zotov D.I., Rumyantseva O.D. Reconstruction of spatial distributions of sound velocity and absorption in soft biological tissues using model ultrasonic tomographic data // Acoustical Physics, 2014, V 60, No. 4, pp. 479-491. DOI: 10.1134/S1063771014040022

Kak A, Slaney M. Principles of computerized tomographic imaging. SIAM, 2001.

Radon, J.; Parks, P.C. (translator) (1986), On the determination of functions from their integral values along certain manifolds, IEEE Transactions on Medical Imaging 5 (4): 170--176, doi:10.1109/TMI.1986.4307775, PMID 18244009.

Schmidt S., Gade-Nielsen N.F., Høstergaard M., Dammann B., Kazantsev I.G., High Resolution Orientation Distribution Function // Materials Science Forum, 2012, Vols. 702-703, pp. 536-539.

Barber B. C. Theory of digital imaging from orbital synthetic aperture radar // IJRS,textbf{ 11}, 1983.

Elachi C., Bicknell T., Jordan R. L., Chialin Wu. Spaceborne synthetic-aperture imaging radars: Applications, techniques, and technology // Proceedings of the IEEE 1982, Vol 70, Issue: 10 pp.1174 - 1209.

Kretzek E.,~ Ruiter N.V. GPU based 3D SAFT reconstruction including phase aberration // Proc. SPIE~9040, Medical Imaging 2014: Ultrasonic Imaging and Tomography, 90400W (March 20, 2014); doi:10.1117/12.2042669

Tikhonov A.N., Goncharskii A.V., Matvienko A.N., Romanov S.Y., Shchetinin V.G., Chubarov I.N., Markachev S.I., Grishko M.I., Ksenofontov E.A. Problems in the digital reconstruction of synthetic-aperture radar images // Soviet Physics Doklady, 1992, Vol. 37, pp. 79.

Rubin G., Berger D., Sager E. GPU Acceleration of SAR/ISAR Imaging Algorithms // Antenna Measurement Techniques Association Symposium 2010 (AMTA 2010), Proceedings of a meeting held 10-15 October 2010, Atlanta, Georgia, USA. A10-0059. pp. 430-435.

Maddikonda S.S., Shanmugha Sundaram G.A. SAR image processing using GPU // Communications and Signal Processing (ICCSP), 2014 International Conference on. pp. 448 -- 452. DOI: 10.1109/ICCSP.2014.6949881

Bakushinsky A.B., Goncharsky A.V. Ill-posed problems. Theory and applications. Dordrect: Kluwer, 1994.

Goncharskii A.V., Romanov S.Y. On a three-dimensional diagnostics problem in the wave Approximation // Computational Mathematics and Mathematical Physics 2000;40:1308--1311. DOI: 10.3103/S0278641910010012

Goncharskii A.V., Ovchinnikov S.L., Romanov S.Y.. On the one problem of wave diagnostics // Moscow University Computational Mathematics and Cybernetics 2010;34:1--7. DOI:~10.3103/S0278641910010012

Ovchinnikov S.L., Romanov S.Yu. Organization of parallel computations when solving the inverse problem of wave diagnostics // Vychisl. Metody Programm. 2008. Vol.9. N 2. pp.338-345. (in Russian).

Goncharskii A.V., Romanov S.Yu. Two Approaches to the Solution of Coefficient Inverse Problems for Wave Equations // Computational Mathematics and Mathematical Physics. 2012, Vol. 52, No. 2, pp. 245--251.

Glover G.H. Computerized time-of-flight ultrasonic tomography for breast examination //Ultrasound in Medicine & Biology Vol, 3, No. 2--3, 1977, pp. 117-127. doi:10.1016/0301-5629(77)90064-3

Toward real-time bent-ray breast ultrasound tomography using GPUs// Proceedings of SPIE - The international society for optical engineering~9040~·~february 2014. DOI: 10.1117/12.2043127

Natterer F. Possibilities and limitations of time domain wave equation imaging. Contemporary Mathematics 2011;559:151--162.

Beilina L. and Klibanov M.V. 2012 Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems (New York: Springer).

Goncharsky A.V., Romanov S.Y. Supercomputer technologies in inverse problems of ultrasound tomography // Inverse Problems. 2013, Vol. 29, No. 7. 075004. DOI: 10.1088/0266-5611/29/7/075004.

Goncharsky A.V., Romanov S.Y. Inverse problems of ultrasound tomography in models with attenuation. Phys Med Biol. 2014;59:1979--2004. DOI: 10.1088/0031-9155/59/8/1979

Goncharsky A.V., Romanov S.Y., Seryozhnikov S.Y. Inverse problems of 3D ultrasonic tomography with complete and incomplete range data. Wave motion 2014;51:389--404. DOI: 10.1016/j.wavemoti.2013.10.001

Huang L., Quan Y. Sound-speed tomography using first-arrival transmission ultrasound for a ring array // Proc. SPIE Medical Imaging. 2007. 6513. doi: 10.1117/12.709647.

Roy O., Jovanovi´c I., Hormati A., Parhizkar R., Vetterli M. Sound Speed Estimation Using Wave-based Ultrasound Tomography:Theory and GPU Implementation // Proc. SPIE 7629, Medical Imaging 2010: Ultrasonic Imaging, Tomography, and Therapy. 2010. 76290J. doi:10.1117/12.844691.

Varadan V.V., Ma Y., Varadan V.K., Lakhtakia A. Scattering of waves by spheres and cylinders // in: Field representations and Introduction to Scattering. (North-Holland), Amsterdam. 1991. 211-324.

Lavarello R.J., Oelze M.L. Tomographic Reconstruction of Three-Dimensional Volumes Using the Distorted Born Iterative Method // IEEE Trans. Med. Imaging. 2009. 28. 1643-1653. DOI: 10.1109/TMI.2009.2026274.

Goncharsky A.V., Romanov S.Yu., and Seryozhnikov S.Yu. Problems of limited-data wave tomography // Vychisl. Metody Programm. 2014 (15), 274--285 (in Russian).

Goncharsky A.V., Romanov S.Y., Seryozhnikov S.Y. A computer simulation study of soft tissue characterization using low-frequency ultrasonic tomography // Ultrasonics, 2016. V. 67, pp. 136--150. DOI: 10.1016/j.ultras.2016.01.008.

Tikhonov A.N. The solution of ill-posed problems and the regularization method, DAN SSSR 151: 3 (1963), pp.501-504 (in Russian)

Tikhonov A.N., Goncharsky A.V., Stepanov V.V., Yagola A.G. Numerical Methods for the Solution of Ill-Posed Problems. Kluwer acad.publ. Dordrecht/Boston/London 1995. ISBN 0-7923-3583-X

Sadovnichy V., Tikhonravov A., Voevodin Vl., and Opanasenko V. "Lomonosov": Supercomputing at Moscow State University. In Contemporary High Performance Computing: From Petascale toward Exascale (Chapman & Hall/CRC Computational Science), pp.283-307, Boca Raton, USA, CRC Press, 2013.

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