Geodesic
Low-frequency 3D ultrasound tomography: dual-frequency method
Numerical methods and programming, Tome 19 (2018) no. 4, pp. 479-495.

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This paper is devoted to the development of efficient methods for 3D acoustic tomography. The inverse problem of acoustic tomography is formulated as a coefficient inverse problem for a hyperbolic equation where the sound speed and the absorption factor are unknown in three-dimensional space. The mathematical model describes the effects of diffraction, refraction, multiple scattering, and the ultrasound absorption. Substantial difficulties in solving this inverse problem are due to its nonlinear nature. A method of low-frequency 3D acoustic tomography based on using short sounding pulses of two different central frequencies not exceeding 500 kHz is proposed. The method employs an iterative 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 by solving a model problem with acoustic parameters close to those of soft tissues. The proposed method makes it possible to obtain a spatial resolution of 2-3 mm while the sound speed contrast does not exceed 10%. The developed algorithms can be efficiently parallelized using GPU clusters.
Keywords: ultrasound tomography, wave equation, nonlinear coefficient inverse problem, iterative algorithms. 
@article{VMP_2018_19_4_a14,
     author = {A. V. Goncharsky and S. Y. Romanov and S. Yu. Seryozhnikov},
     title = {Low-frequency {3D} ultrasound tomography: dual-frequency method},
     journal = {Numerical methods and programming},
     pages = {479--495},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2018_19_4_a14/}
}
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A. V. Goncharsky; S. Y. Romanov; S. Yu. Seryozhnikov. Low-frequency 3D ultrasound tomography: dual-frequency method. Numerical methods and programming, Tome 19 (2018) no. 4, pp. 479-495. http://geodesic.mathdoc.fr/item/VMP_2018_19_4_a14/