Ray-based inversion accounting for scattering for biomedical ultrasound tomography. (English) Zbl 1478.78032


78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
74A45 Theories of fracture and damage
74A05 Kinematics of deformation
76Q05 Hydro- and aero-acoustics
74J20 Wave scattering in solid mechanics
65K10 Numerical optimization and variational techniques
65M80 Fundamental solutions, Green’s function methods, etc. for initial value and initial-boundary value problems involving PDEs
65D25 Numerical differentiation
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
92C55 Biomedical imaging and signal processing
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory


Full Text: DOI arXiv


[1] Tromp, J., Seismic wavefield imaging of Earth’s interior across scales, Nat. Rev. Earth Environ., 1, 40-53 (2020)
[2] Lucka, F.; Pérez-Liva, M.; Treeby, B.; Cox, B., High resolution 3D ultrasonic breast imaging by time-domain full waveform inversion (2021)
[3] Rullan, F.; Betcke, M., Hamilton-Green solver for the forward and adjoint problems in photoacoustic tomography (2018)
[4] Rullan, F., Photoacoustic tomography: flexible acoustic solvers based on geometrical optics, PhD Thesis (2020)
[5] Beck, A., First-order Methods in Optimization (2017), Philadelphia, PA: SIAM, Philadelphia, PA · Zbl 1384.65033
[6] Hopp, T.; Ruiter, N.; Bamber, J. C.; Duric, N.; van Dongen, K. W A., International Workshop on Medical Ultrasound Tomography (2017), Germany: Speyer, Germany
[7] Greenleaf, J. F.; Johnson, S. A.; Lee, S. L.; Hermant, G. T.; Woo, E. H.; Green, P. S., Algebraic reconstruction of spatial distributions of acoustic absorption within tissue from their two-dimensional acoustic projections, Acoustical Holography, 591-603 (1974)
[8] Opielinski, K. J.; Pruchnicki, P.; Szymanowski, P.; Szepieniec, W. K.; Szweda, H.; Swis, E.; Jozwik, M.; Tenderenda, M.; Bułkowskif, M., Multimodal ultrasound computer-assisted tomography: an approach to the recognition of breast lesions, Comput. Med. Imag. Graph., 65, 102-114 (2018)
[9] Ruiter, N. V.; Zapf, M.; Hopp, T.; Dapp, R.; Kretzek, E.; Birk, M.; Kohout, B.; Gemmeke, H., 3D ultrasound computer tomography of the breast: a new era?, Eur. J. Radiol., 81, S133-S134 (2012)
[10] Gemmeke, H.; Hopp, T.; Zapf, M.; Kaiser, C.; Ruiter, N. V., 3D ultrasound computer tomography: hardware setup, reconstruction methods and first clinical results, Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrom. Detect. Assoc. Equip., 873, 59-65 (2017)
[11] Duric, N.; Littrup, P.; Poulo, L.; Babkin, A.; Pevzner, R.; Holsapple, E.; Rama, O.; Glide, C., Detection of breast cancer with ultrasound tomography: first results with the computed ultrasound risk evaluation (CURE) prototype, Med. Phys., 34, 773-785 (2007)
[12] Li, C.; Duric, N.; Littrup, P.; Huang, L., In vivo breast sound-speed imaging with ultrasound tomography, Ultrasound Med. Biol., 35, 1615-1628 (2009)
[13] Anderson, A. H.; Kak, A. C., Simultaneous algebraic reconstruction techniques (SART): a superior implementation of the ART algorithm, Ultrason. Imaging, 6, 81-94 (1984)
[14] Johnson, S. A.; Greenleaf, J. F.; Samayoa, W. F.; Duck, F. A.; Sjostrand, J., Reconstruction of three-dimensional velocity fields and other parameters by acoustic ray tracing, 46-51 (1975)
[15] Devaney, A. J.; Oristaglio, M. L., Inversion procedure for inverse scattering within the distorted-wave Born approximation, Phys. Rev. Lett., 51, 237-240 (1983)
[16] Douglas Mast, T., Aberration correction for time-domain ultrasound diffraction tomography, J. Acoust. Soc. Am., 112, 55-64 (2002)
[17] Borup, D. T.; Johnson, S. A.; Kimz, W. W.; Berggren, M. J., Nonperturbative diffraction tomography via Gauss-Newton iteration applied to the scattering integral equation, Ultrason. Imaging, 14, 69-85 (1992)
[18] Wiskin, J.; Borup, D. T.; Johnson, S. A.; Berggren, M., Non-linear inverse scattering: high resolution quantitative breast tissue tomography, J. Acoust. Soc. Am., 131, 3802-3813 (2012)
[19] Wiskin, J. W.; Borup, D. T.; Iuanow, E.; Klock, J.; Lenox, M. W., 3D nonlinear acoustic inverse scattering: algorithm and quantitative results, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 64, 1161-1174 (2017)
[20] Goncharsky, A. V.; Romanov, S. Y., Iterative methods for solving coefficient inverse problems of wave tomography in models with attenuation, Inverse Problems, 33 (2017) · Zbl 1357.92041
[21] Beydoun, W. B.; Tarantola, A., First Born and Rytov approximations: modeling and inversion conditions in a canonical example, J. Acoust. Soc. Am., 83, 1045-1055 (1988) · Zbl 0662.65110
[22] Engquist, B.; Runborg, O., Computational high frequency wave propagation, Acta Numer., 12, 181-266 (2003) · Zbl 1049.65098
[23] Chapman, C., Fundamentals of Seismic Wave Propagation (2004), Cambridge: Cambridge University Press, Cambridge
[24] Runborg, O., Mathematical models and numerical methods for high frequency waves, Commun. Comput. Phys., 2, 827-880 (2007) · Zbl 1164.78300
[25] Anderson, A. H.; Kak, A. C., Digital ray tracing in two-dimensional refractive fields, J. Acoust. Soc. Am., 72, 1593-1606 (1982) · Zbl 0497.76075
[26] Anderson, A. H., A ray tracing approach to restoration and resolution enhancement in experimental ultrasound tomography, Ultrason. Imaging, 12, 268-291 (1990)
[27] Javaherian, A.; Lucka, F.; Cox, B. T., Refraction-corrected ray-based inversion for three-dimensional ultrasound tomography of the breast, Inverse Problems, 36 (2020) · Zbl 07310606
[28] Bold, G. E J.; Birdsall, T. G., A top‐down philosophy for accurate numerical ray tracing, J. Acoust. Soc. Am., 80, 656-660 (1986)
[29] Kreyszig, E., Advanced Engineering Mathematics (1993), New York: Wiley, New York · Zbl 0803.00001
[30] Virieux, J.; Farra, V., Ray tracing in 3D complex isotropic media: an analysis of the problem, Geophysics, 56, 2057-2069 (1991)
[31] Denis, F.; Basset, O.; Giminez, G., Ultrasonic transmission tomography in refracting media: reduction of refraction artefacts by curved-ray techniques, IEEE Trans. Med. Imag., 14, 173-188 (1995)
[32] Červený, V., Seismic Ray Theory (2001), Cambridge: Cambridge University Press, Cambridge · Zbl 0990.86001
[33] Butcher, J. C., The Numerical Analysis of Ordinary Differential Equations (1987), New York: Wiley, New York · Zbl 0616.65072
[34] Holm, D., Geometric Mechanics, 1-97 (2011), London: Imperial College Press, London
[35] Cox, B. T.; Kara, S.; Arridge, S. R.; Beard, P. C., k-space propagation models for acoustically heterogeneous media: application to biomedical photoacoustics, J. Acoust. Soc. Am., 121, 3453 (2007)
[36] Wise, E. S.; Cox, B. T.; Jaros, J.; Treeby, B. E., Representing arbitrary acoustic source and sensor distributions in Fourier collocation methods, J. Acoust. Soc. Am., 146, 278-288 (2019)
[37] Abramowitz, M.; Stegun, I. A., Handbook of Mathematical Functions (1972), New York: Dover Publications, Inc., New York · Zbl 0543.33001
[38] Ali, R.; Hsieh, S.; Dahl, J., Open-source Gauss-Newton-based methods for refraction-corrected ultrasound computed tomography (2019)
[39] Li, S.; Jackowski, M.; Dione, D. P.; Varslot, T.; Staib, L. H.; Mueller, K., Refraction corrected transmission ultrasound computed tomography for application in the breast imaging, Med. Phys., 37, 2233-2246 (2010)
[40] Rawlinson, N.; Houseman, G. A.; Collins, C. D N., Inversion of seismic refraction and wide-angle reflection traveltimes for three-dimensional layered crustal structure, Geophys. J. Int., 145, 381-400 (2001)
[41] Rawlinson, N.; Hauser, J.; Sambridge, M., Seismic ray tracing and wavefront tracking in laterally heterogeneous media, Adv. Geophys., 49, 203-273 (2008)
[42] Liebler, M.; Ginter, S.; Dreyer, T.; Riedlinger, R. E., Full wave modeling of therapeutic ultrasound: efficient time-domain implementation of the frequency power-law attenuation, J. Acoust. Soc. Am., 116, 2742-2750 (2004)
[43] Szabo, T. L., Time domain wave equations for lossy media obeying a frequency power law, J. Acoust. Soc. Am., 96, 491-500 (1994)
[44] Kelly, J. F.; McGough, R. J.; Meerschaert, M. M., Analytical time-domain Green’s functions for power-law media, J. Acoust. Soc. Am., 124, 2861-2872 (2008)
[45] Treeby, B. E.; Cox, B. T., Modeling power law absorption and dispersion for acoustic propagation using the fractional Laplacian, J. Acoust. Soc. Am., 127, 2741-2748 (2010)
[46] Treeby, B. E.; Zhang, E. Z.; Cox, B. T., Photoacoustic tomography in absorbing acoustic media using time reversal, Inverse Problems, 26 (2010) · Zbl 1204.35178
[47] Goncharsky, A. V.; Romanov, S. Y., Inverse problems of ultrasound tomography in models with attenuation, Phys. Med. Biol., 59, 1979-2004 (2014)
[48] Mojabi, P.; LoVetri, J., Ultrasound tomography for simultaneous reconstruction of acoustic density, attenuation, and compressibility profiles, J. Acoust. Soc. Am., 137, 1813-1825 (2015)
[49] Plessix, R-E, A review of the adjoint-state method for computing the gradient of a functional with geophysical applications, Geophys. J. Int., 167, 495-503 (2006)
[50] Wang, K.; Matthews, T.; Anis, F.; Li, C.; Duric, N.; Anastasio, M. A., Waveform inversion with source encoding for breast sound speed reconstruction in ultrasound computed tomography, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 62, 475-493 (2015)
[51] Matthews, T. P.; Wang, K.; Li, C.; Duric, N.; Anastasio, M. A., Regularized dual averaging image reconstruction for full-wave ultrasound computed tomography, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 64, 811-825 (2017)
[52] Matthews, T. P.; Anastasio, M. A., Joint reconstruction of the initial pressure and speed of sound distributions from combined photoacoustic and ultrasound tomography measurements, Inverse Problems, 33 (2017) · Zbl 1394.92073
[53] Pérez-Liva, M.; Herraiz, J. L.; Udías, J. M.; Miller, E.; Cox, B. T.; Treeby, B. E., Time domain reconstruction of sound speed and attenuation in ultrasound computed tomography using full wave inversion, J. Acoust. Soc. Am., 141, 1595-1604 (2017)
[54] Guasch, L.; Calderón Agudo, O.; Tang, M-X; Nachev, P.; Warner, M., Full-waveform inversion imaging of the human brain, npj Digit. Med., 3, 28 (2020)
[55] Barnett, A.; Greengard, L., A new integral representation for quasi-periodic scattering problems in two dimensions, BIT Numer. Math., 51, 67-90 (2011) · Zbl 1214.65061
[56] Bachmann, E.; Tromp, J., Source encoding for viscoacoustic ultrasound computed tomography, J. Acoust. Soc. Am., 147, 3221-3235 (2020)
[57] Margrave, G.; Yedlin, M.; Innanen, K., Full waveform inversion and the inverse Hessian, CREWES Research Report, vol 23, 1-13 (2011)
[58] Lou, Y.; Zhou, W.; Matthews, T. P.; Appleton, C. M.; Anastasio, M. A., Generation of anatomically realistic numerical phantoms for photoacoustic and ultrasonic breast imaging, J. Biomed. Opt., 22 (2017)
[59] Li, C.; Huang, L.; Duric, N.; Zhang, H.; Rowe, C., An improved automatic time-of-flight picker for medical ultrasound tomography, Ultrasonics, 49, 61-72 (2009)
[60] Coates, R. T.; Chapman, C. H., Ray perturbation theory and the Born approximation, Geophys. J. Int., 100, 379-392 (1990) · Zbl 0692.73030
[61] Treeby, B. E.; Cox, B. T., k-wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields, J. Biomed. Opt., 15 (2010)
[62] Treeby, B.; Cox, B.; Jaros, J., k-Wave: A Matlab Toolbox for the time-domain simulation of acoustic waves
[63] Pierce, A. D., Acoustics An Introduction to its Physical Principles and Applications (1981), MA: ASA Press, MA
[64] Huthwaite, P.; Simonetti, F., High-resolution imaging without iteration: a fast and robust method for breast ultrasound tomography, J. Acoust. Soc. Am., 130, 1721-1734 (2011)
[65] Hudson, J. A., Scattered waves in the coda of P, J. Geophys., 43, 359-374 (1977)
[66] Hudson, J. A.; Heritage, J. R., The use of the Born approximation in seismic scattering problems, Geophys. J. Int., 66, 221-240 (1981) · Zbl 0464.73131
[67] Sarajaervi, M.; Keers, H., Computation of ray-Born seismograms using isochrons, Geophysics, 83, T245-T256 (2018)
[68] Moser, T. J., Review of ray-Born forward modeling for migration and diffraction analysis, Stud. Geophys. Geod., 56, 411-432 (2012)
[69] Devaney, A. J., A filtered backpropagation algorithm for diffraction tomography, Ultrason. Imaging, 4, 336-350 (1982)
[70] Kak, C.; Slaney, M., Principles of Computerized Tomographic Reconstruction, 203-218 (1998), Piscataway, NJ: IEEE, Piscataway, NJ
[71] Simonetti, F.; Huang, L.; Duric, N.; Littrup, P., Diffraction and coherence in breast ultrasound tomography: a study with a toroidal array, Med. Phys., 36, 2955 (2009)
[72] Yun, X.; He, J.; Carevic, A.; Slapnicar, I.; Barlow, J.; Almekkawy, M., Reconstruction of ultrasound tomography for cancer detection using total least squares and conjugate gradient method (2018)
[73] Carevic; Yun, X.; Lee, G.; Slapnicar, I.; Abdou, A.; Barlow, J.; Almekkawy, M., Solving the ultrasound inverse scattering problem of inhomogeneous media using different approaches of total least squares algorithms (2018)
[74] Carevic, X. Y.; Almekkawy, M., Adaptive truncated total least square on distorted born iterative method in ultrasound inverse scattering problem (2019)
[75] Thierry, P.; Operto, S.; Lambaré, G., Fast 2D ray+Born migration/inversion in complex media, Geophysics, 64, 162-181 (1999)
[76] Lambaré, G.; Virieux, J.; Madariaga, R.; Jin, S., Iterative asymptotic inversion in the acoustic approximation, Geophysics, 57, 1138-1154 (1992)
[77] Lambare, G.; Operto, S.; Podvin, P.; Thierry, P., 3D ray+Born migration/inversion: Part 1. Theory, Geophysics, 68, 1348-1356 (2003)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.