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Iterative methods for solving coefficient inverse problems of wave tomography in models with attenuation. (English) Zbl 1357.92041


MSC:

92C55 Biomedical imaging and signal processing
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[1] Duric N, Littrup P, Li C, Roy O, Schmidt S, Janer R, Cheng X, Goll J, Rama O, Bey-Knight L and Greenway W 2012 Breast ultrasound tomography: bridging the gap to clinical practice Proc. SPIE8320 83200O
[2] Duric N, Littrup P, Poulo L, Babkin A, Pevzner R, Holsapple E, Rama O and Glide C 2007 Detection of breast cancer with ultrasound tomography: first results with the computed ultrasound risk evaluation (CURE) prototype Med. Phys.34 773–85
[3] Jiřík R, Peterlík I, Ruiter N, Fousek J, Dapp R, Zapf M and Jan J 2012 Sound-speed image reconstruction in sparse-aperture 3D ultrasound transmission tomography IEEE Trans. Ultrason. Ferroelectr. Freq. Control59 254–64
[4] Gemmeke H, Berger L, Birk M, Gobel G, Menshikov A, Tcherniakhovski D, Zapf M and Ruiter N V 2010 Hardware setup for the next generation of 3D ultrasound computer tomography IEEE Nuclear Science Symp. Conf. Record pp 2449–54
[5] Wiskin J, Borup D, Andre M, Johnson S, Greenleaf J, Parisky Y and Klock J 2013 Three-dimensional nonlinear inverse scattering: quantitative transmission algorithms, refraction corrected reflection, scanner design, and clinical results J. Acoust. Soc. Am.133 3229
[6] Wiskin J, Borup D T, Johnson S A and Berggren M 2012 Non-linear inverse scattering: high resolution quantitative breast tissue tomography J. Acoust. Soc. Am.131 3802–13
[7] Burov V A, Zotov D I and Rumyantseva O D 2014 Reconstruction of spatial distributions of sound velocity and absorption in soft biological tissues using model ultrasonic tomographic data Acoust. Phys.60 479–91
[8] Burov V A, Zotov D I and Rumyantseva O D 2015 Reconstruction of the sound velocity and absorption spatial distributions in soft biological tissue phantoms from experimental ultrasound tomography data Acoust. Phys.61 231–48
[9] Goncharsky A V and Romanov S Y 2013 Supercomputer technologies in inverse problems of ultrasound tomography Inverse Problems29 075004 · Zbl 1278.65144
[10] Huang L and Quan Y 2007 Sound-speed tomography using first-arrival transmission ultrasound for a ring array Proc. SPIE6513 651306
[11] Huang L and Quan Y 2007 Ultrasound pulse-echo imaging using the split-step Fourier propagator Proc. SPIE6513 651305
[12] Glide-Hurst C K, Duric N and Littrup P 2008 Volumetric breast density evaluation from ultrasound tomography images Med. Phys.35 3988–97
[13] Ramm A G 1992 Multidimensional Inverse Scattering Problems (London: Longmans Green) · Zbl 0746.35056
[14] Lavrentiev M M, Romanov V G and Shishatskii S P 1986 Ill-Posed Problems of Mathematical Physics and Analysis (Providence, RI: American Mathematical Society)
[15] Bakushinsky A B and Goncharsky A V 1994 Ill-Posed Problems. Theory and Applications (Dordrect: Kluwer)
[16] Romanov V G and Kabanikhin S I 1994 Inverse Problems for Maxwell’s Equations (Utrecht: VSP) · Zbl 0853.35001
[17] Goncharskii A V, Ovchinnikov S L and Romanov S Y 2010 On the one problem of wave diagnostic Moscow Univ. Comput. Math. Cybern.34 1–7 · Zbl 1402.65142
[18] Lavarello R J and Oelze M L 2009 Tomographic reconstruction of three-dimensional volumes using the distorted born iterative method IEEE Trans. Med. Imaging28 1643–53
[19] Goncharskii A V and Romanov S Y 2012 Two approaches to the solution of coefficient inverse problems for wave equations Comput. Math. Math. Phys.52 245–51
[20] Chavent G 1970 Deux resultats sur le probleme inverse dans les equations aux derivees partielles du deuxieme ordre an t et sur l’unicite de la solution du probleme inverse de la diffusion C. R. Acad. Sci.270 25–8
[21] Natterer F 1996 Numerical solution of bilinear inverse problems p 24 Technical Report 19/96 N http://wwwmath.uni-muenster.de/num/Preprints/1997/natterer_3/paper.pdf
[22] Beilina L, Klibanov M V and Kokurin M Y 2010 Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem J. Math. Sci.167 279–325 · Zbl 1286.65147
[23] Natterer F 2008 Acoustic mammography in the time domain p 7 Technical Reporthttp://wwwmath.uni-muenster.de/num/prep.neu/files/80.pdf
[24] Goncharsky A V and Romanov S Y 2014 Inverse problems of ultrasound tomography in models with attenuation Phys. Med. Biol.59 1979–2004
[25] Andre M, Wiskin J, Borup D, Johnson S, Ojeda-Fournier H and Olson L 2012 Quantitative volumetric breast imaging with 3D inverse scatter computed tomography Conf. Proc. IEEE Engineering in Medicine and Biology Society pp 1110–3
[26] Cray B A 2002 Acoustic vector sensor US Patent Specification 6370084 B1
[27] Berliner M J, Lindberg J F and Wilson O B 1996 Acoustic particle velocity sensors: design, performance, and applications J. Acoust. Soc. Am.100 3478–9
[28] Shipps J C and Deng K 2003 A miniature vector sensor for line array applications OCEANS Proc.5 2367–70
[29] Ladyzhenskaya O A 1985 Boundary Value Problems of Mathematical Physics (Berlin: Springer)
[30] Ladyzhenskaya O A 1953 The Mixed Problem for a Hyperbolic Equation (Moscow: Goztekhizdat)
[31] Evans L C 1998 (Partial Differential Equations, Graduate Studies in Mathematics vol 19) (Providence, RI: American Mathematical Society)
[32] Maia N M, Silva J M and Ribeiro A M 1998 On a general model for damping J. Sound Vib.218 749–67
[33] Gaul L 1999 The influence of damping on waves and vibrations Mech. Syst. Signal Process13 1–30
[34] Szabo T 1994 Time domain wave equations for lossy media obeying a frequency power law J. Acoust. Soc. Am.96 491–500
[35] Chen W and Holm S 2003 Modified Szabo’s wave equation models for lossy media obeying frequency power law J. Acoust. Soc. Am.114 2570–4
[36] Natterer F, Sielschott H, Dorn O, Dierkes T and Palamodov V 2002 Fréchet derivatives for some bilinear inverse problems SIAM J. Appl. Math.62 2092–113 · Zbl 1010.35115
[37] Natterer F 2015 Sonic imaging Handbook of Mathematical Methods in Imaging (New York: Springer) pp 1253–78
[38] Beilina L and Klibanov M V 2012 Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems (New York: Springer) · Zbl 1255.65168
[39] Goncharsky A V, Romanov S Y and Seryozhnikov S Y 2014 Inverse problems of 3D ultrasonic tomography with complete and incomplete range data Wave Motion51 389–404
[40] Goncharsky A V, Romanov S Y and Seryozhnikov S Y 2016 A computer simulation study of soft tissue characterization using low-frequency ultrasonic tomography Ultrasonics67 136–50
[41] Kirsch A and Rieder A 2016 Inverse problems for abstract evolution equations with applications in electrodynamics and elasticity Inverse Problems32 085001 · Zbl 1416.65164
[42] Klibanov M V and Timonov A 2004 Carleman Estimates for Coefficient Inverse Problems and Numerical Applications (Utrecht: VSP) · Zbl 1069.65106
[43] Hendee W R and Ritenour E R 2002 Medical Imaging Physics (New York: Wiley)
[44] Natterer F 2011 Possibilities and limitations of time domain wave equation imaging (Contemporary Mathematics vol 559) (Providence, RI: American Mathematical Society) pp 151–62 · Zbl 1242.65194
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