Regularization in ultrasound tomography using projection-based regularized total least squares

References

• Guillermin R, Lasaygues P, Sessarego JP, et al. Inversion of synthetic and experimental acoustical scattering data for the comparison of two reconstruction methods employing the Born approximation. Ultrasonics. 2001;39(2):121–131. doi: 10.1016/S0041-624X(00)00054-8
   PubMed Web of Science ®Google Scholar
• Jovanovic I. Inverse problems in acoustic tomography [PhD thesis]. Ecole Polytechnique Federale de Lausanne; 2008.
   Google Scholar
• Duric N, Littrup P, Poulo L, et al. Detection of breast cancer with ultrasound tomography: first results with the computed ultrasound risk evaluation (cure) prototype. Med Phys. 2007;34(2):773–785. doi: 10.1118/1.2432161
   PubMed Web of Science ®Google Scholar
• Ozmen N. Ultrasound imaging methods for breast cancer detectionm [PhD thesis]. Delft, The Netherlands: Delft University of Technology; 2014.
   Google Scholar
• Gordon PB, Goldenberg SL. Malignant breast masses detected only by ultrasound. A retrospective review. Cancer. 1995;76(4):626–630. doi: 10.1002/1097-0142(19950815)76:4<626::AID-CNCR2820760413>3.0.CO;2-Z
   PubMed Web of Science ®Google Scholar
• Li C, Duric N, Littrup P, et al. In vivo breast sound-speed imaging with ultrasound tomography. Ultrasound Med Biol. 2009;35(10):1615–1628. doi: 10.1016/j.ultrasmedbio.2009.05.011
   PubMed Web of Science ®Google Scholar
• Lavarello R, Oelze M. A study on the reconstruction of moderate contrast targets using the distorted Born iterative method. IEEE Trans Ultrason Ferroelectr Freq Control. 2008;55(1):112–124. doi: 10.1109/TUFFC.2008.621
   PubMed Web of Science ®Google Scholar
• Norton SJ. The inverse-scattering problem and global convergence. J Acoust Soc Am. 2005;118(3):1534–1539. doi: 10.1121/1.1979407
   Web of Science ®Google Scholar
• Hohage T. On the numerical solution of a three-dimensional inverse medium scattering problem. Inverse Probl. 2001;17(6):1743–1763. doi: 10.1088/0266-5611/17/6/314
   Web of Science ®Google Scholar
• Lehman SK, Devaney AJ. Transmission mode time-reversal super-resolution imaging. J Acoust Soc Am. 2003;113(5):2742–2753. doi: 10.1121/1.1566975
   PubMed Web of Science ®Google Scholar
• Mojabi P. Ultrasound tomography: an inverse scattering approach [PhD thesis]. Canada: University of Manitoba; 2014.
   Google Scholar
• Haddadin OS, Ebbini ES. Imaging strongly scattering media using a multiple frequency distorted Born iterative method. IEEE Trans Ultrason Ferroelectr Freq Control. 1998;45(6):1485–1496. doi: 10.1109/58.738288
   PubMed Web of Science ®Google Scholar
• Haddadin OS, Ebbini ES. Ultrasonic focusing through inhomogeneous media by application of the inverse scattering problem. J Acoust Soc Am. 1998;104(1):313–325. doi: 10.1121/1.423291
   PubMed Web of Science ®Google Scholar
• Mojabi P, LoVetri J. Ultrasound tomography for simultaneous reconstruction of acoustic density, attenuation, and compressibility profiles. J Acoust Soc Am. 2015;137(4):1813–1825. doi: 10.1121/1.4913774
   PubMed Web of Science ®Google Scholar
• Wiskin J, Borup D, Johnson QS, et al. Full-wave, non-linear, inverse scattering. In: Acoustical imaging. Dordrecht: Springer; 2007. p. 183–193.
   Google Scholar
• Roger A. Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem. IEEE Trans Antennas Propag. 1981;29(2):232–238. doi: 10.1109/TAP.1981.1142588
   Web of Science ®Google Scholar
• Remis RF, Van den Berg P. On the equivalence of the Newton–Kantorovich and distorted Born methods. Inverse Probl. 2000;16(1):L1–L4. doi: 10.1088/0266-5611/16/1/101
   Web of Science ®Google Scholar
• Mast TD, Nachman AI, Waag RC. Focusing and imaging using eigenfunctions of the scattering operator. J Acoust Soc Am. 1997;102(2):715–725. doi: 10.1121/1.419898
   PubMed Web of Science ®Google Scholar
• Lin F, Nachman AI, Waag RC. Quantitative imaging using a time-domain eigenfunction method. J Acoust Soc Am. 2000;108(3):899–912. doi: 10.1121/1.1285919
   PubMed Web of Science ®Google Scholar
• Marmarelis VZ, Kim TS, Shehada RE. High resolution ultrasonic transmission tomography. Proc SPIE Med Imaging; San Diego, CA; Vol. 5035; 2003. p. 33–40.
   Google Scholar
• Birk M, Kretzek E, Figuli P, et al. High-speed medical imaging in 3D ultrasound computer tomography. IEEE Trans Parallel Distrib Syst. 2016;27(2):455–467. doi: 10.1109/TPDS.2015.2405508
   Web of Science ®Google Scholar
• Birk M, Koehler S, Balzer M, et al. FPGA-based embedded signal processing for 3D ultrasound computer tomography. Real Time Conference (RT), 2010 17th IEEE-NPSS; Lisbon. IEEE; 2010. p. 1–5.
   Google Scholar
• Ruiter NV, Göbel G, Berger L, et al. Realization of an optimized 3D USCT. Proc. SPIE; Lake Buena Vista, FL; Vol. 7968; 2011. p. 796805.
   Google Scholar
• Wiskin J, Borup D, Iuanow E, et al. 3-D nonlinear acoustic inverse scattering: algorithm and quantitative results. IEEE Trans Ultrason Ferroelectr Freq Control. 2017;64(8):1161–1174. doi: 10.1109/TUFFC.2017.2706189
   PubMed Web of Science ®Google Scholar
• Bernard S, Monteiller V, Komatitsch D, et al. Ultrasonic computed tomography based on full-waveform inversion for bone quantitative imaging. Phys Med Biol. 2017;62(17):7011–7035. doi: 10.1088/1361-6560/aa7e5a
   PubMed Web of Science ®Google Scholar
• Matthews TP, Wang K, Li C, et al. Regularized dual averaging image reconstruction for full-wave ultrasound computed tomography. IEEE Trans Ultrason Ferroelectr Freq Control. 2017;64(5):811–825. doi: 10.1109/TUFFC.2017.2682061
   PubMed Web of Science ®Google Scholar
• Pérez-Liva M, Herraiz J, Udías J, et al. Time domain reconstruction of sound speed and attenuation in ultrasound computed tomography using full wave inversion. J Acoust Soc Am. 2017;141(3):1595–1604. doi: 10.1121/1.4976688
   PubMed Web of Science ®Google Scholar
• Perez-Liva M, Herraiz JL, Udías JM, et al. Full-wave attenuation reconstruction in the time domain for ultrasound computed tomography. 2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI). IEEE; 2016. p. 710–713.
   Google Scholar
• Wang K, Matthews T, Anis F, et al. Waveform inversion with source encoding for breast sound speed reconstruction in ultrasound computed tomography. IEEE Trans Ultrason Ferroelectr Freq Control. 2015;62(3):475–493. doi: 10.1109/TUFFC.2014.006788
   PubMed Web of Science ®Google Scholar
• Chew WC, Wang YM. Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method. IEEE Trans Med Imaging. 1990;9(2):218–225. doi: 10.1109/42.56334
   PubMed Web of Science ®Google Scholar
• Lu C, Lin J, Chew W, et al. Image reconstruction with acoustic measurement using distorted Born iteration method. Ultrason Imaging. 1996;18(2):140–156. doi: 10.1177/016173469601800204
   PubMed Web of Science ®Google Scholar
• Liu C, Wang Y, Heng PA. A comparison of truncated total least squares with Tikhonov regularization in imaging by ultrasound inverse scattering. Phys Med Biol. 2003;48(15):2437–2451. doi: 10.1088/0031-9155/48/15/313
   PubMed Web of Science ®Google Scholar
• Lavarello RJ, Oelze ML. Density imaging using inverse scattering. J Acoust Soc Am. 2009;125(2):793–802. doi: 10.1121/1.3050249
   PubMed Web of Science ®Google Scholar
• Lavarello R, Oelze M. Density imaging using a multiple-frequency DBIM approach. IEEE Trans Ultrason Ferroelectr Freq Control. 2010;57(11):2471–2479. doi: 10.1109/TUFFC.2010.1713
   PubMed Web of Science ®Google Scholar
• Lavarello RJ, Oelze ML. Tomographic reconstruction of three-dimensional volumes using the distorted Born iterative method. IEEE Trans Med Imaging. 2009;28(10):1643–1653. doi: 10.1109/TMI.2009.2026274
   PubMed Web of Science ®Google Scholar
• Hansen PC. Regularization tools version 4.0 for Matlab 7.3. Numer Algorithms. 2007;46(2):189–194. doi: 10.1007/s11075-007-9136-9
   Web of Science ®Google Scholar
• Hansen PC. The truncated SVD as a method for regularization. BIT Numer Math. 1987;27(4):534–553. doi: 10.1007/BF01937276
   Web of Science ®Google Scholar
• Haddadin OS, Ebbini ES. Adaptive regularization of a distorted Born iterative algorithm for diffraction tomography. International Conference on Image Processing, 1996; Lausanne, Switzerland. Proceedings. Vol. 2; IEEE; 1996. p. 725–728.
   Google Scholar
• Carević A, Abdou A, Slapničar I, et al. Employing methods with generalized singular value decomposition for regularization in ultrasound tomography. Medical Imaging 2019: Ultrasonic Imaging and Tomography; Vol. 10955; International Society for Optics and Photonics; San Diego, CA; 2019. p. 1095509.
   Google Scholar
• Yun X, He J, Carevic A, et al. Reconstruction of ultrasound tomography for cancer detection using total least squares and conjugate gradient method. Medical Imaging 2018: Ultrasonic Imaging and Tomography; Vol. 10580; International Society for Optics and Photonics; 2018. p. 105800K.
   Google Scholar
• Fierro RD, Golub GH, Hansen PC, et al. Regularization by truncated total least squares. SIAM J Sci Comput. 1997;18(4):1223–1241. doi: 10.1137/S1064827594263837
   Web of Science ®Google Scholar
• Carević A, Yun X, Lee G, et al. Solving the ultrasound inverse scattering problem of inhomogeneous media using different approaches of total least squares algorithms. Medical Imaging 2018: Ultrasonic Imaging and Tomography; Vol. 10580; International Society for Optics and Photonics; 2018. p. 105800J.
   Google Scholar
• Golub GH, Heath M, Wahba G. Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics. 1979;21(2):215–223. doi: 10.1080/00401706.1979.10489751
   Web of Science ®Google Scholar
• Hansen PC, O'Leary DP. The use of the L-curve in the regularization of discrete ill-posed problems. SIAM J Sci Comput. 1993;14(6):1487–1503. doi: 10.1137/0914086
   Web of Science ®Google Scholar
• Lee G, Barlow JL. Two projection methods for regularized total least squares approximation. Linear Algebra Appl. 2014;461:18–41. doi: 10.1016/j.laa.2014.07.045
   Web of Science ®Google Scholar
• Wiskin J, Borup D, Johnson S, et al. Non-linear inverse scattering: high resolution quantitative breast tissue tomography. J Acoust Soc Am. 2012;131(5):3802–3813. doi: 10.1121/1.3699240
   PubMed Web of Science ®Google Scholar
• Chew WC. Waves and fields in inhomogeneous media. Piscataway (NJ): IEEE Press; 1995.
   Google Scholar
• Johnson SA, Tracy ML. Inverse scattering solutions by a sinc basis, multiple source, moment method – Part I: theory. Ultrason Imaging. 1983;5(4):361–375. doi: 10.1177/016173468300500406
   PubMed Web of Science ®Google Scholar
• Van Huffel S, Vandewalle J. The total least squares problem: computational aspects and analysis. Vol. 9. SIAM; 1991.
   Google Scholar
• Golub GH, Hansen PC, O'Leary DP. Tikhonov regularization and total least squares. SIAM J Matrix Anal Appl. 1999;21(1):185–194. doi: 10.1137/S0895479897326432
   Web of Science ®Google Scholar
• Renaut RA, Guo H. Efficient algorithms for solution of regularized total least squares. SIAM J Matrix Anal Appl. 2004;26(2):457–476. doi: 10.1137/S0895479802419889
   Web of Science ®Google Scholar
• Lou Y, Zhou W, Matthews TP, et al. Generation of anatomically realistic numerical phantoms for photoacoustic and ultrasonic breast imaging. J Biomed Opt. 2017;22(4):041015. doi: 10.1117/1.JBO.22.4.041015
   PubMed Web of Science ®Google Scholar
• Carević A, Yun X, Almekkawy M. Adaptive truncated total least squares on distorted born iterative method in ultrasound inverse scattering problem. Medical Imaging 2019: Ultrasonic Imaging and Tomography; International Society for Optics and Photonics; San Diego, CA; 2019.
   Google Scholar