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Sound speed uncertainty in acousto-electric tomography. (English) Zbl 1479.35950

MSC:

35R30 Inverse problems for PDEs
35L15 Initial value problems for second-order hyperbolic equations
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
92C55 Biomedical imaging and signal processing

Software:

SyFi; FEniCS
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Full Text: DOI arXiv

References:

[1] Adams, R. A.; Fournier, J. J., Sobolev Spaces, vol 140 (2003), Amsterdam: Elsevier, Amsterdam · Zbl 1098.46001
[2] Adesokan, B. J.; Jensen, B.; Jin, B.; Knudsen, K., Acousto-electric tomography with total variation regularization, Inverse Problems, 35 (2019) · Zbl 1410.65429
[3] Adesokan, B. J.; Knudsen, K.; Krishnan, V. P.; Roy, S., A fully non-linear optimization approach to acousto-electric tomography, Inverse Problems, 34 (2018) · Zbl 1397.78053
[4] Alberti, G. S.; Capdeboscq, Y., Lectures on Elliptic Methods for Hybrid Inverse Problems, vol 25 (2018), Paris: Société Mathématique de France, Paris · Zbl 1391.35002
[5] Ammari, H.; Bonnetier, E.; Capdeboscq, Y.; Tanter, M.; Fink, M., Electrical impedance tomography by elastic deformation, SIAM J. Appl. Math., 68, 1557-1573 (2008) · Zbl 1156.35101
[6] Bal, G.; Bonnetier, E.; Monard, F.; Triki, F., Inverse diffusion from knowledge of power densities, Inverse Problems Imaging, 7, 353-375 (2013) · Zbl 1267.35249
[7] Bal, G.; Guo, C.; Monard, F., Imaging of anisotropic conductivities from current densities in two dimensions, SIAM J. Imaging Sci., 7, 2538-2557 (2014) · Zbl 1361.94005
[8] Bal, G.; Naetar, W.; Scherzer, O.; Schotland, J., The Levenberg-Marquardt iteration for numerical inversion of the power density operator, J. Inverse Ill-Posed Problems, 21, 265-280 (2013) · Zbl 1273.35307
[9] Barrett, R., Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, vol 43 (1994), Philadelphia, PA: SIAM, Philadelphia, PA
[10] Capdeboscq, Y.; Fehrenbach, J.; de Gournay, F.; Kavian, O., Imaging by modification: numerical reconstruction of local conductivities from corresponding power density measurements, SIAM J. Imaging Sci., 2, 1003-1030 (2009) · Zbl 1180.35549
[11] Cheney, M.; Isaacson, D.; Newell, J. C., Electrical impedance tomography, SIAM Rev., 41, 85-101 (1999) · Zbl 0927.35130
[12] Duck, F. A., Physical Properties of Tissues: A Comprehensive Reference Book (2013), London: Academic, London
[13] Engl, H. W.; Hanke, M.; Neubauer, A., Regularization of Inverse Problems (1996), Dordrecht: Kluwer, Dordrecht · Zbl 0859.65054
[14] Evans, L. C., Partial Differential Equations, vol 19 (2010), Providence, RI: American Mathematical Society, Providence, RI
[15] Harhanen, L.; Hyvönen, N.; Majander, H.; Staboulis, S., Edge-enhancing reconstruction algorithm for three-dimensional electrical impedance tomography, SIAM J. Sci. Comput., 37, B60-B78 (2015) · Zbl 1325.78007
[16] Holder, D. S., Electrical Impedance Tomography: Methods History and Applications (2010), Bristol: Institute of Physics Publishing, Bristol
[17] Hubmer, S.; Knudsen, K.; Li, C.; Sherina, E., Limited-angle acousto-electrical tomography, Inverse Problems Sci. Eng., 27, 1298-1317 (2018) · Zbl 1466.92088
[18] Jensen, B.; Kirkeby, A.; Knudsen, K., Feasibility of acousto-electric tomography (2019)
[19] Jossinet, J.; Lavandier, B.; Cathignol, D., The phenomenology of acousto-electric interaction signals in aqueous solutions of electrolytes, Ultrasonics, 36, 607-613 (1998)
[20] Kirsch, A., An Introduction to the Mathematical Theory of Inverse Problems (1996), New York: Springer, New York · Zbl 0865.35004
[21] Kuchment, P.; Kunyansky, L., Synthetic focusing in ultrasound modulated tomography, Inverse Problems Imaging, 4, 665-673 (2010) · Zbl 1286.44002
[22] Kuchment, P.; Kunyansky, L., 2D and 3D reconstructions in acousto-electric tomography, Inverse Problems, 27 (2011) · Zbl 1217.35211
[23] Lavandier, B.; Jossinet, J.; Cathignol, D., Experimental measurement of the acousto-electric interaction signal in saline solution, Ultrasonics, 38, 929-936 (2000)
[24] Li, C.; Karamehmedović, M.; Sherina, E.; Knudsen, K., Levenberg-Marquardt algorithm for acousto-electric tomography based on the complete electrode model (2019)
[25] Logg, A.; Mardal, K-A; Wells, G., Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book, vol 84 (2012), Berlin: Springer, Berlin · Zbl 1247.65105
[26] Malone, E.; Jehl, M.; Arridge, S.; Betcke, T.; Holder, D., Stroke type differentiation using spectrally constrained multifrequency EIT: evaluation of feasibility in a realistic head model, Physiol. Meas., 35, 1051-1066 (2014)
[27] Monard, F.; Bal, G., Inverse anisotropic diffusion from power density measurements in two dimensions, Inverse Problems, 28 (2012) · Zbl 1250.35187
[28] Oksanen, L.; Uhlmann, G., Photoacoustic and thermoacoustic tomography with an uncertain wave speed, Math. Res. Lett., 21, 1199-1214 (2014) · Zbl 1402.35314
[29] Reinartz, S. D., EIT monitors valid and robust regional ventilation distribution in pathologic ventilation states in porcine study using differential dualenergy-CT (ΔDECT), Sci. Rep., 9, 9796 (2019)
[30] Reiser, I.; Edwards, A.; Nishikawa, R. M., Validation of a power-law noise model for simulating small-scale breast tissue, Phys. Med. Biol., 58, 6011 (2013)
[31] Roy, S.; Borzì, A., A new optimization approach to sparse reconstruction of log-conductivity in acousto-electric tomography, SIAM J. Imaging Sci., 11, 1759-1784 (2018) · Zbl 1401.35351
[32] Tick, J.; Pulkkinen, A.; Tarvainen, T., Modelling of errors due to speed of sound variations in photoacoustic tomography using a Bayesian framework, Biomed. Phys. Eng. Express, 6 (2019)
[33] Zhang, H.; Wang, L. V., Acousto-electric tomography, Prog. Biomed. Opt. Imaging, 5, 145-149 (2004)
[34] Zou, Y.; Guo, Z., A review of electrical impedance techniques for breast cancer detection, Med. Eng. Phys., 25, 79-90 (2003)
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