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Multi-wave imaging in attenuating media
1. | Department of Mathematics, Purdue University, West Lafayette, IN 47906, United States |
References:
[1] |
H. Ammari, E. Bretin, J. Garnier and A. Wahab, Time reversal in attenuating acoustic media, Contemp. Math., 548 (2011), 151-163.
doi: 10.1090/conm/548/10841. |
[2] |
G. Bal, K. Ren, G. Uhlmann and T. Zhou, Quantitative thermo-acoustics and related problems, Inverse Problems, 27 (2011), 055007.
doi: 10.1088/0266-5611/27/5/055007. |
[3] |
P. Burgholzer, F. Camacho-Gonzales, D. Sponseiler, G. Mayer and G. Hendorfer, Information changes and time reversal for diffusion-related periodic fields, Proc. SPIE, 7177 (2009), 717723.
doi: 10.1117/12.809074. |
[4] |
B. T. Cox, J. G. Laufer and P. C. Beard, The challenges for photoacoustic imaging, Proc. SPIE, 7177 (2009), 717713.
doi: 10.1117/12.806788. |
[5] |
X. L. Deán-Ben, D. Razansky and V. Ntziachristos, The effects of attenuation in optoacoustic signals, Phys. Med. Biol., 56 (2011), 6129-6148. |
[6] |
D. Finch, S. K. Patch and Rakesh, Determining a function from its mean values over a family of spheres, SIAM J. Math. Anal., 35 (2004), 1213-1240.
doi: 10.1137/S0036141002417814. |
[7] |
Y. Hristova, Time reversal in thermoacoustic tomography - an error estimate, Inverse Problems, 25 (2009), 055008.
doi: 10.1088/0266-5611/25/5/055008. |
[8] |
Y. Hristova, P. Kuchment and L. Nyugen, On reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media, Inverse Problems, 24 (2008), 055006.
doi: 10.1088/0266-5611/24/5/055006. |
[9] |
X. Jin, C. Li and L. Wang, Effects of acoustic heterogeneities on transcranial brain imaging with microwave-induced thermoacoustic tomography, Med. Phys., 35 (2008), 3205-3214.
doi: 10.1118/1.2938731. |
[10] |
K. Kalimeris and O. Scherzer, Photoacoustic imaging in attenuating acoustic media based on strongly causal models, Math. Meth. Appl. Sci., to appear.
doi: 10.1002/mma.2756. |
[11] |
R. Kowar, Integral equation models for thermoacoustic imaging of acoustic dissipative tissue, Inverse Problems, 26 (2010), 095005.
doi: 10.1088/0266-5611/26/9/095005. |
[12] |
R. Kowar, O. Scherzer and X. Bonnefond, Causality analysis of frequency-dependent wave attenuation, Math. Meth. in Appl. Sci., 34 (2011), 108-124.
doi: 10.1002/mma.1344. |
[13] |
P. Kuchment and L. Kunyansky, Mathematics of thermoacoustic tomography, Euro. J. Appl. Math., 19 (2008), 191-224.
doi: 10.1017/S0956792508007353. |
[14] |
I. Lasiecka, J. L. Lions and R. Triggiani, Nonhomogeneous boundary value problems for second order hyperbolic operators, J. Math. Pures Appl., 65 (1986), 149-192. |
[15] |
D. Modgil, M. Anastasio and P. J. La Rivière, Photoacoustic image reconstruction in an attenuating medium using singular value decomposition, Proc. SPIE, 7177 (2009), 71771B. |
[16] |
S. K. Patch and M. Haltmeier, Thermoacoustic tomography - ultrasound attenuation effects, IEEE Nucl. Sci. Symp. Conf. Rec., 4 (2006), 2604-2606. |
[17] |
J. Qian, P. Stefanov, G. Uhlmann and H. Zhao, An effecient Neumann-series based algorithm for thermoacoustic and photoacoustic tomography with variable sound speed, SIAM J. Imaging Sciences, 4 (2011), 850-883.
doi: 10.1137/100817280. |
[18] |
M. Reed and B. Simon, Methods of Modern Mathematical Physics, volume 2, Academic Press, 1975. |
[19] |
P. J. La Rivière, J. Zhang and M. Anastasio, Image reconstruction in optoacoustic tomography for dispersive acoustic media, Optics Letters, 31 (2006), 781-783. |
[20] |
H. Roitner and P. Burgholzer, Effecient modeling and compensation of ultrasound attenuation losses in photoacoustic imaging, Inverse Problems, 27 (2011), 015003.
doi: 10.1088/0266-5611/27/1/015003. |
[21] |
P. Stefanov and G. Uhlmann, Thermoacoustic tomography with variable sound speed, Inverse Problems, 25 (2009), 075011.
doi: 10.1088/0266-5611/25/7/075011. |
[22] |
D. Tataru, Unqiue continuation for operators with partially analytic coefficients, J. Math. Pures Appl., 78 (1999), 505-521.
doi: 10.1016/S0021-7824(99)00016-1. |
[23] |
M. Taylor, Pseudodifferential Operators, Princeton University Press, 1981. |
[24] |
J. Tittlefitz, Thermoacoustic tomography in elastic media, Inverse Problems, 28 (2012), 055004.
doi: 10.1088/0266-5611/28/5/055004. |
[25] |
B. Treeby, E. Zhang and B. T. Cox, Photoacoustic tomography in absorbing acoustic media using time reversal, Inverse Problems, 26 (2010), 115003.
doi: 10.1088/0266-5611/26/11/115003. |
show all references
References:
[1] |
H. Ammari, E. Bretin, J. Garnier and A. Wahab, Time reversal in attenuating acoustic media, Contemp. Math., 548 (2011), 151-163.
doi: 10.1090/conm/548/10841. |
[2] |
G. Bal, K. Ren, G. Uhlmann and T. Zhou, Quantitative thermo-acoustics and related problems, Inverse Problems, 27 (2011), 055007.
doi: 10.1088/0266-5611/27/5/055007. |
[3] |
P. Burgholzer, F. Camacho-Gonzales, D. Sponseiler, G. Mayer and G. Hendorfer, Information changes and time reversal for diffusion-related periodic fields, Proc. SPIE, 7177 (2009), 717723.
doi: 10.1117/12.809074. |
[4] |
B. T. Cox, J. G. Laufer and P. C. Beard, The challenges for photoacoustic imaging, Proc. SPIE, 7177 (2009), 717713.
doi: 10.1117/12.806788. |
[5] |
X. L. Deán-Ben, D. Razansky and V. Ntziachristos, The effects of attenuation in optoacoustic signals, Phys. Med. Biol., 56 (2011), 6129-6148. |
[6] |
D. Finch, S. K. Patch and Rakesh, Determining a function from its mean values over a family of spheres, SIAM J. Math. Anal., 35 (2004), 1213-1240.
doi: 10.1137/S0036141002417814. |
[7] |
Y. Hristova, Time reversal in thermoacoustic tomography - an error estimate, Inverse Problems, 25 (2009), 055008.
doi: 10.1088/0266-5611/25/5/055008. |
[8] |
Y. Hristova, P. Kuchment and L. Nyugen, On reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media, Inverse Problems, 24 (2008), 055006.
doi: 10.1088/0266-5611/24/5/055006. |
[9] |
X. Jin, C. Li and L. Wang, Effects of acoustic heterogeneities on transcranial brain imaging with microwave-induced thermoacoustic tomography, Med. Phys., 35 (2008), 3205-3214.
doi: 10.1118/1.2938731. |
[10] |
K. Kalimeris and O. Scherzer, Photoacoustic imaging in attenuating acoustic media based on strongly causal models, Math. Meth. Appl. Sci., to appear.
doi: 10.1002/mma.2756. |
[11] |
R. Kowar, Integral equation models for thermoacoustic imaging of acoustic dissipative tissue, Inverse Problems, 26 (2010), 095005.
doi: 10.1088/0266-5611/26/9/095005. |
[12] |
R. Kowar, O. Scherzer and X. Bonnefond, Causality analysis of frequency-dependent wave attenuation, Math. Meth. in Appl. Sci., 34 (2011), 108-124.
doi: 10.1002/mma.1344. |
[13] |
P. Kuchment and L. Kunyansky, Mathematics of thermoacoustic tomography, Euro. J. Appl. Math., 19 (2008), 191-224.
doi: 10.1017/S0956792508007353. |
[14] |
I. Lasiecka, J. L. Lions and R. Triggiani, Nonhomogeneous boundary value problems for second order hyperbolic operators, J. Math. Pures Appl., 65 (1986), 149-192. |
[15] |
D. Modgil, M. Anastasio and P. J. La Rivière, Photoacoustic image reconstruction in an attenuating medium using singular value decomposition, Proc. SPIE, 7177 (2009), 71771B. |
[16] |
S. K. Patch and M. Haltmeier, Thermoacoustic tomography - ultrasound attenuation effects, IEEE Nucl. Sci. Symp. Conf. Rec., 4 (2006), 2604-2606. |
[17] |
J. Qian, P. Stefanov, G. Uhlmann and H. Zhao, An effecient Neumann-series based algorithm for thermoacoustic and photoacoustic tomography with variable sound speed, SIAM J. Imaging Sciences, 4 (2011), 850-883.
doi: 10.1137/100817280. |
[18] |
M. Reed and B. Simon, Methods of Modern Mathematical Physics, volume 2, Academic Press, 1975. |
[19] |
P. J. La Rivière, J. Zhang and M. Anastasio, Image reconstruction in optoacoustic tomography for dispersive acoustic media, Optics Letters, 31 (2006), 781-783. |
[20] |
H. Roitner and P. Burgholzer, Effecient modeling and compensation of ultrasound attenuation losses in photoacoustic imaging, Inverse Problems, 27 (2011), 015003.
doi: 10.1088/0266-5611/27/1/015003. |
[21] |
P. Stefanov and G. Uhlmann, Thermoacoustic tomography with variable sound speed, Inverse Problems, 25 (2009), 075011.
doi: 10.1088/0266-5611/25/7/075011. |
[22] |
D. Tataru, Unqiue continuation for operators with partially analytic coefficients, J. Math. Pures Appl., 78 (1999), 505-521.
doi: 10.1016/S0021-7824(99)00016-1. |
[23] |
M. Taylor, Pseudodifferential Operators, Princeton University Press, 1981. |
[24] |
J. Tittlefitz, Thermoacoustic tomography in elastic media, Inverse Problems, 28 (2012), 055004.
doi: 10.1088/0266-5611/28/5/055004. |
[25] |
B. Treeby, E. Zhang and B. T. Cox, Photoacoustic tomography in absorbing acoustic media using time reversal, Inverse Problems, 26 (2010), 115003.
doi: 10.1088/0266-5611/26/11/115003. |
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