Abstract

An image reconstruction formula is presented for photoacoustic computed tomography that accounts for conversion between longitudinal and shear waves in a planar-layered acoustic medium. We assume the optical absorber that produces the photoacoustic wave field is embedded in a single fluid layer and any elastic solid layers present are separated by one or more fluid layers. The measurement aperture is assumed to be planar. Computer simulation studies are conducted to demonstrate and investigate the proposed reconstruction formula.

© 2011 Optical Society of America

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  1. L. V. Wang, “Prospects of photoacoustic tomography,” Med. Phys. 35, 5758–5767 (2008).
    [CrossRef]
  2. M. Xu and L. V. Wang, “Biomedical photoacoustics,” Rev. Sci. Instrum. 77, 041101 (2006).
    [CrossRef]
  3. A. A. Oraevsky and A. A. Karabutov, “Optoacoustic tomography,” in Biomedical Photonics Handbook, T.Vo-Dinh, ed. (CRC Press, 2003).
  4. L.Wang, ed., Photoacoustic Imaging and Spectroscopy (CRC, 2009).
    [CrossRef]
  5. W. Joines, R. Jirtle, M. Rafal, and D. Schaeffer, “Microwave power absorption differences between normal and malignant tissue,” Int. J. Radiat. Oncol. Biol. Phys. 6, 681–687 (1980).
    [CrossRef] [PubMed]
  6. W. Cheong, S. Prahl, and A. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
    [CrossRef]
  7. V. Ntziachristos and D. Razansky, “Molecular imaging by means of multispectral optoacoustic tomography (MSOT),” Chem. Rev. 110, 2783–2794 (2010).
    [CrossRef] [PubMed]
  8. R. Kruger, D. Reinecke, and G. Kruger, “Thermoacoustic computed tomography—technical considerations,” Med. Phys. 26, 1832–1837 (1999).
    [CrossRef] [PubMed]
  9. M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltauf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl. 20, 1663–1673 (2004).
    [CrossRef]
  10. P. Ephrat, L. Keenliside, A. Seabrook, F. S. Prato, and J. J. L. Carson, “Three-dimensional photoacoustic imaging by sparse-array detection and iterative image reconstruction,” J. Biomed. Opt. 13, 054052 (2008).
    [CrossRef] [PubMed]
  11. B. T. Cox, S. R. Arridge, K. P. Köstli, and P. C. Beard, “Two-dimensional quantitative photoacoustic image reconstruction of absorption distributions in scattering media by use of a simple iterative method,” Appl. Opt. 45, 1866–1875 (2006).
    [CrossRef] [PubMed]
  12. K. Wang, S. Ermilov, R. Su, H. Brecht, A. Oraevsky, and M. Anastasio, “An imaging model incorporating ultrasonic transducer properties for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 30, 203–214 (2011).
    [CrossRef]
  13. M. A. Anastasio, J. Zhang, D. Modgil, and P. J. L. Riviere, “Application of inverse source concepts to photoacoustic tomography,” Inverse Probl. 23, S21–S35 (2007).
    [CrossRef]
  14. L. A. Kunyansky, “Explicit inversion formulae for the spherical mean radon transform,” Inverse Probl. 23, 373–383(2007).
    [CrossRef]
  15. D. Finch, M. Haltmeier, and Rakesh, “Inversion of spherical means and the wave equation in even dimensions,” SIAM J. Appl. Math. 68, 392–412 (2007).
    [CrossRef]
  16. M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E 71, 016706 (2005).
    [CrossRef]
  17. D. Finch, S. Patch, and Rakesh, “Determining a function from its mean values over a family of spheres,” SIAM J. Math. Anal. 35, 1213–1240 (2004).
    [CrossRef]
  18. Y. Xu, D. Feng, and L. V. Wang, “Exact frequency-domain reconstruction for thermoacoustic tomography: I. Planar geometry,” IEEE Trans. Med. Imaging 21, 823–828 (2002).
    [CrossRef] [PubMed]
  19. K. P. Köstli, M. Frenz, H. Bebie, and H. P. Weber, “Temporal backward projection of optoacoustic pressure transients using Fourier transform methods,” Phys. Med. Biol. 46, 1863–1872(2001).
    [CrossRef] [PubMed]
  20. R. A. Kruger, P. Liu, R. Fang, and C. Appledorn, “Photoacoustic ultrasound (PAUS) reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
    [CrossRef] [PubMed]
  21. Y. Xu and L. V. Wang, “Effects of acoustic heterogeneity in breast thermoacoustic tomography,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 1134–1146 (2003).
    [CrossRef] [PubMed]
  22. M. A. Anastasio, J. Zhang, X. Pan, Y. Zou, G. Keng, and L. V. Wang, “Half-time image reconstruction in thermoacoustic tomography,” IEEE Trans. Med. Imaging 24, 199–210 (2005).
    [CrossRef] [PubMed]
  23. P. J. La Riviere, J. Zhang, and M. A. Anastasio, “Image reconstruction in optoacoustic tomography for dispersive acoustic media,” Opt. Lett. 31, 781–783 (2006).
    [CrossRef] [PubMed]
  24. B. Treeby, E. Zhang, and B. Cox, “Photoacoustic tomography in absorbing acoustic media using time reversal,” Inverse Probl. 26, 115003 (2010).
    [CrossRef]
  25. L. Wang and X. Yang, “Boundary conditions in photoacoustic tomography and image reconstruction,” J. Biomed. Opt. 12, 014027 (2007).
    [CrossRef] [PubMed]
  26. R. W. Schoonover and M. A. Anastasio, “Image reconstruction in photoacoustic tomography involving layered acoustic media,” J. Opt. Soc. Am. A 28, 1114–1120 (2011).
    [CrossRef]
  27. D. Modgil, M. A. Anastasio, and P. J. L. Rivière, “Image reconstruction in photoacoustic tomography with variable speed of sound using a higher-order geometrical acoustics approximation,” J. Biomed. Opt. 15, 021308 (2010).
    [CrossRef] [PubMed]
  28. M. Agranovsky and P. Kuchment, “Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed,” Inverse Probl. 23, 2089–2102 (2007).
    [CrossRef]
  29. X. Jin and L. V. Wang, “Thermoacoustic tomography with correction for acoustic speed variations,” Phys. Med. Biol. 51, 6437–6448 (2006).
    [CrossRef] [PubMed]
  30. R. Willemink, S. Manohar, Y. Purwar, C. Slump, F. van der Heijden, and T. van Leeuwen, “Imaging of acoustic attenuation and speed of sound maps using photoacoustic measurements,” Proc. SPIE 6920, 692013 (2008).
    [CrossRef]
  31. Y. Hristova, P. Kuchment, and L. Nguyen, “Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media,” Inverse Probl. 24, 055006 (2008).
    [CrossRef]
  32. P. Stefanov and G. Uhlmann, “Thermoacoustic tomography with variable sound speed,” Inverse Probl. 25, 075011 (2009).
    [CrossRef]
  33. X. Yang and L. V. Wang, “Monkey brain cortex imaging by photoacoustic tomography,” J. Biomed. Opt. 13, 044009 (2008).
    [CrossRef] [PubMed]
  34. X. Jin, C. Li, and L. V. Wang, “Effects of acoustic heterogeneities on transcranial brain imaging with microwave-induced thermoacoustic tomography,” Med. Phys. 35, 3205–3214 (2008).
    [CrossRef] [PubMed]
  35. F. Fry and J. Barger, “Acoustical properties of the human skull,” J. Acoust. Soc. Am. 63, 1576–1590 (1978).
    [CrossRef] [PubMed]
  36. A. Yousefi, D. Goertz, and K. Hynynen, “Transcranial shear-mode ultrasound: assessment of imaging performance and excitation techniques,” IEEE Trans. Med. Imaging 28, 763–774(2009).
    [CrossRef] [PubMed]
  37. M. Hayner and K. Hynynen, “Numerical analysis of ultrasonic transmission and absorption of oblique plane waves through the human skull,” J. Acoust. Soc. Am. 110, 3319–3330 (2001).
    [CrossRef]
  38. S. Baikov, A. Molotilov, and V. Svet, “Physical and technological aspects of ultrasonic imaging of brain structures through thick skull bones: 1. theoretical and model studies,” Acoust. Phys. 49, 276–284 (2003).
    [CrossRef]
  39. M. Haltmeier, O. Scherzer, and G. Zangerl, “A reconstruction algorithm for photoacoustic imaging based on the nonuniform FFT,” IEEE Trans. Med. Imaging 28, 1727–1735 (2009).
    [CrossRef] [PubMed]
  40. P. M. Morse and K. U. Ingard, Theoretical Acoustics (Princeton Univ. Press, 1986).
  41. W. C. Chew, Waves and Fields in Inhomogeneous Media (Springer, 1995).
  42. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).
  43. K. Graff, Wave Motion in Elastic Solids (Dover, 1975).
  44. H. Schmidt and F. Jensen, “A full wave solution for propagation in multilayered viscoelastic media with application to Gaussian beam reflection at fluid–solid interfaces,” J. Acoust. Soc. Am. 77, 813–825 (1985).
    [CrossRef]

2011 (2)

K. Wang, S. Ermilov, R. Su, H. Brecht, A. Oraevsky, and M. Anastasio, “An imaging model incorporating ultrasonic transducer properties for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 30, 203–214 (2011).
[CrossRef]

R. W. Schoonover and M. A. Anastasio, “Image reconstruction in photoacoustic tomography involving layered acoustic media,” J. Opt. Soc. Am. A 28, 1114–1120 (2011).
[CrossRef]

2010 (3)

D. Modgil, M. A. Anastasio, and P. J. L. Rivière, “Image reconstruction in photoacoustic tomography with variable speed of sound using a higher-order geometrical acoustics approximation,” J. Biomed. Opt. 15, 021308 (2010).
[CrossRef] [PubMed]

B. Treeby, E. Zhang, and B. Cox, “Photoacoustic tomography in absorbing acoustic media using time reversal,” Inverse Probl. 26, 115003 (2010).
[CrossRef]

V. Ntziachristos and D. Razansky, “Molecular imaging by means of multispectral optoacoustic tomography (MSOT),” Chem. Rev. 110, 2783–2794 (2010).
[CrossRef] [PubMed]

2009 (3)

P. Stefanov and G. Uhlmann, “Thermoacoustic tomography with variable sound speed,” Inverse Probl. 25, 075011 (2009).
[CrossRef]

A. Yousefi, D. Goertz, and K. Hynynen, “Transcranial shear-mode ultrasound: assessment of imaging performance and excitation techniques,” IEEE Trans. Med. Imaging 28, 763–774(2009).
[CrossRef] [PubMed]

M. Haltmeier, O. Scherzer, and G. Zangerl, “A reconstruction algorithm for photoacoustic imaging based on the nonuniform FFT,” IEEE Trans. Med. Imaging 28, 1727–1735 (2009).
[CrossRef] [PubMed]

2008 (6)

R. Willemink, S. Manohar, Y. Purwar, C. Slump, F. van der Heijden, and T. van Leeuwen, “Imaging of acoustic attenuation and speed of sound maps using photoacoustic measurements,” Proc. SPIE 6920, 692013 (2008).
[CrossRef]

Y. Hristova, P. Kuchment, and L. Nguyen, “Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media,” Inverse Probl. 24, 055006 (2008).
[CrossRef]

X. Yang and L. V. Wang, “Monkey brain cortex imaging by photoacoustic tomography,” J. Biomed. Opt. 13, 044009 (2008).
[CrossRef] [PubMed]

X. Jin, C. Li, and L. V. Wang, “Effects of acoustic heterogeneities on transcranial brain imaging with microwave-induced thermoacoustic tomography,” Med. Phys. 35, 3205–3214 (2008).
[CrossRef] [PubMed]

L. V. Wang, “Prospects of photoacoustic tomography,” Med. Phys. 35, 5758–5767 (2008).
[CrossRef]

P. Ephrat, L. Keenliside, A. Seabrook, F. S. Prato, and J. J. L. Carson, “Three-dimensional photoacoustic imaging by sparse-array detection and iterative image reconstruction,” J. Biomed. Opt. 13, 054052 (2008).
[CrossRef] [PubMed]

2007 (5)

M. A. Anastasio, J. Zhang, D. Modgil, and P. J. L. Riviere, “Application of inverse source concepts to photoacoustic tomography,” Inverse Probl. 23, S21–S35 (2007).
[CrossRef]

L. A. Kunyansky, “Explicit inversion formulae for the spherical mean radon transform,” Inverse Probl. 23, 373–383(2007).
[CrossRef]

D. Finch, M. Haltmeier, and Rakesh, “Inversion of spherical means and the wave equation in even dimensions,” SIAM J. Appl. Math. 68, 392–412 (2007).
[CrossRef]

L. Wang and X. Yang, “Boundary conditions in photoacoustic tomography and image reconstruction,” J. Biomed. Opt. 12, 014027 (2007).
[CrossRef] [PubMed]

M. Agranovsky and P. Kuchment, “Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed,” Inverse Probl. 23, 2089–2102 (2007).
[CrossRef]

2006 (4)

2005 (2)

M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E 71, 016706 (2005).
[CrossRef]

M. A. Anastasio, J. Zhang, X. Pan, Y. Zou, G. Keng, and L. V. Wang, “Half-time image reconstruction in thermoacoustic tomography,” IEEE Trans. Med. Imaging 24, 199–210 (2005).
[CrossRef] [PubMed]

2004 (2)

D. Finch, S. Patch, and Rakesh, “Determining a function from its mean values over a family of spheres,” SIAM J. Math. Anal. 35, 1213–1240 (2004).
[CrossRef]

M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltauf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl. 20, 1663–1673 (2004).
[CrossRef]

2003 (2)

Y. Xu and L. V. Wang, “Effects of acoustic heterogeneity in breast thermoacoustic tomography,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 1134–1146 (2003).
[CrossRef] [PubMed]

S. Baikov, A. Molotilov, and V. Svet, “Physical and technological aspects of ultrasonic imaging of brain structures through thick skull bones: 1. theoretical and model studies,” Acoust. Phys. 49, 276–284 (2003).
[CrossRef]

2002 (1)

Y. Xu, D. Feng, and L. V. Wang, “Exact frequency-domain reconstruction for thermoacoustic tomography: I. Planar geometry,” IEEE Trans. Med. Imaging 21, 823–828 (2002).
[CrossRef] [PubMed]

2001 (2)

K. P. Köstli, M. Frenz, H. Bebie, and H. P. Weber, “Temporal backward projection of optoacoustic pressure transients using Fourier transform methods,” Phys. Med. Biol. 46, 1863–1872(2001).
[CrossRef] [PubMed]

M. Hayner and K. Hynynen, “Numerical analysis of ultrasonic transmission and absorption of oblique plane waves through the human skull,” J. Acoust. Soc. Am. 110, 3319–3330 (2001).
[CrossRef]

1999 (1)

R. Kruger, D. Reinecke, and G. Kruger, “Thermoacoustic computed tomography—technical considerations,” Med. Phys. 26, 1832–1837 (1999).
[CrossRef] [PubMed]

1995 (1)

R. A. Kruger, P. Liu, R. Fang, and C. Appledorn, “Photoacoustic ultrasound (PAUS) reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[CrossRef] [PubMed]

1990 (1)

W. Cheong, S. Prahl, and A. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

1985 (1)

H. Schmidt and F. Jensen, “A full wave solution for propagation in multilayered viscoelastic media with application to Gaussian beam reflection at fluid–solid interfaces,” J. Acoust. Soc. Am. 77, 813–825 (1985).
[CrossRef]

1980 (1)

W. Joines, R. Jirtle, M. Rafal, and D. Schaeffer, “Microwave power absorption differences between normal and malignant tissue,” Int. J. Radiat. Oncol. Biol. Phys. 6, 681–687 (1980).
[CrossRef] [PubMed]

1978 (1)

F. Fry and J. Barger, “Acoustical properties of the human skull,” J. Acoust. Soc. Am. 63, 1576–1590 (1978).
[CrossRef] [PubMed]

Agranovsky, M.

M. Agranovsky and P. Kuchment, “Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed,” Inverse Probl. 23, 2089–2102 (2007).
[CrossRef]

Anastasio, M.

K. Wang, S. Ermilov, R. Su, H. Brecht, A. Oraevsky, and M. Anastasio, “An imaging model incorporating ultrasonic transducer properties for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 30, 203–214 (2011).
[CrossRef]

Anastasio, M. A.

R. W. Schoonover and M. A. Anastasio, “Image reconstruction in photoacoustic tomography involving layered acoustic media,” J. Opt. Soc. Am. A 28, 1114–1120 (2011).
[CrossRef]

D. Modgil, M. A. Anastasio, and P. J. L. Rivière, “Image reconstruction in photoacoustic tomography with variable speed of sound using a higher-order geometrical acoustics approximation,” J. Biomed. Opt. 15, 021308 (2010).
[CrossRef] [PubMed]

M. A. Anastasio, J. Zhang, D. Modgil, and P. J. L. Riviere, “Application of inverse source concepts to photoacoustic tomography,” Inverse Probl. 23, S21–S35 (2007).
[CrossRef]

P. J. La Riviere, J. Zhang, and M. A. Anastasio, “Image reconstruction in optoacoustic tomography for dispersive acoustic media,” Opt. Lett. 31, 781–783 (2006).
[CrossRef] [PubMed]

M. A. Anastasio, J. Zhang, X. Pan, Y. Zou, G. Keng, and L. V. Wang, “Half-time image reconstruction in thermoacoustic tomography,” IEEE Trans. Med. Imaging 24, 199–210 (2005).
[CrossRef] [PubMed]

Appledorn, C.

R. A. Kruger, P. Liu, R. Fang, and C. Appledorn, “Photoacoustic ultrasound (PAUS) reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[CrossRef] [PubMed]

Arridge, S. R.

Baikov, S.

S. Baikov, A. Molotilov, and V. Svet, “Physical and technological aspects of ultrasonic imaging of brain structures through thick skull bones: 1. theoretical and model studies,” Acoust. Phys. 49, 276–284 (2003).
[CrossRef]

Barger, J.

F. Fry and J. Barger, “Acoustical properties of the human skull,” J. Acoust. Soc. Am. 63, 1576–1590 (1978).
[CrossRef] [PubMed]

Beard, P. C.

Bebie, H.

K. P. Köstli, M. Frenz, H. Bebie, and H. P. Weber, “Temporal backward projection of optoacoustic pressure transients using Fourier transform methods,” Phys. Med. Biol. 46, 1863–1872(2001).
[CrossRef] [PubMed]

Brecht, H.

K. Wang, S. Ermilov, R. Su, H. Brecht, A. Oraevsky, and M. Anastasio, “An imaging model incorporating ultrasonic transducer properties for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 30, 203–214 (2011).
[CrossRef]

Burgholzer, P.

M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltauf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl. 20, 1663–1673 (2004).
[CrossRef]

Carson, J. J. L.

P. Ephrat, L. Keenliside, A. Seabrook, F. S. Prato, and J. J. L. Carson, “Three-dimensional photoacoustic imaging by sparse-array detection and iterative image reconstruction,” J. Biomed. Opt. 13, 054052 (2008).
[CrossRef] [PubMed]

Cheong, W.

W. Cheong, S. Prahl, and A. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Chew, W. C.

W. C. Chew, Waves and Fields in Inhomogeneous Media (Springer, 1995).

Cox, B.

B. Treeby, E. Zhang, and B. Cox, “Photoacoustic tomography in absorbing acoustic media using time reversal,” Inverse Probl. 26, 115003 (2010).
[CrossRef]

Cox, B. T.

Ephrat, P.

P. Ephrat, L. Keenliside, A. Seabrook, F. S. Prato, and J. J. L. Carson, “Three-dimensional photoacoustic imaging by sparse-array detection and iterative image reconstruction,” J. Biomed. Opt. 13, 054052 (2008).
[CrossRef] [PubMed]

Ermilov, S.

K. Wang, S. Ermilov, R. Su, H. Brecht, A. Oraevsky, and M. Anastasio, “An imaging model incorporating ultrasonic transducer properties for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 30, 203–214 (2011).
[CrossRef]

Fang, R.

R. A. Kruger, P. Liu, R. Fang, and C. Appledorn, “Photoacoustic ultrasound (PAUS) reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[CrossRef] [PubMed]

Feng, D.

Y. Xu, D. Feng, and L. V. Wang, “Exact frequency-domain reconstruction for thermoacoustic tomography: I. Planar geometry,” IEEE Trans. Med. Imaging 21, 823–828 (2002).
[CrossRef] [PubMed]

Finch, D.

D. Finch, M. Haltmeier, and Rakesh, “Inversion of spherical means and the wave equation in even dimensions,” SIAM J. Appl. Math. 68, 392–412 (2007).
[CrossRef]

D. Finch, S. Patch, and Rakesh, “Determining a function from its mean values over a family of spheres,” SIAM J. Math. Anal. 35, 1213–1240 (2004).
[CrossRef]

Frenz, M.

K. P. Köstli, M. Frenz, H. Bebie, and H. P. Weber, “Temporal backward projection of optoacoustic pressure transients using Fourier transform methods,” Phys. Med. Biol. 46, 1863–1872(2001).
[CrossRef] [PubMed]

Fry, F.

F. Fry and J. Barger, “Acoustical properties of the human skull,” J. Acoust. Soc. Am. 63, 1576–1590 (1978).
[CrossRef] [PubMed]

Goertz, D.

A. Yousefi, D. Goertz, and K. Hynynen, “Transcranial shear-mode ultrasound: assessment of imaging performance and excitation techniques,” IEEE Trans. Med. Imaging 28, 763–774(2009).
[CrossRef] [PubMed]

Graff, K.

K. Graff, Wave Motion in Elastic Solids (Dover, 1975).

Haltmeier, M.

M. Haltmeier, O. Scherzer, and G. Zangerl, “A reconstruction algorithm for photoacoustic imaging based on the nonuniform FFT,” IEEE Trans. Med. Imaging 28, 1727–1735 (2009).
[CrossRef] [PubMed]

D. Finch, M. Haltmeier, and Rakesh, “Inversion of spherical means and the wave equation in even dimensions,” SIAM J. Appl. Math. 68, 392–412 (2007).
[CrossRef]

M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltauf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl. 20, 1663–1673 (2004).
[CrossRef]

Hayner, M.

M. Hayner and K. Hynynen, “Numerical analysis of ultrasonic transmission and absorption of oblique plane waves through the human skull,” J. Acoust. Soc. Am. 110, 3319–3330 (2001).
[CrossRef]

Hristova, Y.

Y. Hristova, P. Kuchment, and L. Nguyen, “Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media,” Inverse Probl. 24, 055006 (2008).
[CrossRef]

Hynynen, K.

A. Yousefi, D. Goertz, and K. Hynynen, “Transcranial shear-mode ultrasound: assessment of imaging performance and excitation techniques,” IEEE Trans. Med. Imaging 28, 763–774(2009).
[CrossRef] [PubMed]

M. Hayner and K. Hynynen, “Numerical analysis of ultrasonic transmission and absorption of oblique plane waves through the human skull,” J. Acoust. Soc. Am. 110, 3319–3330 (2001).
[CrossRef]

Ingard, K. U.

P. M. Morse and K. U. Ingard, Theoretical Acoustics (Princeton Univ. Press, 1986).

Jensen, F.

H. Schmidt and F. Jensen, “A full wave solution for propagation in multilayered viscoelastic media with application to Gaussian beam reflection at fluid–solid interfaces,” J. Acoust. Soc. Am. 77, 813–825 (1985).
[CrossRef]

Jin, X.

X. Jin, C. Li, and L. V. Wang, “Effects of acoustic heterogeneities on transcranial brain imaging with microwave-induced thermoacoustic tomography,” Med. Phys. 35, 3205–3214 (2008).
[CrossRef] [PubMed]

X. Jin and L. V. Wang, “Thermoacoustic tomography with correction for acoustic speed variations,” Phys. Med. Biol. 51, 6437–6448 (2006).
[CrossRef] [PubMed]

Jirtle, R.

W. Joines, R. Jirtle, M. Rafal, and D. Schaeffer, “Microwave power absorption differences between normal and malignant tissue,” Int. J. Radiat. Oncol. Biol. Phys. 6, 681–687 (1980).
[CrossRef] [PubMed]

Joines, W.

W. Joines, R. Jirtle, M. Rafal, and D. Schaeffer, “Microwave power absorption differences between normal and malignant tissue,” Int. J. Radiat. Oncol. Biol. Phys. 6, 681–687 (1980).
[CrossRef] [PubMed]

Karabutov, A. A.

A. A. Oraevsky and A. A. Karabutov, “Optoacoustic tomography,” in Biomedical Photonics Handbook, T.Vo-Dinh, ed. (CRC Press, 2003).

Keenliside, L.

P. Ephrat, L. Keenliside, A. Seabrook, F. S. Prato, and J. J. L. Carson, “Three-dimensional photoacoustic imaging by sparse-array detection and iterative image reconstruction,” J. Biomed. Opt. 13, 054052 (2008).
[CrossRef] [PubMed]

Keng, G.

M. A. Anastasio, J. Zhang, X. Pan, Y. Zou, G. Keng, and L. V. Wang, “Half-time image reconstruction in thermoacoustic tomography,” IEEE Trans. Med. Imaging 24, 199–210 (2005).
[CrossRef] [PubMed]

Köstli, K. P.

B. T. Cox, S. R. Arridge, K. P. Köstli, and P. C. Beard, “Two-dimensional quantitative photoacoustic image reconstruction of absorption distributions in scattering media by use of a simple iterative method,” Appl. Opt. 45, 1866–1875 (2006).
[CrossRef] [PubMed]

K. P. Köstli, M. Frenz, H. Bebie, and H. P. Weber, “Temporal backward projection of optoacoustic pressure transients using Fourier transform methods,” Phys. Med. Biol. 46, 1863–1872(2001).
[CrossRef] [PubMed]

Kruger, G.

R. Kruger, D. Reinecke, and G. Kruger, “Thermoacoustic computed tomography—technical considerations,” Med. Phys. 26, 1832–1837 (1999).
[CrossRef] [PubMed]

Kruger, R.

R. Kruger, D. Reinecke, and G. Kruger, “Thermoacoustic computed tomography—technical considerations,” Med. Phys. 26, 1832–1837 (1999).
[CrossRef] [PubMed]

Kruger, R. A.

R. A. Kruger, P. Liu, R. Fang, and C. Appledorn, “Photoacoustic ultrasound (PAUS) reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[CrossRef] [PubMed]

Kuchment, P.

Y. Hristova, P. Kuchment, and L. Nguyen, “Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media,” Inverse Probl. 24, 055006 (2008).
[CrossRef]

M. Agranovsky and P. Kuchment, “Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed,” Inverse Probl. 23, 2089–2102 (2007).
[CrossRef]

Kunyansky, L. A.

L. A. Kunyansky, “Explicit inversion formulae for the spherical mean radon transform,” Inverse Probl. 23, 373–383(2007).
[CrossRef]

La Riviere, P. J.

Li, C.

X. Jin, C. Li, and L. V. Wang, “Effects of acoustic heterogeneities on transcranial brain imaging with microwave-induced thermoacoustic tomography,” Med. Phys. 35, 3205–3214 (2008).
[CrossRef] [PubMed]

Liu, P.

R. A. Kruger, P. Liu, R. Fang, and C. Appledorn, “Photoacoustic ultrasound (PAUS) reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[CrossRef] [PubMed]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).

Manohar, S.

R. Willemink, S. Manohar, Y. Purwar, C. Slump, F. van der Heijden, and T. van Leeuwen, “Imaging of acoustic attenuation and speed of sound maps using photoacoustic measurements,” Proc. SPIE 6920, 692013 (2008).
[CrossRef]

Modgil, D.

D. Modgil, M. A. Anastasio, and P. J. L. Rivière, “Image reconstruction in photoacoustic tomography with variable speed of sound using a higher-order geometrical acoustics approximation,” J. Biomed. Opt. 15, 021308 (2010).
[CrossRef] [PubMed]

M. A. Anastasio, J. Zhang, D. Modgil, and P. J. L. Riviere, “Application of inverse source concepts to photoacoustic tomography,” Inverse Probl. 23, S21–S35 (2007).
[CrossRef]

Molotilov, A.

S. Baikov, A. Molotilov, and V. Svet, “Physical and technological aspects of ultrasonic imaging of brain structures through thick skull bones: 1. theoretical and model studies,” Acoust. Phys. 49, 276–284 (2003).
[CrossRef]

Morse, P. M.

P. M. Morse and K. U. Ingard, Theoretical Acoustics (Princeton Univ. Press, 1986).

Nguyen, L.

Y. Hristova, P. Kuchment, and L. Nguyen, “Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media,” Inverse Probl. 24, 055006 (2008).
[CrossRef]

Ntziachristos, V.

V. Ntziachristos and D. Razansky, “Molecular imaging by means of multispectral optoacoustic tomography (MSOT),” Chem. Rev. 110, 2783–2794 (2010).
[CrossRef] [PubMed]

Oraevsky, A.

K. Wang, S. Ermilov, R. Su, H. Brecht, A. Oraevsky, and M. Anastasio, “An imaging model incorporating ultrasonic transducer properties for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 30, 203–214 (2011).
[CrossRef]

Oraevsky, A. A.

A. A. Oraevsky and A. A. Karabutov, “Optoacoustic tomography,” in Biomedical Photonics Handbook, T.Vo-Dinh, ed. (CRC Press, 2003).

Paltauf, G.

M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltauf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl. 20, 1663–1673 (2004).
[CrossRef]

Pan, X.

M. A. Anastasio, J. Zhang, X. Pan, Y. Zou, G. Keng, and L. V. Wang, “Half-time image reconstruction in thermoacoustic tomography,” IEEE Trans. Med. Imaging 24, 199–210 (2005).
[CrossRef] [PubMed]

Patch, S.

D. Finch, S. Patch, and Rakesh, “Determining a function from its mean values over a family of spheres,” SIAM J. Math. Anal. 35, 1213–1240 (2004).
[CrossRef]

Prahl, S.

W. Cheong, S. Prahl, and A. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Prato, F. S.

P. Ephrat, L. Keenliside, A. Seabrook, F. S. Prato, and J. J. L. Carson, “Three-dimensional photoacoustic imaging by sparse-array detection and iterative image reconstruction,” J. Biomed. Opt. 13, 054052 (2008).
[CrossRef] [PubMed]

Purwar, Y.

R. Willemink, S. Manohar, Y. Purwar, C. Slump, F. van der Heijden, and T. van Leeuwen, “Imaging of acoustic attenuation and speed of sound maps using photoacoustic measurements,” Proc. SPIE 6920, 692013 (2008).
[CrossRef]

Rafal, M.

W. Joines, R. Jirtle, M. Rafal, and D. Schaeffer, “Microwave power absorption differences between normal and malignant tissue,” Int. J. Radiat. Oncol. Biol. Phys. 6, 681–687 (1980).
[CrossRef] [PubMed]

Rakesh,

D. Finch, M. Haltmeier, and Rakesh, “Inversion of spherical means and the wave equation in even dimensions,” SIAM J. Appl. Math. 68, 392–412 (2007).
[CrossRef]

D. Finch, S. Patch, and Rakesh, “Determining a function from its mean values over a family of spheres,” SIAM J. Math. Anal. 35, 1213–1240 (2004).
[CrossRef]

Razansky, D.

V. Ntziachristos and D. Razansky, “Molecular imaging by means of multispectral optoacoustic tomography (MSOT),” Chem. Rev. 110, 2783–2794 (2010).
[CrossRef] [PubMed]

Reinecke, D.

R. Kruger, D. Reinecke, and G. Kruger, “Thermoacoustic computed tomography—technical considerations,” Med. Phys. 26, 1832–1837 (1999).
[CrossRef] [PubMed]

Riviere, P. J. L.

M. A. Anastasio, J. Zhang, D. Modgil, and P. J. L. Riviere, “Application of inverse source concepts to photoacoustic tomography,” Inverse Probl. 23, S21–S35 (2007).
[CrossRef]

Rivière, P. J. L.

D. Modgil, M. A. Anastasio, and P. J. L. Rivière, “Image reconstruction in photoacoustic tomography with variable speed of sound using a higher-order geometrical acoustics approximation,” J. Biomed. Opt. 15, 021308 (2010).
[CrossRef] [PubMed]

Schaeffer, D.

W. Joines, R. Jirtle, M. Rafal, and D. Schaeffer, “Microwave power absorption differences between normal and malignant tissue,” Int. J. Radiat. Oncol. Biol. Phys. 6, 681–687 (1980).
[CrossRef] [PubMed]

Scherzer, O.

M. Haltmeier, O. Scherzer, and G. Zangerl, “A reconstruction algorithm for photoacoustic imaging based on the nonuniform FFT,” IEEE Trans. Med. Imaging 28, 1727–1735 (2009).
[CrossRef] [PubMed]

M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltauf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl. 20, 1663–1673 (2004).
[CrossRef]

Schmidt, H.

H. Schmidt and F. Jensen, “A full wave solution for propagation in multilayered viscoelastic media with application to Gaussian beam reflection at fluid–solid interfaces,” J. Acoust. Soc. Am. 77, 813–825 (1985).
[CrossRef]

Schoonover, R. W.

Seabrook, A.

P. Ephrat, L. Keenliside, A. Seabrook, F. S. Prato, and J. J. L. Carson, “Three-dimensional photoacoustic imaging by sparse-array detection and iterative image reconstruction,” J. Biomed. Opt. 13, 054052 (2008).
[CrossRef] [PubMed]

Slump, C.

R. Willemink, S. Manohar, Y. Purwar, C. Slump, F. van der Heijden, and T. van Leeuwen, “Imaging of acoustic attenuation and speed of sound maps using photoacoustic measurements,” Proc. SPIE 6920, 692013 (2008).
[CrossRef]

Stefanov, P.

P. Stefanov and G. Uhlmann, “Thermoacoustic tomography with variable sound speed,” Inverse Probl. 25, 075011 (2009).
[CrossRef]

Su, R.

K. Wang, S. Ermilov, R. Su, H. Brecht, A. Oraevsky, and M. Anastasio, “An imaging model incorporating ultrasonic transducer properties for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 30, 203–214 (2011).
[CrossRef]

Svet, V.

S. Baikov, A. Molotilov, and V. Svet, “Physical and technological aspects of ultrasonic imaging of brain structures through thick skull bones: 1. theoretical and model studies,” Acoust. Phys. 49, 276–284 (2003).
[CrossRef]

Treeby, B.

B. Treeby, E. Zhang, and B. Cox, “Photoacoustic tomography in absorbing acoustic media using time reversal,” Inverse Probl. 26, 115003 (2010).
[CrossRef]

Uhlmann, G.

P. Stefanov and G. Uhlmann, “Thermoacoustic tomography with variable sound speed,” Inverse Probl. 25, 075011 (2009).
[CrossRef]

van der Heijden, F.

R. Willemink, S. Manohar, Y. Purwar, C. Slump, F. van der Heijden, and T. van Leeuwen, “Imaging of acoustic attenuation and speed of sound maps using photoacoustic measurements,” Proc. SPIE 6920, 692013 (2008).
[CrossRef]

van Leeuwen, T.

R. Willemink, S. Manohar, Y. Purwar, C. Slump, F. van der Heijden, and T. van Leeuwen, “Imaging of acoustic attenuation and speed of sound maps using photoacoustic measurements,” Proc. SPIE 6920, 692013 (2008).
[CrossRef]

Wang, K.

K. Wang, S. Ermilov, R. Su, H. Brecht, A. Oraevsky, and M. Anastasio, “An imaging model incorporating ultrasonic transducer properties for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 30, 203–214 (2011).
[CrossRef]

Wang, L.

L. Wang and X. Yang, “Boundary conditions in photoacoustic tomography and image reconstruction,” J. Biomed. Opt. 12, 014027 (2007).
[CrossRef] [PubMed]

Wang, L. V.

X. Yang and L. V. Wang, “Monkey brain cortex imaging by photoacoustic tomography,” J. Biomed. Opt. 13, 044009 (2008).
[CrossRef] [PubMed]

X. Jin, C. Li, and L. V. Wang, “Effects of acoustic heterogeneities on transcranial brain imaging with microwave-induced thermoacoustic tomography,” Med. Phys. 35, 3205–3214 (2008).
[CrossRef] [PubMed]

L. V. Wang, “Prospects of photoacoustic tomography,” Med. Phys. 35, 5758–5767 (2008).
[CrossRef]

M. Xu and L. V. Wang, “Biomedical photoacoustics,” Rev. Sci. Instrum. 77, 041101 (2006).
[CrossRef]

X. Jin and L. V. Wang, “Thermoacoustic tomography with correction for acoustic speed variations,” Phys. Med. Biol. 51, 6437–6448 (2006).
[CrossRef] [PubMed]

M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E 71, 016706 (2005).
[CrossRef]

M. A. Anastasio, J. Zhang, X. Pan, Y. Zou, G. Keng, and L. V. Wang, “Half-time image reconstruction in thermoacoustic tomography,” IEEE Trans. Med. Imaging 24, 199–210 (2005).
[CrossRef] [PubMed]

Y. Xu and L. V. Wang, “Effects of acoustic heterogeneity in breast thermoacoustic tomography,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 1134–1146 (2003).
[CrossRef] [PubMed]

Y. Xu, D. Feng, and L. V. Wang, “Exact frequency-domain reconstruction for thermoacoustic tomography: I. Planar geometry,” IEEE Trans. Med. Imaging 21, 823–828 (2002).
[CrossRef] [PubMed]

Weber, H. P.

K. P. Köstli, M. Frenz, H. Bebie, and H. P. Weber, “Temporal backward projection of optoacoustic pressure transients using Fourier transform methods,” Phys. Med. Biol. 46, 1863–1872(2001).
[CrossRef] [PubMed]

Welch, A.

W. Cheong, S. Prahl, and A. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Willemink, R.

R. Willemink, S. Manohar, Y. Purwar, C. Slump, F. van der Heijden, and T. van Leeuwen, “Imaging of acoustic attenuation and speed of sound maps using photoacoustic measurements,” Proc. SPIE 6920, 692013 (2008).
[CrossRef]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).

Xu, M.

M. Xu and L. V. Wang, “Biomedical photoacoustics,” Rev. Sci. Instrum. 77, 041101 (2006).
[CrossRef]

M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E 71, 016706 (2005).
[CrossRef]

Xu, Y.

Y. Xu and L. V. Wang, “Effects of acoustic heterogeneity in breast thermoacoustic tomography,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 1134–1146 (2003).
[CrossRef] [PubMed]

Y. Xu, D. Feng, and L. V. Wang, “Exact frequency-domain reconstruction for thermoacoustic tomography: I. Planar geometry,” IEEE Trans. Med. Imaging 21, 823–828 (2002).
[CrossRef] [PubMed]

Yang, X.

X. Yang and L. V. Wang, “Monkey brain cortex imaging by photoacoustic tomography,” J. Biomed. Opt. 13, 044009 (2008).
[CrossRef] [PubMed]

L. Wang and X. Yang, “Boundary conditions in photoacoustic tomography and image reconstruction,” J. Biomed. Opt. 12, 014027 (2007).
[CrossRef] [PubMed]

Yousefi, A.

A. Yousefi, D. Goertz, and K. Hynynen, “Transcranial shear-mode ultrasound: assessment of imaging performance and excitation techniques,” IEEE Trans. Med. Imaging 28, 763–774(2009).
[CrossRef] [PubMed]

Zangerl, G.

M. Haltmeier, O. Scherzer, and G. Zangerl, “A reconstruction algorithm for photoacoustic imaging based on the nonuniform FFT,” IEEE Trans. Med. Imaging 28, 1727–1735 (2009).
[CrossRef] [PubMed]

Zhang, E.

B. Treeby, E. Zhang, and B. Cox, “Photoacoustic tomography in absorbing acoustic media using time reversal,” Inverse Probl. 26, 115003 (2010).
[CrossRef]

Zhang, J.

M. A. Anastasio, J. Zhang, D. Modgil, and P. J. L. Riviere, “Application of inverse source concepts to photoacoustic tomography,” Inverse Probl. 23, S21–S35 (2007).
[CrossRef]

P. J. La Riviere, J. Zhang, and M. A. Anastasio, “Image reconstruction in optoacoustic tomography for dispersive acoustic media,” Opt. Lett. 31, 781–783 (2006).
[CrossRef] [PubMed]

M. A. Anastasio, J. Zhang, X. Pan, Y. Zou, G. Keng, and L. V. Wang, “Half-time image reconstruction in thermoacoustic tomography,” IEEE Trans. Med. Imaging 24, 199–210 (2005).
[CrossRef] [PubMed]

Zou, Y.

M. A. Anastasio, J. Zhang, X. Pan, Y. Zou, G. Keng, and L. V. Wang, “Half-time image reconstruction in thermoacoustic tomography,” IEEE Trans. Med. Imaging 24, 199–210 (2005).
[CrossRef] [PubMed]

Acoust. Phys. (1)

S. Baikov, A. Molotilov, and V. Svet, “Physical and technological aspects of ultrasonic imaging of brain structures through thick skull bones: 1. theoretical and model studies,” Acoust. Phys. 49, 276–284 (2003).
[CrossRef]

Appl. Opt. (1)

Chem. Rev. (1)

V. Ntziachristos and D. Razansky, “Molecular imaging by means of multispectral optoacoustic tomography (MSOT),” Chem. Rev. 110, 2783–2794 (2010).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

W. Cheong, S. Prahl, and A. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

IEEE Trans. Med. Imaging (5)

K. Wang, S. Ermilov, R. Su, H. Brecht, A. Oraevsky, and M. Anastasio, “An imaging model incorporating ultrasonic transducer properties for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 30, 203–214 (2011).
[CrossRef]

M. Haltmeier, O. Scherzer, and G. Zangerl, “A reconstruction algorithm for photoacoustic imaging based on the nonuniform FFT,” IEEE Trans. Med. Imaging 28, 1727–1735 (2009).
[CrossRef] [PubMed]

Y. Xu, D. Feng, and L. V. Wang, “Exact frequency-domain reconstruction for thermoacoustic tomography: I. Planar geometry,” IEEE Trans. Med. Imaging 21, 823–828 (2002).
[CrossRef] [PubMed]

M. A. Anastasio, J. Zhang, X. Pan, Y. Zou, G. Keng, and L. V. Wang, “Half-time image reconstruction in thermoacoustic tomography,” IEEE Trans. Med. Imaging 24, 199–210 (2005).
[CrossRef] [PubMed]

A. Yousefi, D. Goertz, and K. Hynynen, “Transcranial shear-mode ultrasound: assessment of imaging performance and excitation techniques,” IEEE Trans. Med. Imaging 28, 763–774(2009).
[CrossRef] [PubMed]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

Y. Xu and L. V. Wang, “Effects of acoustic heterogeneity in breast thermoacoustic tomography,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 1134–1146 (2003).
[CrossRef] [PubMed]

Int. J. Radiat. Oncol. Biol. Phys. (1)

W. Joines, R. Jirtle, M. Rafal, and D. Schaeffer, “Microwave power absorption differences between normal and malignant tissue,” Int. J. Radiat. Oncol. Biol. Phys. 6, 681–687 (1980).
[CrossRef] [PubMed]

Inverse Probl. (7)

M. A. Anastasio, J. Zhang, D. Modgil, and P. J. L. Riviere, “Application of inverse source concepts to photoacoustic tomography,” Inverse Probl. 23, S21–S35 (2007).
[CrossRef]

L. A. Kunyansky, “Explicit inversion formulae for the spherical mean radon transform,” Inverse Probl. 23, 373–383(2007).
[CrossRef]

M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltauf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl. 20, 1663–1673 (2004).
[CrossRef]

M. Agranovsky and P. Kuchment, “Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed,” Inverse Probl. 23, 2089–2102 (2007).
[CrossRef]

Y. Hristova, P. Kuchment, and L. Nguyen, “Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media,” Inverse Probl. 24, 055006 (2008).
[CrossRef]

P. Stefanov and G. Uhlmann, “Thermoacoustic tomography with variable sound speed,” Inverse Probl. 25, 075011 (2009).
[CrossRef]

B. Treeby, E. Zhang, and B. Cox, “Photoacoustic tomography in absorbing acoustic media using time reversal,” Inverse Probl. 26, 115003 (2010).
[CrossRef]

J. Acoust. Soc. Am. (3)

M. Hayner and K. Hynynen, “Numerical analysis of ultrasonic transmission and absorption of oblique plane waves through the human skull,” J. Acoust. Soc. Am. 110, 3319–3330 (2001).
[CrossRef]

F. Fry and J. Barger, “Acoustical properties of the human skull,” J. Acoust. Soc. Am. 63, 1576–1590 (1978).
[CrossRef] [PubMed]

H. Schmidt and F. Jensen, “A full wave solution for propagation in multilayered viscoelastic media with application to Gaussian beam reflection at fluid–solid interfaces,” J. Acoust. Soc. Am. 77, 813–825 (1985).
[CrossRef]

J. Biomed. Opt. (4)

L. Wang and X. Yang, “Boundary conditions in photoacoustic tomography and image reconstruction,” J. Biomed. Opt. 12, 014027 (2007).
[CrossRef] [PubMed]

X. Yang and L. V. Wang, “Monkey brain cortex imaging by photoacoustic tomography,” J. Biomed. Opt. 13, 044009 (2008).
[CrossRef] [PubMed]

D. Modgil, M. A. Anastasio, and P. J. L. Rivière, “Image reconstruction in photoacoustic tomography with variable speed of sound using a higher-order geometrical acoustics approximation,” J. Biomed. Opt. 15, 021308 (2010).
[CrossRef] [PubMed]

P. Ephrat, L. Keenliside, A. Seabrook, F. S. Prato, and J. J. L. Carson, “Three-dimensional photoacoustic imaging by sparse-array detection and iterative image reconstruction,” J. Biomed. Opt. 13, 054052 (2008).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

Med. Phys. (4)

R. Kruger, D. Reinecke, and G. Kruger, “Thermoacoustic computed tomography—technical considerations,” Med. Phys. 26, 1832–1837 (1999).
[CrossRef] [PubMed]

L. V. Wang, “Prospects of photoacoustic tomography,” Med. Phys. 35, 5758–5767 (2008).
[CrossRef]

R. A. Kruger, P. Liu, R. Fang, and C. Appledorn, “Photoacoustic ultrasound (PAUS) reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[CrossRef] [PubMed]

X. Jin, C. Li, and L. V. Wang, “Effects of acoustic heterogeneities on transcranial brain imaging with microwave-induced thermoacoustic tomography,” Med. Phys. 35, 3205–3214 (2008).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Med. Biol. (2)

K. P. Köstli, M. Frenz, H. Bebie, and H. P. Weber, “Temporal backward projection of optoacoustic pressure transients using Fourier transform methods,” Phys. Med. Biol. 46, 1863–1872(2001).
[CrossRef] [PubMed]

X. Jin and L. V. Wang, “Thermoacoustic tomography with correction for acoustic speed variations,” Phys. Med. Biol. 51, 6437–6448 (2006).
[CrossRef] [PubMed]

Phys. Rev. E (1)

M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E 71, 016706 (2005).
[CrossRef]

Proc. SPIE (1)

R. Willemink, S. Manohar, Y. Purwar, C. Slump, F. van der Heijden, and T. van Leeuwen, “Imaging of acoustic attenuation and speed of sound maps using photoacoustic measurements,” Proc. SPIE 6920, 692013 (2008).
[CrossRef]

Rev. Sci. Instrum. (1)

M. Xu and L. V. Wang, “Biomedical photoacoustics,” Rev. Sci. Instrum. 77, 041101 (2006).
[CrossRef]

SIAM J. Appl. Math. (1)

D. Finch, M. Haltmeier, and Rakesh, “Inversion of spherical means and the wave equation in even dimensions,” SIAM J. Appl. Math. 68, 392–412 (2007).
[CrossRef]

SIAM J. Math. Anal. (1)

D. Finch, S. Patch, and Rakesh, “Determining a function from its mean values over a family of spheres,” SIAM J. Math. Anal. 35, 1213–1240 (2004).
[CrossRef]

Other (6)

A. A. Oraevsky and A. A. Karabutov, “Optoacoustic tomography,” in Biomedical Photonics Handbook, T.Vo-Dinh, ed. (CRC Press, 2003).

L.Wang, ed., Photoacoustic Imaging and Spectroscopy (CRC, 2009).
[CrossRef]

P. M. Morse and K. U. Ingard, Theoretical Acoustics (Princeton Univ. Press, 1986).

W. C. Chew, Waves and Fields in Inhomogeneous Media (Springer, 1995).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).

K. Graff, Wave Motion in Elastic Solids (Dover, 1975).

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Figures (7)

Fig. 1
Fig. 1

Diagram of a layered medium. The detection plane is denoted z = z d and marked with a dashed line. Each layer is characterized by density, ρ n , and longitudinal speed of sound, c n . Layer 1 (shaded) is assumed to be an elastic solid, characterized by longitudinal speed of sound c 1 and shear speed of sound c s . Layers in which absorption is considered contain α n in the material properties.

Fig. 2
Fig. 2

Intensity transmission coefficients for a four-layer medium for the case when the third layer is 3 mm thick. The transmission coefficients are shown for a plane wave incident on the medium at 10 ° when the first layer is assumed to be an elastic solid (green solid line) and a fluid (red dashed line), and when a plane wave is incident on the medium at 30 ° when the first layer is assumed to be an elastic solid (black dashed line) and a fluid (blue dotted line). Note that T f denotes the transmission coefficients when the first layer is assumed to be a fluid and T s denotes the transmission coefficient when the first layer is assumed to be an elastic solid.

Fig. 3
Fig. 3

Intensity transmission coefficients for a four-layer medium for the case when the third layer is 9 mm thick. The transmission coefficients are shown for a plane wave incident on the medium at 10 ° when the third layer is assumed to be an elastic solid (green solid line) and a fluid (red dashed line), and when a plane wave is incident on the medium at 30 ° when the third layer is assumed to be an elastic solid (black dashed line) and a fluid (blue dotted line). Note that T f denotes the transmission coefficients when the first layer is assumed a fluid and T s denotes the transmission coefficient when the first layer is assumed an elastic solid.

Fig. 4
Fig. 4

Top left panel: An image of the numerical phantom in the plane z = 2.76 cm reconstructed by use of Eq. (25) from noiseless data. Top right panel: A profile through the reconstructed image (black) and original phantom (blue dashes) along the line x = 0.75 cm and z = 2.76 cm . Bottom left panel: The corresponding profiles along the line y = 1.33 cm and z = 2.61 cm . Bottom right panel: The corresponding profiles along the line y = 1.42 cm and z = 2.52 cm . Note that the reconstructed and original objects are so similar as to be indistinguishable.

Fig. 5
Fig. 5

Top left panel: An image of the numerical phantom in the plane z = 2.76 cm reconstructed by use of algorithm (b) from noiseless data, i.e., the reconstruction assumes no elastic solids are present in the layered medium. Top right panel: A profile through the reconstructed image (black) and original phantom (blue dashes) along the line x = 0.75 cm and z = 2.76 cm . Bottom left panel: The corresponding profiles along the line y = 1.33 cm and z = 2.61 cm . Bottom right panel: The corresponding profiles along the line y = 1.42 cm and z = 2.52 cm .

Fig. 6
Fig. 6

Top left panel: An image of the numerical phantom in the plane z = 2.76 cm reconstructed by use of algorithm (c) from noiseless data, i.e., the reconstruction algorithm assumes a homogenous background surrounding the PCT object. Top right panel: A profile through the reconstructed image (black) and original phantom (blue dashes) along the line x = 0.75 cm and z = 2.76 cm . Bottom left panel: The corresponding profiles along the line y = 1.33 cm and z = 2.61 cm . Bottom right panel: The corresponding profiles along the line y = 1.42 cm and z = 2.52 cm .

Fig. 7
Fig. 7

Images of the numerical phantom reconstructed in the plane z = 2.76 cm for four different noise levels: 0.05% (top left panel), 0.1% (top right panel), 0.5% (bottom left panel), and 1% (bottom right panel).

Equations (48)

Equations on this page are rendered with MathJax. Learn more.

p ˜ ( r , ω ) = d t p ( r , t ) e i ω t ,
[ 2 + k 2 ] p ˜ ( r , ω ) = i ω Γ A ( r ) H ( ω ) ,
p ˜ ( r , ω ) = i ω Γ H ( ω ) V d 3 r G ( r , r , ω ) A ( r ) ,
p ¯ ( k x , k y , ω ) = d x d y p ˜ ( x , y , z = 0 , ω ) e i ( k x x + k y y ) .
A ( k x , k y , k z ) = d x d y d z A ( x , y , z ) e i ( k x x + k y y + k z z ) .
A ( k x , k y , ω 2 / c 2 k x 2 k y 2 ) = 2 p ¯ ( k x , k y , ω ) ω Γ H ( ω ) ω 2 / c 2 k x 2 k y 2 .
ρ ω 2 u ( r , ω ) = p ( r , ω ) ,
· u ( r , ω ) = 1 λ p ( r , ω ) .
[ 2 + k 2 ] u ( r , ω ) = i Γ ρ ω H ( ω ) A ( r ) .
G ¯ ( r , r , ω ) = G 0 ( r , r , ω ) ,
G 0 ( r , r , ω ) = i 2 d 2 k ( 2 π ) 2 1 k z ( k , ω ) exp ( i k · ( r r ) ) exp ( i k z | z z | ) ,
k z ( k , ω ) = ω 2 / c 2 k x 2 k y 2 .
G ¯ ( r , r , ω ) = i 2 d 2 k ( 2 π ) 2 1 k z ( k , ω ) exp ( i k · ( r r ) ) exp ( i k z ( z z ) ) k ^ k ^ ,
u ( r , ω ) = d 3 r G ¯ ( r , r , ω ) · i Γ ρ ω H ( ω ) A ( r ) ,
= i Γ ρ ω H ( ω ) i 2 d 3 r d 2 k ( 2 π ) 2 1 k z ( k , ω ) × exp [ i k · ( r r ) ] exp ( i k z | z z | ) k ^ k ^ · A ( r ) ,
= i Γ k 2 ρ ω H ( ω ) d 2 k ( 2 π ) 2 1 k z ( k , ω ) exp ( i k · r ) exp ( i k z z ) A ( k x , k y , k z ) k ^ .
[ 2 + k n 2 ] u l ( r , ω ) = 0 × u = 0 ,
[ 2 + k s 2 ] u s ( r , ω ) = 0 · u s = 0 ,
[ 2 + k m 2 ] u l ( r , ω ) = 0 × u l = 0 ,
u l ( r , ω ) = d 2 k ( 2 π ) 2 exp ( i k · r ) [ T n ( k ) e i k z ( n ) z k ^ n + + R n ( k ) e i k z ( n ) z k ^ n ] ,
u s ( r , ω ) = d 2 k ( 2 π ) 2 exp ( i k · r ) [ P n ( k ) e i k z ( s ) z g ^ n + + Q n ( k ) e i k z ( s ) z g ^ n ] ,
k z ( n ) = k n 2 k x 2 k y 2 ,
k z ( s ) = k s 2 k x 2 k y 2 .
p ¯ ( k x , k y , ω ) = ω Γ ρ 0 c 0 ρ M c M H ( ω ) T 0 ( k ) 2 k z ( M ) A ( k x , k y , k z ( M ) ) e i k z ( 0 ) d 0 ,
A ( k x , k y , k z ( M ) ) = 2 k z ( M ) ω Γ H ( ω ) T 0 ( k ) ρ M c M ρ 0 c 0 e i k z ( 0 ) d 0 p ¯ ( k x , k y , ω ) .
k m K m = ω c m ( ω ) + i α m ω ,
1 c m ( ω ) = 1 c 0 m 2 α m π ln ω ω 0 ,
k z ( m ) = K m 2 k 2 .
λ m ( ω ) = ρ [ ω 2 K m 2 2 ω 2 K s 2 ] ,
μ m ( ω ) = ρ ω 2 K s 2 .
z ^ · u ( r , ω ) | z = z n = z ^ · u ( r , ω ) | z = z n + ,
σ z z | z = z n = σ z z | z = z n + ,
σ x z | z = z n = 0 , σ y z | z = z n = 0 ,
σ z z = λ n · u + 2 μ n z u z ,
σ x i z = μ n ( x i u z + z u x i ) , x i = x , y .
σ z z | z = z n + = λ n k n ( T n e i k z ( n ) d n + R n e i k z ( n ) d n ) ,
σ z z | z = z n 1 = λ n k n ( T n + R n ) ,
z ^ · u | z = z n + = k z n k n ( T n e i k z ( n ) d n R n e i k z ( n ) d n ) ,
z ^ · u | z = z n 1 = k z n k n ( T n R n )
σ z z | z = z n + = ( λ n k n + 2 μ n ( k z ( n ) ) 2 k n ) ( T n e i k z ( n ) d n + R n e i k z ( n ) d n ) + 2 μ n ( P n e i k z ( s ) z + Q n e i k z ( s ) z ) k z ( s ) g z ,
σ z z | z = z n 1 = ( λ n k n + 2 μ n ( k z ( n ) ) 2 k n ) ( T n + R n ) + 2 μ n ( P n + Q n ) k z ( s ) g z ,
z ^ · u | z = z n + = k z n k n ( T n e i k z ( n ) d n R n e i k z ( n ) d n ) + g z ( P n e i k z ( s ) z Q n e i k z ( s ) z ) ,
z ^ · u | z = z n 1 = k z n k n ( T n R n ) + g z ( P n Q n )
g ^ n ± = 1 k s k ( k x k z ( s ) , k y k z ( s ) , k 2 ) T .
2 k z ( n ) k n ( T n e i k z ( n ) d n R n e i k z ( n ) d n ) + 2 ( k z ( s ) ) 2 k s 2 k k s ( P n e i k z ( s ) z Q n e i k z ( s ) z ) = 0 ,
2 k z ( n ) k n ( T n R n ) + 2 ( k z ( s ) ) 2 k s 2 k k s ( P n Q n ) = 0.
G ¯ D ( r , r , ω ) = i 2 d 2 k ( 2 π ) 2 T 0 ( k ) k z ( k , ω ) exp ( i k · ( r r ) ) exp ( i k z ( m ) ( z d z ) exp ( i k z ( 0 ) z ) k ^ 0 k ^ M ,
u ( k , ω ) = i Γ ρ M c M H ( ω ) T 0 k z ( M ) ( k ) A ( k ; k z ( M ) ) e i k z ( 0 ) d 0 k ^ 0 + .

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