Abstract

The optical absorption of tissues provides important information for clinical and pre-clinical studies. The challenge in recovering optical absorption from photoacoustic images is that the measured pressure depends on absorption and local fluence. One reconstruction approach uses a fixed-point iterative technique based on minimizing the mean-squared error combined with modeling of the light source to determine optical absorption. With this technique, convergence is not guaranteed even with an accurate measure of optical scattering. In this work we demonstrate using simulations that a new multiple illumination least squares fixed-point iteration algorithm improves convergence - even with poor estimates of optical scattering.

© 2013 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2013 (1)

K. Ren, H. Gao, and H. Zhao, “A Hybrid Reconstruction Method for Quantitative PAT,” SIAM J. Imaging Sci.6, 32–55 (2013).
[CrossRef]

2012 (3)

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt.17, 061202 (2012).
[CrossRef] [PubMed]

G. Bal and K. Ren, “On multi-spectral quantitative photoacoustic tomography in diffusive regime,” Inverse Probl.28, 025010 (2012).
[CrossRef]

P. Shao, T. Harrison, and R. J. Zemp, “Iterative algorithm for multiple illumination photoacoustic tomography (mipat) using ultrasound channel data,” Biomed. Opt. Express3, 3240–3249 (2012).
[CrossRef] [PubMed]

2011 (2)

2010 (3)

G. Bal and G. Uhlmann, “Inverse diffusion theory of photoacoustics,” Inverse Probl.26, 085010 (2010).
[CrossRef]

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt.15, 021311 (2010).
[CrossRef] [PubMed]

R. J. Zemp, “Quantitative photoacoustic tomography with multiple optical sources,” Appl. Opt.49, 3566–3572 (2010).
[CrossRef] [PubMed]

2009 (2)

B. T. Cox, S. R. Arridge, and P. C. Beard, “Estimating chromophore distributions from multiwavelength photoacoustic images,” J. Opt. Soc. Am. A26, 443–455 (2009).
[CrossRef]

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K. H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett.95, 013703 (2009).
[CrossRef]

2008 (2)

2007 (1)

2006 (2)

2005 (1)

J. Ripoll and V. Ntziachristos, “Quantitative point source photoacoustic inversion formulas for scattering and absorbing media,” Phys. Rev. E71, 031912 (2005).
[CrossRef]

2003 (1)

M. Xu and L. V. Wang, “Analytic explanation of spatial resolution related to bandwidth and detector aperture size in thermoacoustic or photoacoustic reconstruction,” Phys. Rev. E67, 056605 (2003).
[CrossRef]

1999 (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl.15, R41 (1999).
[CrossRef]

Arridge, S.

B. Cox, T. Tarvainen, and S. Arridge, “Multiple illumination quantitative photoacoustic tomography using transport and diffusion models,” in “Tomography and Inverse Transport Theory,” G. Bal, D. Finch, J. Schotland, P. Kuchment, and P. Stefanov, eds. (American Mathematical Society, Providence, RI, USA, 2012), pp. 1–12.

Arridge, S. R.

Bagchi, S.

Bal, G.

G. Bal and K. Ren, “On multi-spectral quantitative photoacoustic tomography in diffusive regime,” Inverse Probl.28, 025010 (2012).
[CrossRef]

G. Bal and K. Ren, “Multi-source quantitative photoacoustic tomography in a diffusive regime,” Inverse Probl.27, 075003 (2011).
[CrossRef]

G. Bal and G. Uhlmann, “Inverse diffusion theory of photoacoustics,” Inverse Probl.26, 085010 (2010).
[CrossRef]

Banerjee, B.

Beard, P. C.

Cox, B.

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt.17, 061202 (2012).
[CrossRef] [PubMed]

P. Shao, B. Cox, and R. J. Zemp, “Estimating optical absorption, scattering, and grueneisen distributions with multiple-illumination photoacoustic tomography,” Appl. Opt.50, 3145–3154 (2011).
[CrossRef] [PubMed]

B. Cox, T. Tarvainen, and S. Arridge, “Multiple illumination quantitative photoacoustic tomography using transport and diffusion models,” in “Tomography and Inverse Transport Theory,” G. Bal, D. Finch, J. Schotland, P. Kuchment, and P. Stefanov, eds. (American Mathematical Society, Providence, RI, USA, 2012), pp. 1–12.

Cox, B. T.

Englmeier, K. H.

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K. H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett.95, 013703 (2009).
[CrossRef]

Gao, H.

K. Ren, H. Gao, and H. Zhao, “A Hybrid Reconstruction Method for Quantitative PAT,” SIAM J. Imaging Sci.6, 32–55 (2013).
[CrossRef]

H. Gao, S. Osher, and H. Zhao, “Quantitative photoacoustic tomography,” in “Mathematical Modeling in Biomedical Imaging II: Optical, Ultrasound, and Opto-Acoustic Tomographiess,” vol. 2035 of Lecture Notes in Mathematics: Mathematical Biosciences Subseries, H. Ammari, ed. (Springer-Verlag, Berlin, 2011), pp. 131–158.

Guo, Z.

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt.15, 021311 (2010).
[CrossRef] [PubMed]

Harrison, T.

Jetzfellner, T.

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K. H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett.95, 013703 (2009).
[CrossRef]

Jiang, H.

L. Yin, Q. Wang, Q. Zhang, and H. Jiang, “Tomographic imaging of absolute optical absorption coefficient in turbid media using combined photoacoustic and diffusing light measurements,” Opt. Lett.32, 2556–2558 (2007).
[CrossRef] [PubMed]

Z. Yuan and H. Jiang, “Quantitative photoacoustic tomography: Recovery of optical absorption coefficient maps of heterogeneous media,” Appl. Phys. Lett.88, 231101 (2006).
[CrossRef]

Köstli, K. P.

Laufer, J. G.

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt.17, 061202 (2012).
[CrossRef] [PubMed]

Li, C.

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt.15, 021311 (2010).
[CrossRef] [PubMed]

Ntziachristos, V.

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K. H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett.95, 013703 (2009).
[CrossRef]

J. Ripoll and V. Ntziachristos, “Quantitative point source photoacoustic inversion formulas for scattering and absorbing media,” Phys. Rev. E71, 031912 (2005).
[CrossRef]

Osher, S.

H. Gao, S. Osher, and H. Zhao, “Quantitative photoacoustic tomography,” in “Mathematical Modeling in Biomedical Imaging II: Optical, Ultrasound, and Opto-Acoustic Tomographiess,” vol. 2035 of Lecture Notes in Mathematics: Mathematical Biosciences Subseries, H. Ammari, ed. (Springer-Verlag, Berlin, 2011), pp. 131–158.

Razansky, D.

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K. H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett.95, 013703 (2009).
[CrossRef]

Ren, K.

K. Ren, H. Gao, and H. Zhao, “A Hybrid Reconstruction Method for Quantitative PAT,” SIAM J. Imaging Sci.6, 32–55 (2013).
[CrossRef]

G. Bal and K. Ren, “On multi-spectral quantitative photoacoustic tomography in diffusive regime,” Inverse Probl.28, 025010 (2012).
[CrossRef]

G. Bal and K. Ren, “Multi-source quantitative photoacoustic tomography in a diffusive regime,” Inverse Probl.27, 075003 (2011).
[CrossRef]

Ripoll, J.

J. Ripoll and V. Ntziachristos, “Quantitative point source photoacoustic inversion formulas for scattering and absorbing media,” Phys. Rev. E71, 031912 (2005).
[CrossRef]

Rosenthal, A.

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K. H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett.95, 013703 (2009).
[CrossRef]

Roy, D.

Schulz, R.

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K. H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett.95, 013703 (2009).
[CrossRef]

Shao, P.

Song, L.

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt.15, 021311 (2010).
[CrossRef] [PubMed]

Tarvainen, T.

B. Cox, T. Tarvainen, and S. Arridge, “Multiple illumination quantitative photoacoustic tomography using transport and diffusion models,” in “Tomography and Inverse Transport Theory,” G. Bal, D. Finch, J. Schotland, P. Kuchment, and P. Stefanov, eds. (American Mathematical Society, Providence, RI, USA, 2012), pp. 1–12.

Uhlmann, G.

G. Bal and G. Uhlmann, “Inverse diffusion theory of photoacoustics,” Inverse Probl.26, 085010 (2010).
[CrossRef]

Vasu, R. M.

Wang, L.

L. Wang, “Tutorial on photoacoustic microscopy and computed tomography,” IEEE J. Sel. Top. Quant.14, 171–179 (2008).
[CrossRef]

Wang, L. V.

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt.15, 021311 (2010).
[CrossRef] [PubMed]

M. Xu and L. V. Wang, “Analytic explanation of spatial resolution related to bandwidth and detector aperture size in thermoacoustic or photoacoustic reconstruction,” Phys. Rev. E67, 056605 (2003).
[CrossRef]

Wang, Q.

Xu, M.

M. Xu and L. V. Wang, “Analytic explanation of spatial resolution related to bandwidth and detector aperture size in thermoacoustic or photoacoustic reconstruction,” Phys. Rev. E67, 056605 (2003).
[CrossRef]

Yin, L.

Yuan, Z.

Z. Yuan and H. Jiang, “Quantitative photoacoustic tomography: Recovery of optical absorption coefficient maps of heterogeneous media,” Appl. Phys. Lett.88, 231101 (2006).
[CrossRef]

Zemp, R. J.

Zhang, Q.

Zhao, H.

K. Ren, H. Gao, and H. Zhao, “A Hybrid Reconstruction Method for Quantitative PAT,” SIAM J. Imaging Sci.6, 32–55 (2013).
[CrossRef]

H. Gao, S. Osher, and H. Zhao, “Quantitative photoacoustic tomography,” in “Mathematical Modeling in Biomedical Imaging II: Optical, Ultrasound, and Opto-Acoustic Tomographiess,” vol. 2035 of Lecture Notes in Mathematics: Mathematical Biosciences Subseries, H. Ammari, ed. (Springer-Verlag, Berlin, 2011), pp. 131–158.

Appl. Opt. (3)

Appl. Phys. Lett. (2)

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K. H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett.95, 013703 (2009).
[CrossRef]

Z. Yuan and H. Jiang, “Quantitative photoacoustic tomography: Recovery of optical absorption coefficient maps of heterogeneous media,” Appl. Phys. Lett.88, 231101 (2006).
[CrossRef]

Biomed. Opt. Express (1)

IEEE J. Sel. Top. Quant. (1)

L. Wang, “Tutorial on photoacoustic microscopy and computed tomography,” IEEE J. Sel. Top. Quant.14, 171–179 (2008).
[CrossRef]

Inverse Probl. (4)

G. Bal and K. Ren, “Multi-source quantitative photoacoustic tomography in a diffusive regime,” Inverse Probl.27, 075003 (2011).
[CrossRef]

G. Bal and K. Ren, “On multi-spectral quantitative photoacoustic tomography in diffusive regime,” Inverse Probl.28, 025010 (2012).
[CrossRef]

G. Bal and G. Uhlmann, “Inverse diffusion theory of photoacoustics,” Inverse Probl.26, 085010 (2010).
[CrossRef]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl.15, R41 (1999).
[CrossRef]

J. Biomed. Opt. (2)

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt.15, 021311 (2010).
[CrossRef] [PubMed]

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt.17, 061202 (2012).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (2)

Opt. Lett. (1)

Phys. Rev. E (2)

J. Ripoll and V. Ntziachristos, “Quantitative point source photoacoustic inversion formulas for scattering and absorbing media,” Phys. Rev. E71, 031912 (2005).
[CrossRef]

M. Xu and L. V. Wang, “Analytic explanation of spatial resolution related to bandwidth and detector aperture size in thermoacoustic or photoacoustic reconstruction,” Phys. Rev. E67, 056605 (2003).
[CrossRef]

SIAM J. Imaging Sci. (1)

K. Ren, H. Gao, and H. Zhao, “A Hybrid Reconstruction Method for Quantitative PAT,” SIAM J. Imaging Sci.6, 32–55 (2013).
[CrossRef]

Other (2)

B. Cox, T. Tarvainen, and S. Arridge, “Multiple illumination quantitative photoacoustic tomography using transport and diffusion models,” in “Tomography and Inverse Transport Theory,” G. Bal, D. Finch, J. Schotland, P. Kuchment, and P. Stefanov, eds. (American Mathematical Society, Providence, RI, USA, 2012), pp. 1–12.

H. Gao, S. Osher, and H. Zhao, “Quantitative photoacoustic tomography,” in “Mathematical Modeling in Biomedical Imaging II: Optical, Ultrasound, and Opto-Acoustic Tomographiess,” vol. 2035 of Lecture Notes in Mathematics: Mathematical Biosciences Subseries, H. Ammari, ed. (Springer-Verlag, Berlin, 2011), pp. 131–158.

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Figures (3)

Fig. 1
Fig. 1

(a) μa phantom; Single uniform illumination: (b) PA image (top) and true Φ (bottom), (c) first iteration, and (d) 30th iteration. Four illumination MIPAT: (e) PA images (top) and true Φ (bottom), (f) first iteration, and (g) 30th iteration. μa in cm−1.

Fig. 2
Fig. 2

Simulated results of MIPAT with (a) 4, (b) 16, and (c) 512 illuminations with β = 0.032.

Fig. 3
Fig. 3

Simulated results of MIPAT after 30 iterations over different image signal-to-noise-ratios (SNR) and β values with (a) 4 and (b) 16 illuminations. The high SNR portion of (b) is presented in (c). Note that here, the standard deviation of the noise added to individual images is equal to that of the uniform illumination case.

Equations (3)

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

p 0 = Γ Φ μ a
μ ^ a ( r ) = 1 Γ k Φ ^ k ( r ) p ^ 0 k ( r ) k Φ k 2 ( r )
μ ^ a ( i + 1 ) ( r ) = 1 Γ k Φ ^ k ( i ) ( r ) p ^ 0 k ( r ) k [ Φ k ( i ) ( r ) ] 2 + β 2

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