Abstract

This paper proposes a multigrid inversion framework for quantitative photoacoustic tomography reconstruction. The forward model of optical fluence distribution and the inverse problem are solved at multiple resolutions. A fixed-point iteration scheme is formulated for each resolution and used as a cost function. The simulated and experimental results for quantitative photoacoustic tomography reconstruction show that the proposed multigrid inversion can dramatically reduce the required number of iterations for the optimization process without loss of reliability in the results.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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  6. D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91(11), 4887–4891 (1994).
    [Crossref] [PubMed]
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  9. A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43(5), 1285–1302 (1998).
    [Crossref] [PubMed]
  10. D. Razansky and V. Ntziachristos, “Hybrid photoacoustic fluorescence molecular tomography using finite-element-based inversion,” Med. Phys. 34(11), 4293–4301 (2007).
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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]
  29. H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
    [Crossref] [PubMed]
  30. M. Jermyn, H. Ghadyani, M. A. Mastanduno, W. Turner, S. C. Davis, H. Dehghani, and B. W. Pogue, “Fast segmentation and high-quality three-dimensional volume mesh creation from medical images for diffuse optical tomography,” J. Biomed. Opt. 18(8), 086007 (2013).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  32. P. Burgholzer, G. J. Matt, M. Haltmeier, and G. Paltauf, “Exact and approximative imaging methods for photoacoustic tomography using an arbitrary detection surface,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(4), 046706 (2007).
    [Crossref] [PubMed]

2014 (2)

2013 (1)

M. Jermyn, H. Ghadyani, M. A. Mastanduno, W. Turner, S. C. Davis, H. Dehghani, and B. W. Pogue, “Fast segmentation and high-quality three-dimensional volume mesh creation from medical images for diffuse optical tomography,” J. Biomed. Opt. 18(8), 086007 (2013).
[Crossref] [PubMed]

2012 (1)

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt. 17(6), 061202 (2012).
[Crossref] [PubMed]

2011 (1)

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

2010 (2)

B. E. Treeby and B. T. Cox, “k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields,” J. Biomed. Opt. 15(2), 021314 (2010).
[Crossref] [PubMed]

B. T. Cox, J. G. Laufer, and P. C. Beard, “Quantitative Photoacoustic Image Reconstruction using Fluence Dependent Chromophores,” Biomed. Opt. Express 1(1), 201–208 (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. A 26(2), 443–455 (2009).
[Crossref] [PubMed]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[Crossref] [PubMed]

2008 (2)

T. Tarvainen, M. Vauhkonen, and S. R. Arridge, “Gauss–Newton reconstruction method for optical tomography using the finite element solution of the radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transf. 109(17-18), 2767–2778 (2008).
[Crossref]

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13(4), 041302 (2008).
[Crossref] [PubMed]

2007 (5)

B. T. Cox, S. R. Arridge, and P. C. Beard, “Gradient-based quantitative photoacoustic image reconstruction for molecular imaging,” Proc. SPIE 6437, 64371T (2007).

D. Razansky and V. Ntziachristos, “Hybrid photoacoustic fluorescence molecular tomography using finite-element-based inversion,” Med. Phys. 34(11), 4293–4301 (2007).
[Crossref] [PubMed]

Z. Yuan, Q. Wang, and H. Jiang, “Reconstruction of optical absorption coefficient maps of heterogeneous media by photoacoustic tomography coupled with diffusion equation based regularized Newton method,” Opt. Express 15(26), 18076–18081 (2007).
[Crossref] [PubMed]

J. Laufer, D. Delpy, C. Elwell, and P. Beard, “Quantitative spatially resolved measurement of tissue chromophore concentrations using photoacoustic spectroscopy: application to the measurement of blood oxygenation and haemoglobin concentration,” Phys. Med. Biol. 52(1), 141–168 (2007).
[Crossref] [PubMed]

P. Burgholzer, G. J. Matt, M. Haltmeier, and G. Paltauf, “Exact and approximative imaging methods for photoacoustic tomography using an arbitrary detection surface,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(4), 046706 (2007).
[Crossref] [PubMed]

2006 (3)

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(8), 1866–1875 (2006).
[Crossref] [PubMed]

Z. Yuan and H. Jiang, “Quantitative photoacoustic tomography: Recovery of optical absorption coefficient maps of heterogeneous media,” Appl. Phys. Lett. 88(23), 231101 (2006).
[Crossref]

M. Xu and L. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum. 77(4), 041101 (2006).
[Crossref]

2005 (1)

M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(1), 016706 (2005).
[Crossref] [PubMed]

2002 (2)

T. Tanifuji and M. Hijikata, “Finite difference time domain (FDTD) analysis of optical pulse responses in biological tissues for spectroscopic diffused optical tomography,” IEEE Trans. Med. Imaging 21(2), 181–184 (2002).
[Crossref] [PubMed]

D. Boas, J. Culver, J. Stott, and A. Dunn, “Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head,” Opt. Express 10(3), 159–170 (2002).
[Crossref] [PubMed]

2001 (1)

J. C. Ye, C. A. Bouman, K. J. Webb, S. Member, R. P. Millane, and S. Member, “Nonlinear Multigrid Algorithms for Bayesian Optical Diffusion Tomography,” IEEE Trans. Image Process. 10(6), 909–922 (2001).
[Crossref]

2000 (1)

T. Dreyer, B. Maar, and V. Schulz, “Multigrid optimization in applications,” Int. J. Comp. Appl. Math. 120, 67–84 (2000).

1998 (3)

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43(5), 1285–1302 (1998).
[Crossref] [PubMed]

S. A. Walker, D. A. Boas, and E. Gratton, “Photon density waves scattered from cylindrical inhomogeneities: theory and experiments,” Appl. Opt. 37(10), 1935–1944 (1998).
[Crossref] [PubMed]

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43(5), 1285–1302 (1998).
[Crossref] [PubMed]

1997 (1)

1994 (1)

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91(11), 4887–4891 (1994).
[Crossref] [PubMed]

1989 (1)

Alcouffe, R. E.

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43(5), 1285–1302 (1998).
[Crossref] [PubMed]

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43(5), 1285–1302 (1998).
[Crossref] [PubMed]

Arridge, S. R.

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt. 17(6), 061202 (2012).
[Crossref] [PubMed]

B. T. Cox, S. R. Arridge, and P. C. Beard, “Estimating chromophore distributions from multiwavelength photoacoustic images,” J. Opt. Soc. Am. A 26(2), 443–455 (2009).
[Crossref] [PubMed]

T. Tarvainen, M. Vauhkonen, and S. R. Arridge, “Gauss–Newton reconstruction method for optical tomography using the finite element solution of the radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transf. 109(17-18), 2767–2778 (2008).
[Crossref]

B. T. Cox, S. R. Arridge, and P. C. Beard, “Gradient-based quantitative photoacoustic image reconstruction for molecular imaging,” Proc. SPIE 6437, 64371T (2007).

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(8), 1866–1875 (2006).
[Crossref] [PubMed]

Bal, G.

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

Bansal, S.

A. K. Garg, I. Kumar, S. Bansal, and I. Goyal, “Multigrid approach for solving elliptic type partial differential equations,” Int. J. Sci. Res. 3, 473–475 (2014).

Barbour, R. L.

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43(5), 1285–1302 (1998).
[Crossref] [PubMed]

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43(5), 1285–1302 (1998).
[Crossref] [PubMed]

Beard, P.

J. Laufer, D. Delpy, C. Elwell, and P. Beard, “Quantitative spatially resolved measurement of tissue chromophore concentrations using photoacoustic spectroscopy: application to the measurement of blood oxygenation and haemoglobin concentration,” Phys. Med. Biol. 52(1), 141–168 (2007).
[Crossref] [PubMed]

Beard, P. C.

Boas, D.

Boas, D. A.

S. A. Walker, D. A. Boas, and E. Gratton, “Photon density waves scattered from cylindrical inhomogeneities: theory and experiments,” Appl. Opt. 37(10), 1935–1944 (1998).
[Crossref] [PubMed]

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91(11), 4887–4891 (1994).
[Crossref] [PubMed]

Bouman, C. A.

J. C. Ye, C. A. Bouman, K. J. Webb, S. Member, R. P. Millane, and S. Member, “Nonlinear Multigrid Algorithms for Bayesian Optical Diffusion Tomography,” IEEE Trans. Image Process. 10(6), 909–922 (2001).
[Crossref]

Burgholzer, P.

P. Burgholzer, G. J. Matt, M. Haltmeier, and G. Paltauf, “Exact and approximative imaging methods for photoacoustic tomography using an arbitrary detection surface,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(4), 046706 (2007).
[Crossref] [PubMed]

Carpenter, C. M.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[Crossref] [PubMed]

Chance, B.

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91(11), 4887–4891 (1994).
[Crossref] [PubMed]

M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. 28(12), 2331–2336 (1989).
[Crossref] [PubMed]

Cox, B.

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt. 17(6), 061202 (2012).
[Crossref] [PubMed]

Cox, B. T.

Culver, J.

Davis, S. C.

M. Jermyn, H. Ghadyani, M. A. Mastanduno, W. Turner, S. C. Davis, H. Dehghani, and B. W. Pogue, “Fast segmentation and high-quality three-dimensional volume mesh creation from medical images for diffuse optical tomography,” J. Biomed. Opt. 18(8), 086007 (2013).
[Crossref] [PubMed]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[Crossref] [PubMed]

Dehghani, H.

M. Jermyn, H. Ghadyani, M. A. Mastanduno, W. Turner, S. C. Davis, H. Dehghani, and B. W. Pogue, “Fast segmentation and high-quality three-dimensional volume mesh creation from medical images for diffuse optical tomography,” J. Biomed. Opt. 18(8), 086007 (2013).
[Crossref] [PubMed]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[Crossref] [PubMed]

Delpy, D.

J. Laufer, D. Delpy, C. Elwell, and P. Beard, “Quantitative spatially resolved measurement of tissue chromophore concentrations using photoacoustic spectroscopy: application to the measurement of blood oxygenation and haemoglobin concentration,” Phys. Med. Biol. 52(1), 141–168 (2007).
[Crossref] [PubMed]

Dreyer, T.

T. Dreyer, B. Maar, and V. Schulz, “Multigrid optimization in applications,” Int. J. Comp. Appl. Math. 120, 67–84 (2000).

Dunn, A.

Eames, M. E.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[Crossref] [PubMed]

Elwell, C.

J. Laufer, D. Delpy, C. Elwell, and P. Beard, “Quantitative spatially resolved measurement of tissue chromophore concentrations using photoacoustic spectroscopy: application to the measurement of blood oxygenation and haemoglobin concentration,” Phys. Med. Biol. 52(1), 141–168 (2007).
[Crossref] [PubMed]

Garg, A. K.

A. K. Garg, I. Kumar, S. Bansal, and I. Goyal, “Multigrid approach for solving elliptic type partial differential equations,” Int. J. Sci. Res. 3, 473–475 (2014).

Ghadyani, H.

M. Jermyn, H. Ghadyani, M. A. Mastanduno, W. Turner, S. C. Davis, H. Dehghani, and B. W. Pogue, “Fast segmentation and high-quality three-dimensional volume mesh creation from medical images for diffuse optical tomography,” J. Biomed. Opt. 18(8), 086007 (2013).
[Crossref] [PubMed]

Goyal, I.

A. K. Garg, I. Kumar, S. Bansal, and I. Goyal, “Multigrid approach for solving elliptic type partial differential equations,” Int. J. Sci. Res. 3, 473–475 (2014).

Gratton, E.

Haltmeier, M.

P. Burgholzer, G. J. Matt, M. Haltmeier, and G. Paltauf, “Exact and approximative imaging methods for photoacoustic tomography using an arbitrary detection surface,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(4), 046706 (2007).
[Crossref] [PubMed]

Hielscher, A. H.

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43(5), 1285–1302 (1998).
[Crossref] [PubMed]

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43(5), 1285–1302 (1998).
[Crossref] [PubMed]

Hijikata, M.

T. Tanifuji and M. Hijikata, “Finite difference time domain (FDTD) analysis of optical pulse responses in biological tissues for spectroscopic diffused optical tomography,” IEEE Trans. Med. Imaging 21(2), 181–184 (2002).
[Crossref] [PubMed]

Jacques, S. L.

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13(4), 041302 (2008).
[Crossref] [PubMed]

Jermyn, M.

M. Jermyn, H. Ghadyani, M. A. Mastanduno, W. Turner, S. C. Davis, H. Dehghani, and B. W. Pogue, “Fast segmentation and high-quality three-dimensional volume mesh creation from medical images for diffuse optical tomography,” J. Biomed. Opt. 18(8), 086007 (2013).
[Crossref] [PubMed]

Jiang, H.

Kienle, A.

Köstli, K. P.

Kumar, I.

A. K. Garg, I. Kumar, S. Bansal, and I. Goyal, “Multigrid approach for solving elliptic type partial differential equations,” Int. J. Sci. Res. 3, 473–475 (2014).

Laufer, J.

J. Laufer, D. Delpy, C. Elwell, and P. Beard, “Quantitative spatially resolved measurement of tissue chromophore concentrations using photoacoustic spectroscopy: application to the measurement of blood oxygenation and haemoglobin concentration,” Phys. Med. Biol. 52(1), 141–168 (2007).
[Crossref] [PubMed]

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(6), 061202 (2012).
[Crossref] [PubMed]

B. T. Cox, J. G. Laufer, and P. C. Beard, “Quantitative Photoacoustic Image Reconstruction using Fluence Dependent Chromophores,” Biomed. Opt. Express 1(1), 201–208 (2010).
[Crossref] [PubMed]

Li, S.

Liu, W.

Maar, B.

T. Dreyer, B. Maar, and V. Schulz, “Multigrid optimization in applications,” Int. J. Comp. Appl. Math. 120, 67–84 (2000).

Mastanduno, M. A.

M. Jermyn, H. Ghadyani, M. A. Mastanduno, W. Turner, S. C. Davis, H. Dehghani, and B. W. Pogue, “Fast segmentation and high-quality three-dimensional volume mesh creation from medical images for diffuse optical tomography,” J. Biomed. Opt. 18(8), 086007 (2013).
[Crossref] [PubMed]

Matt, G. J.

P. Burgholzer, G. J. Matt, M. Haltmeier, and G. Paltauf, “Exact and approximative imaging methods for photoacoustic tomography using an arbitrary detection surface,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(4), 046706 (2007).
[Crossref] [PubMed]

Member, S.

J. C. Ye, C. A. Bouman, K. J. Webb, S. Member, R. P. Millane, and S. Member, “Nonlinear Multigrid Algorithms for Bayesian Optical Diffusion Tomography,” IEEE Trans. Image Process. 10(6), 909–922 (2001).
[Crossref]

J. C. Ye, C. A. Bouman, K. J. Webb, S. Member, R. P. Millane, and S. Member, “Nonlinear Multigrid Algorithms for Bayesian Optical Diffusion Tomography,” IEEE Trans. Image Process. 10(6), 909–922 (2001).
[Crossref]

Millane, R. P.

J. C. Ye, C. A. Bouman, K. J. Webb, S. Member, R. P. Millane, and S. Member, “Nonlinear Multigrid Algorithms for Bayesian Optical Diffusion Tomography,” IEEE Trans. Image Process. 10(6), 909–922 (2001).
[Crossref]

Montcel, B.

Ntziachristos, V.

D. Razansky and V. Ntziachristos, “Hybrid photoacoustic fluorescence molecular tomography using finite-element-based inversion,” Med. Phys. 34(11), 4293–4301 (2007).
[Crossref] [PubMed]

O’Leary, M. A.

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91(11), 4887–4891 (1994).
[Crossref] [PubMed]

Paltauf, G.

P. Burgholzer, G. J. Matt, M. Haltmeier, and G. Paltauf, “Exact and approximative imaging methods for photoacoustic tomography using an arbitrary detection surface,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(4), 046706 (2007).
[Crossref] [PubMed]

Patterson, M. S.

Paulsen, K. D.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[Crossref] [PubMed]

Pogue, B. W.

M. Jermyn, H. Ghadyani, M. A. Mastanduno, W. Turner, S. C. Davis, H. Dehghani, and B. W. Pogue, “Fast segmentation and high-quality three-dimensional volume mesh creation from medical images for diffuse optical tomography,” J. Biomed. Opt. 18(8), 086007 (2013).
[Crossref] [PubMed]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[Crossref] [PubMed]

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13(4), 041302 (2008).
[Crossref] [PubMed]

Razansky, D.

D. Razansky and V. Ntziachristos, “Hybrid photoacoustic fluorescence molecular tomography using finite-element-based inversion,” Med. Phys. 34(11), 4293–4301 (2007).
[Crossref] [PubMed]

Ren, K.

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

Schulz, V.

T. Dreyer, B. Maar, and V. Schulz, “Multigrid optimization in applications,” Int. J. Comp. Appl. Math. 120, 67–84 (2000).

Srinivasan, S.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[Crossref] [PubMed]

Stott, J.

Tanifuji, T.

T. Tanifuji and M. Hijikata, “Finite difference time domain (FDTD) analysis of optical pulse responses in biological tissues for spectroscopic diffused optical tomography,” IEEE Trans. Med. Imaging 21(2), 181–184 (2002).
[Crossref] [PubMed]

Tarvainen, T.

T. Tarvainen, M. Vauhkonen, and S. R. Arridge, “Gauss–Newton reconstruction method for optical tomography using the finite element solution of the radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transf. 109(17-18), 2767–2778 (2008).
[Crossref]

Treeby, B. E.

B. E. Treeby and B. T. Cox, “k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields,” J. Biomed. Opt. 15(2), 021314 (2010).
[Crossref] [PubMed]

Turner, W.

M. Jermyn, H. Ghadyani, M. A. Mastanduno, W. Turner, S. C. Davis, H. Dehghani, and B. W. Pogue, “Fast segmentation and high-quality three-dimensional volume mesh creation from medical images for diffuse optical tomography,” J. Biomed. Opt. 18(8), 086007 (2013).
[Crossref] [PubMed]

Vauhkonen, M.

T. Tarvainen, M. Vauhkonen, and S. R. Arridge, “Gauss–Newton reconstruction method for optical tomography using the finite element solution of the radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transf. 109(17-18), 2767–2778 (2008).
[Crossref]

Vray, D.

Walker, S. A.

Wang, L. V.

M. Xu and L. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum. 77(4), 041101 (2006).
[Crossref]

M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(1), 016706 (2005).
[Crossref] [PubMed]

Wang, Q.

Webb, K. J.

J. C. Ye, C. A. Bouman, K. J. Webb, S. Member, R. P. Millane, and S. Member, “Nonlinear Multigrid Algorithms for Bayesian Optical Diffusion Tomography,” IEEE Trans. Image Process. 10(6), 909–922 (2001).
[Crossref]

Wilson, B. C.

Xu, M.

M. Xu and L. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum. 77(4), 041101 (2006).
[Crossref]

M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(1), 016706 (2005).
[Crossref] [PubMed]

Yalavarthy, P. K.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[Crossref] [PubMed]

Ye, J. C.

J. C. Ye, C. A. Bouman, K. J. Webb, S. Member, R. P. Millane, and S. Member, “Nonlinear Multigrid Algorithms for Bayesian Optical Diffusion Tomography,” IEEE Trans. Image Process. 10(6), 909–922 (2001).
[Crossref]

Yodh, A. G.

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91(11), 4887–4891 (1994).
[Crossref] [PubMed]

Yuan, Z.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

Z. Yuan and H. Jiang, “Quantitative photoacoustic tomography: Recovery of optical absorption coefficient maps of heterogeneous media,” Appl. Phys. Lett. 88(23), 231101 (2006).
[Crossref]

Biomed. Opt. Express (1)

Commun. Numer. Methods Eng. (1)

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[Crossref] [PubMed]

IEEE Trans. Image Process. (1)

J. C. Ye, C. A. Bouman, K. J. Webb, S. Member, R. P. Millane, and S. Member, “Nonlinear Multigrid Algorithms for Bayesian Optical Diffusion Tomography,” IEEE Trans. Image Process. 10(6), 909–922 (2001).
[Crossref]

IEEE Trans. Med. Imaging (1)

T. Tanifuji and M. Hijikata, “Finite difference time domain (FDTD) analysis of optical pulse responses in biological tissues for spectroscopic diffused optical tomography,” IEEE Trans. Med. Imaging 21(2), 181–184 (2002).
[Crossref] [PubMed]

Int. J. Comp. Appl. Math. (1)

T. Dreyer, B. Maar, and V. Schulz, “Multigrid optimization in applications,” Int. J. Comp. Appl. Math. 120, 67–84 (2000).

Int. J. Sci. Res. (1)

A. K. Garg, I. Kumar, S. Bansal, and I. Goyal, “Multigrid approach for solving elliptic type partial differential equations,” Int. J. Sci. Res. 3, 473–475 (2014).

Inverse Probl. (1)

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

J. Biomed. Opt. (4)

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13(4), 041302 (2008).
[Crossref] [PubMed]

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt. 17(6), 061202 (2012).
[Crossref] [PubMed]

M. Jermyn, H. Ghadyani, M. A. Mastanduno, W. Turner, S. C. Davis, H. Dehghani, and B. W. Pogue, “Fast segmentation and high-quality three-dimensional volume mesh creation from medical images for diffuse optical tomography,” J. Biomed. Opt. 18(8), 086007 (2013).
[Crossref] [PubMed]

B. E. Treeby and B. T. Cox, “k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields,” J. Biomed. Opt. 15(2), 021314 (2010).
[Crossref] [PubMed]

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

J. Quant. Spectrosc. Radiat. Transf. (1)

T. Tarvainen, M. Vauhkonen, and S. R. Arridge, “Gauss–Newton reconstruction method for optical tomography using the finite element solution of the radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transf. 109(17-18), 2767–2778 (2008).
[Crossref]

Med. Phys. (1)

D. Razansky and V. Ntziachristos, “Hybrid photoacoustic fluorescence molecular tomography using finite-element-based inversion,” Med. Phys. 34(11), 4293–4301 (2007).
[Crossref] [PubMed]

Opt. Express (3)

Phys. Med. Biol. (3)

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43(5), 1285–1302 (1998).
[Crossref] [PubMed]

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43(5), 1285–1302 (1998).
[Crossref] [PubMed]

J. Laufer, D. Delpy, C. Elwell, and P. Beard, “Quantitative spatially resolved measurement of tissue chromophore concentrations using photoacoustic spectroscopy: application to the measurement of blood oxygenation and haemoglobin concentration,” Phys. Med. Biol. 52(1), 141–168 (2007).
[Crossref] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(1), 016706 (2005).
[Crossref] [PubMed]

P. Burgholzer, G. J. Matt, M. Haltmeier, and G. Paltauf, “Exact and approximative imaging methods for photoacoustic tomography using an arbitrary detection surface,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(4), 046706 (2007).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91(11), 4887–4891 (1994).
[Crossref] [PubMed]

Proc. SPIE (1)

B. T. Cox, S. R. Arridge, and P. C. Beard, “Gradient-based quantitative photoacoustic image reconstruction for molecular imaging,” Proc. SPIE 6437, 64371T (2007).

Rev. Sci. Instrum. (1)

M. Xu and L. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum. 77(4), 041101 (2006).
[Crossref]

Other (2)

H. Gao and H. Zhao, “A fast forward solver of radiative transfer equation,” (ftp://ftp.math.ucla.edu/pub/camreport/cam09-94.pdf).
[Crossref]

W. L. Briggs and V. E. Henson, “A Multigrid Tutorial,” ( http://computation.llnl.gov/casc/people /henson/mgtut/welcome.html ).

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Figures (8)

Fig. 1
Fig. 1 An iteration procedure of the V-cycle. The grid levels are noted (0) to (3). The red line represents the path that the multigrid algorithm traverses. The dotted lines represent the grid with different spacing.
Fig. 2
Fig. 2 Multiple iterations to obtain a solution. The grid levels are noted (0) to (3). The red line represents the multigrid algorithm recursively moving back and forth. The dotted lines represent the grid with different spacing. The position of each update of x(0) is noted by black dots along the green line with an arrow. The number of updates is noted by 1,2,….
Fig. 3
Fig. 3 The geometry and simulated absorbed energy. (a) The geometry. (b) Relative positions of inhomogeneities, c1, c2 and c3. (c) The absorbed energy distribution produced by NIRFAST.
Fig. 4
Fig. 4 Simulation tests of quantitative reconstruction of the absorption coefficient using the fixed grid and multigrid algorithm. (A) Recovered absorption coefficient. True (black line) and recovered absorption coefficient profile (red and green lines) plotted along the lines x = −0.5 cm (B), x = 0.25 cm (C) and x = 0.5 cm (D). The curves of relative errors versus the number of iterations (E) and CPU time (F) for the multigrid and fixed grid algorithms.
Fig. 5
Fig. 5 Schematic of experimental setup (left) and top-view photograph of the phantom (right).
Fig. 6
Fig. 6 Recovered absorbed energy distribution corresponding to the area [−1 cm, 1 cm ] × [−1 cm, 1 cm ].
Fig. 7
Fig. 7 Experimental validation of quantitative reconstruction of the absorption coefficient using the fixed grid and multigrid algorithm. (A) Recovered absorption coefficient. True (black line) and recovered absorption coefficient profile (red and green lines) plotted along the lines x = −0.5 cm (B), x = 0.25 cm (C) and x = 0.5 cm (D). The curves of relative errors versus the number of iterations (E) and CPU time (F) for the multigrid and fixed grid algorithm.
Fig. 8
Fig. 8 Comparison of the convergence speed of multigrid-based algorithms with different numbers of grid levels.

Tables (1)

Tables Icon

Table 1 Parameters of the numerical phantom

Equations (15)

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( μ ^ a , μ ^ s ' ) = arg min ( μ a , μ s ) ( H m ( r ) C H ( μ a , μ s ' , r ) 2 )
μ ^ a = arg min μ a ( H m ( r ) C H ( μ a , r ) 2 )
A x = b
A ( q ) x ( q ) = b ( q )
A ( q + 1 ) ( e ( q + 1 ) ) = I ( q ) ( q + 1 ) r ( q )
x ^ ( q ) x ^ ( q ) + e ( q )
D ( r ) Φ ( r ) μ a ( r ) Φ ( r ) = S ( r )
μ ( n + 1 ) a ( q ) = H ( m ) ( q ) C Φ ( q ) ( μ ( n ) a ( q ) )
C ( H ( q + 1 ) ( μ a ( q + 1 ) + e ( q + 1 ) ) H ( q + 1 ) ( μ a ( q + 1 ) ) ) = r ( q + 1 )
C H ( q + 1 ) ( I ( q ) ( q + 1 ) μ ^ a ( q ) + e ( q + 1 ) ) = C H ( q + 1 ) ( I ( q ) ( q + 1 ) μ ^ a ( q ) ) + I ( q ) ( q + 1 ) ( H ( m ) ( q ) C H ( q ) ( μ ^ a ( q ) ) )
μ a ( q + 1 ) = I ( q ) ( q + 1 ) μ ^ a ( q ) + e ( q + 1 )
μ ( n + 1 ) a ( q + 1 ) = C H ( q + 1 ) ( I ( q ) ( q + 1 ) μ ^ a ( q ) ) + I ( q ) ( q + 1 ) ( H ( m ) ( q ) C H ( q ) ( μ ^ a ( q ) ) ) C Φ ( q + 1 ) ( μ ( n ) a ( q + 1 ) )
μ ^ a ( q ) μ ^ a ( q ) + I ( q + 1 ) ( q ) ( μ ^ a ( q + 1 ) I ( q ) ( q + 1 ) μ ^ a ( q ) )
E = H m C H ( μ ^ a ) H m
E n E n 1 E n 1 < 0.1

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