Abstract

A model based reconstruction algorithm that exploits translational symmetries for photoacoustic microscopy to drastically reduce the memory cost is presented. The memory size needed to store the model matrix is independent of the number of acquisitions at different positions. This helps us to overcome one of the main limitations of previous algorithms. Furthermore, using the algebraic reconstruction technique and building the model matrix “on the fly”, we have obtained fast reconstructions of simulated and experimental data on both two- and three-dimensional grids using a traditional dark field photoacoustic microscope and a standard personal computer.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. V. Wang, S. Hu, “Photoacoustic tomography: in vivo imaging from organelles to organs,” Science 335(6075), 1458–1462 (2012).
    [CrossRef] [PubMed]
  2. L. V. Wang, “Multiscale photoacoustic microscopy and computed tomography,” Nat. Photonics 3(9), 503–509 (2009).
    [CrossRef] [PubMed]
  3. V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods 7(8), 603–614 (2010).
    [CrossRef] [PubMed]
  4. H. F. Zhang, K. Maslov, L. V. Wang, “In vivo imaging of subcutaneous structures using functional photoacoustic microscopy,” Nat. Protoc. 2(4), 797–804 (2007).
    [CrossRef] [PubMed]
  5. E. Z. Zhang, J. G. Laufer, R. B. Pedley, P. C. Beard, “In vivo high-resolution 3D photoacoustic imaging of superficial vascular anatomy,” Phys. Med. Biol. 54(4), 1035–1046 (2009).
    [CrossRef] [PubMed]
  6. V. Ntziachristos, “Clinical translation of optical and optoacoustic imaging,” Philos Trans A Math Phys. Eng. Sci. 369, 4666–4678 (2011).
  7. P. B. Garcia-Allende, J. Glatz, M. Koch, V. Ntziachristos, “Enriching the Interventional Vision of Cancer with Fluorescence and Optoacoustic Imaging,” J. Nucl. Med. 54(5), 664–667 (2013).
    [CrossRef] [PubMed]
  8. D. Razansky, A. Buehler, V. Ntziachristos, “Volumetric real-time multispectral optoacoustic tomography of biomarkers,” Nat. Protoc. 6(8), 1121–1129 (2011).
    [CrossRef] [PubMed]
  9. J. Yao, C. H. Huang, L. Wang, J. M. Yang, L. Gao, K. I. Maslov, J. Zou, L. V. Wang, “Wide-field fast-scanning photoacoustic microscopy based on a water-immersible MEMS scanning mirror,” J. Biomed. Opt. 17(8), 080505 (2012).
    [CrossRef] [PubMed]
  10. R. Ma, S. Söntges, S. Shoham, V. Ntziachristos, D. Razansky, “Fast scanning coaxial optoacoustic microscopy,” Biomed. Opt. Express 3(7), 1724–1731 (2012).
    [CrossRef] [PubMed]
  11. L. Wang, K. Maslov, W. Xing, A. Garcia-Uribe, L. V. Wang, “Video-rate functional photoacoustic microscopy at depths,” J. Biomed. Opt. 17(10), 106007 (2012).
    [CrossRef] [PubMed]
  12. K. Maslov, G. Stoica, L. V. Wang, “In vivo dark-field reflection-mode photoacoustic microscopy,” Opt. Lett. 30(6), 625–627 (2005).
    [CrossRef] [PubMed]
  13. H. F. Zhang, K. Maslov, M. L. Li, G. Stoica, L. V. Wang, “In vivo volumetric imaging of subcutaneous microvasculature by photoacoustic microscopy,” Opt. Express 14(20), 9317–9323 (2006).
    [CrossRef] [PubMed]
  14. M. L. Li, H. E. Zhang, K. Maslov, G. Stoica, L. V. Wang, “Improved in vivo photoacoustic microscopy based on a virtual-detector concept,” Opt. Lett. 31(4), 474–476 (2006).
    [CrossRef] [PubMed]
  15. M. A. Araque Caballero, A. Rosenthal, J. Gateau, D. Razansky, V. Ntziachristos, “Model-based optoacoustic imaging using focused detector scanning,” Opt. Lett. 37(19), 4080–4082 (2012).
    [CrossRef] [PubMed]
  16. X. L. Deán-Ben, A. Buehler, V. Ntziachristos, D. Razansky, “Accurate model-based reconstruction algorithm for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 31(10), 1922–1928 (2012).
    [CrossRef] [PubMed]
  17. A. Rosenthal, D. Razansky, V. Ntziachristos, “Fast semi-analytical model-based acoustic inversion for quantitative optoacoustic tomography,” IEEE Trans. Med. Imaging 29(6), 1275–1285 (2010).
    [CrossRef] [PubMed]
  18. A. Rosenthal, V. Ntziachristos, D. Razansky, “Model-based optoacoustic inversion with arbitrary-shape detectors,” Med. Phys. 38(7), 4285–4295 (2011).
    [CrossRef] [PubMed]
  19. S. Bu, Z. Liu, T. Shiina, K. Kondo, M. Yamakawa, K. Fukutani, Y. Someda, Y. Asao, “Model-based reconstruction integrated with fluence compensation for photoacoustic tomography,” IEEE Trans. Biomed. Eng. 59(5), 1354–1363 (2012).
    [CrossRef] [PubMed]
  20. X. L. Dean-Ben, R. Ma, D. Razansky, V. Ntziachristos, “Statistical approach for optoacoustic image reconstruction in the presence of strong acoustic heterogeneities,” IEEE Trans. Med. Imaging 30(2), 401–408 (2011).
    [CrossRef] [PubMed]
  21. M. Xu, 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]
  22. P. Burgholzer, G. J. Matt, M. Haltmeier, 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]
  23. B. E. Treeby, 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]
  24. J. Laufer, F. Norris, J. Cleary, E. Zhang, B. Treeby, B. Cox, P. Johnson, P. Scambler, M. Lythgoe, P. Beard, “In vivo photoacoustic imaging of mouse embryos,” J. Biomed. Opt. 17(6), 061220 (2012).
    [CrossRef] [PubMed]
  25. G. Paltauf, J. A. Viator, S. A. Prahl, S. L. Jacques, “Iterative reconstruction algorithm for optoacoustic imaging,” J. Acoust. Soc. Am. 112(4), 1536–1544 (2002).
    [CrossRef] [PubMed]
  26. P. Ephrat, L. Keenliside, A. Seabrook, F. S. Prato, J. J. Carson, “Three-dimensional photoacoustic imaging by sparse-array detection and iterative image reconstruction,” J. Biomed. Opt. 13(5), 054052 (2008).
    [CrossRef] [PubMed]
  27. K. Wang, S. A. Ermilov, R. Su, H. P. Brecht, A. A. Oraevsky, M. A. Anastasio, “An imaging model incorporating ultrasonic transducer properties for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 30(2), 203–214 (2011).
    [CrossRef] [PubMed]
  28. D. Queirós, X. L. Déan-Ben, A. Buehler, D. Razansky, A. Rosenthal, V. Ntziachristos, “Modeling the shape of cylindrically focused transducers in three-dimensional optoacoustic tomography,” J. Biomed. Opt. 18(7), 076014 (2013).
    [CrossRef] [PubMed]
  29. L. H. Wang, Biomedical Optics: Principles and Imaging (Wiley, Hoboken, New Jersey, 2007).
  30. C. G. Hoelen, F. F. de Mul, “A new theoretical approach to photoacoustic signal generation,” J. Acoust. Soc. Am. 106, 11 (1999).
  31. K. P. Köstli, P. C. Beard, “Two-dimensional photoacoustic imaging by use of Fourier-transform image reconstruction and a detector with an anisotropic response,” Appl. Opt. 42(10), 1899–1908 (2003).
    [CrossRef] [PubMed]
  32. X. Intes, V. Ntziachristos, J. P. Culver, A. Yodh, B. Chance, “Projection access order in algebraic reconstruction technique for diffuse optical tomography,” Phys. Med. Biol. 47(1), N1–N10 (2002).
    [CrossRef] [PubMed]
  33. G. T. Herman, L. B. Meyer, “Algebraic reconstruction techniques can be made computationally efficient [positron emission tomography application],” IEEE Trans. Med. Imaging 12(3), 600–609 (1993).
    [CrossRef] [PubMed]
  34. D. Ros, C. Falcón, I. Juvells, J. Pavía, “The influence of a relaxation parameter on SPECT iterative reconstruction algorithms,” Phys. Med. Biol. 41(5), 925–937 (1996).
    [CrossRef] [PubMed]
  35. T. Shin, J. F. Nielsen, K. S. Nayak, “Accelerating dynamic spiral MRI by algebraic reconstruction from undersampled k--t space,” IEEE Trans. Med. Imaging 26(7), 917–924 (2007).
    [CrossRef] [PubMed]
  36. A. H. Andersen, “Algebraic reconstruction in CT from limited views,” IEEE Trans. Med. Imaging 8(1), 50–55 (1989).
    [CrossRef] [PubMed]
  37. T. Durduran, R. Choe, W. B. Baker, A. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73(7), 076701 (2010).
    [CrossRef]
  38. M. B. Taisuke, A. Pau Giannoula, and T. Durduran, “MBio: a comprehensive Monte-carlo package for Diffuse Correñation Spectroscopy/Tomography,” in European Conferences on iomedical Optics, 2013)
  39. A. Rosenthal, T. Jetzfellner, D. Razansky, V. Ntziachristos, “Efficient framework for model-based tomographic image reconstruction using wavelet packets,” IEEE Trans. Med. Imaging 31(7), 1346–1357 (2012).
    [CrossRef] [PubMed]
  40. T. Koichi, W. Katsuhiro, F. Kazuhiko, and S. Tsuyoshi, “Advanced model-based reconstruction algorithm for practical three-dimensional photoacoustic imaginbg,” in SPIE, 2011)
  41. B. Shuhui, L. Zhenbao, S. Tsuyoshi, and F. Kazuhiko, “Matrix compression and Compressed sensing reconstruction for photoacoustic tomography,” Elektonika Ir Elektrotechnika, 18 (2012).
  42. B. E. Treeby, T. K. Varslot, E. Z. Zhang, J. G. Laufer, P. C. Beard, “Automatic sound speed selection in photoacoustic image reconstruction using an autofocus approach,” J. Biomed. Opt. 16(9), 090501 (2011).
    [CrossRef] [PubMed]
  43. X. L. Deán-Ben, V. Ntziachristos, D. Razansky, “Artefact reduction in optoacoustic tomographic imaging by estimating the distribution of acoustic scatterers,” J. Biomed. Opt. 17(11), 110504 (2012).
    [CrossRef] [PubMed]
  44. J. Chamorro-Servent, J. Aguirre, J. Ripoll, J. J. Vaquero, M. Desco, “Feasibility of U-curve method to select the regularization parameter for fluorescence diffuse optical tomography in phantom and small animal studies,” Opt. Express 19(12), 11490–11506 (2011).
    [CrossRef] [PubMed]
  45. J. L. Herraiz, S. España, J. J. Vaquero, M. Desco, J. M. Udías, “FIRST: Fast Iterative Reconstruction Software for (PET) tomography,” Phys. Med. Biol. 51(18), 4547–4565 (2006).
    [CrossRef] [PubMed]

2013 (2)

P. B. Garcia-Allende, J. Glatz, M. Koch, V. Ntziachristos, “Enriching the Interventional Vision of Cancer with Fluorescence and Optoacoustic Imaging,” J. Nucl. Med. 54(5), 664–667 (2013).
[CrossRef] [PubMed]

D. Queirós, X. L. Déan-Ben, A. Buehler, D. Razansky, A. Rosenthal, V. Ntziachristos, “Modeling the shape of cylindrically focused transducers in three-dimensional optoacoustic tomography,” J. Biomed. Opt. 18(7), 076014 (2013).
[CrossRef] [PubMed]

2012 (10)

S. Bu, Z. Liu, T. Shiina, K. Kondo, M. Yamakawa, K. Fukutani, Y. Someda, Y. Asao, “Model-based reconstruction integrated with fluence compensation for photoacoustic tomography,” IEEE Trans. Biomed. Eng. 59(5), 1354–1363 (2012).
[CrossRef] [PubMed]

J. Laufer, F. Norris, J. Cleary, E. Zhang, B. Treeby, B. Cox, P. Johnson, P. Scambler, M. Lythgoe, P. Beard, “In vivo photoacoustic imaging of mouse embryos,” J. Biomed. Opt. 17(6), 061220 (2012).
[CrossRef] [PubMed]

L. V. Wang, S. Hu, “Photoacoustic tomography: in vivo imaging from organelles to organs,” Science 335(6075), 1458–1462 (2012).
[CrossRef] [PubMed]

J. Yao, C. H. Huang, L. Wang, J. M. Yang, L. Gao, K. I. Maslov, J. Zou, L. V. Wang, “Wide-field fast-scanning photoacoustic microscopy based on a water-immersible MEMS scanning mirror,” J. Biomed. Opt. 17(8), 080505 (2012).
[CrossRef] [PubMed]

R. Ma, S. Söntges, S. Shoham, V. Ntziachristos, D. Razansky, “Fast scanning coaxial optoacoustic microscopy,” Biomed. Opt. Express 3(7), 1724–1731 (2012).
[CrossRef] [PubMed]

L. Wang, K. Maslov, W. Xing, A. Garcia-Uribe, L. V. Wang, “Video-rate functional photoacoustic microscopy at depths,” J. Biomed. Opt. 17(10), 106007 (2012).
[CrossRef] [PubMed]

M. A. Araque Caballero, A. Rosenthal, J. Gateau, D. Razansky, V. Ntziachristos, “Model-based optoacoustic imaging using focused detector scanning,” Opt. Lett. 37(19), 4080–4082 (2012).
[CrossRef] [PubMed]

X. L. Deán-Ben, A. Buehler, V. Ntziachristos, D. Razansky, “Accurate model-based reconstruction algorithm for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 31(10), 1922–1928 (2012).
[CrossRef] [PubMed]

A. Rosenthal, T. Jetzfellner, D. Razansky, V. Ntziachristos, “Efficient framework for model-based tomographic image reconstruction using wavelet packets,” IEEE Trans. Med. Imaging 31(7), 1346–1357 (2012).
[CrossRef] [PubMed]

X. L. Deán-Ben, V. Ntziachristos, D. Razansky, “Artefact reduction in optoacoustic tomographic imaging by estimating the distribution of acoustic scatterers,” J. Biomed. Opt. 17(11), 110504 (2012).
[CrossRef] [PubMed]

2011 (7)

J. Chamorro-Servent, J. Aguirre, J. Ripoll, J. J. Vaquero, M. Desco, “Feasibility of U-curve method to select the regularization parameter for fluorescence diffuse optical tomography in phantom and small animal studies,” Opt. Express 19(12), 11490–11506 (2011).
[CrossRef] [PubMed]

B. E. Treeby, T. K. Varslot, E. Z. Zhang, J. G. Laufer, P. C. Beard, “Automatic sound speed selection in photoacoustic image reconstruction using an autofocus approach,” J. Biomed. Opt. 16(9), 090501 (2011).
[CrossRef] [PubMed]

D. Razansky, A. Buehler, V. Ntziachristos, “Volumetric real-time multispectral optoacoustic tomography of biomarkers,” Nat. Protoc. 6(8), 1121–1129 (2011).
[CrossRef] [PubMed]

V. Ntziachristos, “Clinical translation of optical and optoacoustic imaging,” Philos Trans A Math Phys. Eng. Sci. 369, 4666–4678 (2011).

X. L. Dean-Ben, R. Ma, D. Razansky, V. Ntziachristos, “Statistical approach for optoacoustic image reconstruction in the presence of strong acoustic heterogeneities,” IEEE Trans. Med. Imaging 30(2), 401–408 (2011).
[CrossRef] [PubMed]

A. Rosenthal, V. Ntziachristos, D. Razansky, “Model-based optoacoustic inversion with arbitrary-shape detectors,” Med. Phys. 38(7), 4285–4295 (2011).
[CrossRef] [PubMed]

K. Wang, S. A. Ermilov, R. Su, H. P. Brecht, A. A. Oraevsky, M. A. Anastasio, “An imaging model incorporating ultrasonic transducer properties for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 30(2), 203–214 (2011).
[CrossRef] [PubMed]

2010 (4)

B. E. Treeby, 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]

V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods 7(8), 603–614 (2010).
[CrossRef] [PubMed]

A. Rosenthal, D. Razansky, V. Ntziachristos, “Fast semi-analytical model-based acoustic inversion for quantitative optoacoustic tomography,” IEEE Trans. Med. Imaging 29(6), 1275–1285 (2010).
[CrossRef] [PubMed]

T. Durduran, R. Choe, W. B. Baker, A. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73(7), 076701 (2010).
[CrossRef]

2009 (2)

L. V. Wang, “Multiscale photoacoustic microscopy and computed tomography,” Nat. Photonics 3(9), 503–509 (2009).
[CrossRef] [PubMed]

E. Z. Zhang, J. G. Laufer, R. B. Pedley, P. C. Beard, “In vivo high-resolution 3D photoacoustic imaging of superficial vascular anatomy,” Phys. Med. Biol. 54(4), 1035–1046 (2009).
[CrossRef] [PubMed]

2008 (1)

P. Ephrat, L. Keenliside, A. Seabrook, F. S. Prato, J. J. Carson, “Three-dimensional photoacoustic imaging by sparse-array detection and iterative image reconstruction,” J. Biomed. Opt. 13(5), 054052 (2008).
[CrossRef] [PubMed]

2007 (3)

P. Burgholzer, G. J. Matt, M. Haltmeier, 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]

T. Shin, J. F. Nielsen, K. S. Nayak, “Accelerating dynamic spiral MRI by algebraic reconstruction from undersampled k--t space,” IEEE Trans. Med. Imaging 26(7), 917–924 (2007).
[CrossRef] [PubMed]

H. F. Zhang, K. Maslov, L. V. Wang, “In vivo imaging of subcutaneous structures using functional photoacoustic microscopy,” Nat. Protoc. 2(4), 797–804 (2007).
[CrossRef] [PubMed]

2006 (3)

2005 (2)

K. Maslov, G. Stoica, L. V. Wang, “In vivo dark-field reflection-mode photoacoustic microscopy,” Opt. Lett. 30(6), 625–627 (2005).
[CrossRef] [PubMed]

M. Xu, 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]

2003 (1)

2002 (2)

X. Intes, V. Ntziachristos, J. P. Culver, A. Yodh, B. Chance, “Projection access order in algebraic reconstruction technique for diffuse optical tomography,” Phys. Med. Biol. 47(1), N1–N10 (2002).
[CrossRef] [PubMed]

G. Paltauf, J. A. Viator, S. A. Prahl, S. L. Jacques, “Iterative reconstruction algorithm for optoacoustic imaging,” J. Acoust. Soc. Am. 112(4), 1536–1544 (2002).
[CrossRef] [PubMed]

1999 (1)

C. G. Hoelen, F. F. de Mul, “A new theoretical approach to photoacoustic signal generation,” J. Acoust. Soc. Am. 106, 11 (1999).

1996 (1)

D. Ros, C. Falcón, I. Juvells, J. Pavía, “The influence of a relaxation parameter on SPECT iterative reconstruction algorithms,” Phys. Med. Biol. 41(5), 925–937 (1996).
[CrossRef] [PubMed]

1993 (1)

G. T. Herman, L. B. Meyer, “Algebraic reconstruction techniques can be made computationally efficient [positron emission tomography application],” IEEE Trans. Med. Imaging 12(3), 600–609 (1993).
[CrossRef] [PubMed]

1989 (1)

A. H. Andersen, “Algebraic reconstruction in CT from limited views,” IEEE Trans. Med. Imaging 8(1), 50–55 (1989).
[CrossRef] [PubMed]

Aguirre, J.

Anastasio, M. A.

K. Wang, S. A. Ermilov, R. Su, H. P. Brecht, A. A. Oraevsky, M. A. Anastasio, “An imaging model incorporating ultrasonic transducer properties for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 30(2), 203–214 (2011).
[CrossRef] [PubMed]

Andersen, A. H.

A. H. Andersen, “Algebraic reconstruction in CT from limited views,” IEEE Trans. Med. Imaging 8(1), 50–55 (1989).
[CrossRef] [PubMed]

Araque Caballero, M. A.

Asao, Y.

S. Bu, Z. Liu, T. Shiina, K. Kondo, M. Yamakawa, K. Fukutani, Y. Someda, Y. Asao, “Model-based reconstruction integrated with fluence compensation for photoacoustic tomography,” IEEE Trans. Biomed. Eng. 59(5), 1354–1363 (2012).
[CrossRef] [PubMed]

Baker, W. B.

T. Durduran, R. Choe, W. B. Baker, A. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73(7), 076701 (2010).
[CrossRef]

Beard, P.

J. Laufer, F. Norris, J. Cleary, E. Zhang, B. Treeby, B. Cox, P. Johnson, P. Scambler, M. Lythgoe, P. Beard, “In vivo photoacoustic imaging of mouse embryos,” J. Biomed. Opt. 17(6), 061220 (2012).
[CrossRef] [PubMed]

Beard, P. C.

B. E. Treeby, T. K. Varslot, E. Z. Zhang, J. G. Laufer, P. C. Beard, “Automatic sound speed selection in photoacoustic image reconstruction using an autofocus approach,” J. Biomed. Opt. 16(9), 090501 (2011).
[CrossRef] [PubMed]

E. Z. Zhang, J. G. Laufer, R. B. Pedley, P. C. Beard, “In vivo high-resolution 3D photoacoustic imaging of superficial vascular anatomy,” Phys. Med. Biol. 54(4), 1035–1046 (2009).
[CrossRef] [PubMed]

K. P. Köstli, P. C. Beard, “Two-dimensional photoacoustic imaging by use of Fourier-transform image reconstruction and a detector with an anisotropic response,” Appl. Opt. 42(10), 1899–1908 (2003).
[CrossRef] [PubMed]

Brecht, H. P.

K. Wang, S. A. Ermilov, R. Su, H. P. Brecht, A. A. Oraevsky, M. A. Anastasio, “An imaging model incorporating ultrasonic transducer properties for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 30(2), 203–214 (2011).
[CrossRef] [PubMed]

Bu, S.

S. Bu, Z. Liu, T. Shiina, K. Kondo, M. Yamakawa, K. Fukutani, Y. Someda, Y. Asao, “Model-based reconstruction integrated with fluence compensation for photoacoustic tomography,” IEEE Trans. Biomed. Eng. 59(5), 1354–1363 (2012).
[CrossRef] [PubMed]

Buehler, A.

D. Queirós, X. L. Déan-Ben, A. Buehler, D. Razansky, A. Rosenthal, V. Ntziachristos, “Modeling the shape of cylindrically focused transducers in three-dimensional optoacoustic tomography,” J. Biomed. Opt. 18(7), 076014 (2013).
[CrossRef] [PubMed]

X. L. Deán-Ben, A. Buehler, V. Ntziachristos, D. Razansky, “Accurate model-based reconstruction algorithm for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 31(10), 1922–1928 (2012).
[CrossRef] [PubMed]

D. Razansky, A. Buehler, V. Ntziachristos, “Volumetric real-time multispectral optoacoustic tomography of biomarkers,” Nat. Protoc. 6(8), 1121–1129 (2011).
[CrossRef] [PubMed]

Burgholzer, P.

P. Burgholzer, G. J. Matt, M. Haltmeier, 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]

Carson, J. J.

P. Ephrat, L. Keenliside, A. Seabrook, F. S. Prato, J. J. Carson, “Three-dimensional photoacoustic imaging by sparse-array detection and iterative image reconstruction,” J. Biomed. Opt. 13(5), 054052 (2008).
[CrossRef] [PubMed]

Chamorro-Servent, J.

Chance, B.

X. Intes, V. Ntziachristos, J. P. Culver, A. Yodh, B. Chance, “Projection access order in algebraic reconstruction technique for diffuse optical tomography,” Phys. Med. Biol. 47(1), N1–N10 (2002).
[CrossRef] [PubMed]

Choe, R.

T. Durduran, R. Choe, W. B. Baker, A. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73(7), 076701 (2010).
[CrossRef]

Cleary, J.

J. Laufer, F. Norris, J. Cleary, E. Zhang, B. Treeby, B. Cox, P. Johnson, P. Scambler, M. Lythgoe, P. Beard, “In vivo photoacoustic imaging of mouse embryos,” J. Biomed. Opt. 17(6), 061220 (2012).
[CrossRef] [PubMed]

Cox, B.

J. Laufer, F. Norris, J. Cleary, E. Zhang, B. Treeby, B. Cox, P. Johnson, P. Scambler, M. Lythgoe, P. Beard, “In vivo photoacoustic imaging of mouse embryos,” J. Biomed. Opt. 17(6), 061220 (2012).
[CrossRef] [PubMed]

Cox, B. T.

B. E. Treeby, 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]

Culver, J. P.

X. Intes, V. Ntziachristos, J. P. Culver, A. Yodh, B. Chance, “Projection access order in algebraic reconstruction technique for diffuse optical tomography,” Phys. Med. Biol. 47(1), N1–N10 (2002).
[CrossRef] [PubMed]

de Mul, F. F.

C. G. Hoelen, F. F. de Mul, “A new theoretical approach to photoacoustic signal generation,” J. Acoust. Soc. Am. 106, 11 (1999).

Dean-Ben, X. L.

X. L. Dean-Ben, R. Ma, D. Razansky, V. Ntziachristos, “Statistical approach for optoacoustic image reconstruction in the presence of strong acoustic heterogeneities,” IEEE Trans. Med. Imaging 30(2), 401–408 (2011).
[CrossRef] [PubMed]

Deán-Ben, X. L.

X. L. Deán-Ben, A. Buehler, V. Ntziachristos, D. Razansky, “Accurate model-based reconstruction algorithm for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 31(10), 1922–1928 (2012).
[CrossRef] [PubMed]

X. L. Deán-Ben, V. Ntziachristos, D. Razansky, “Artefact reduction in optoacoustic tomographic imaging by estimating the distribution of acoustic scatterers,” J. Biomed. Opt. 17(11), 110504 (2012).
[CrossRef] [PubMed]

Déan-Ben, X. L.

D. Queirós, X. L. Déan-Ben, A. Buehler, D. Razansky, A. Rosenthal, V. Ntziachristos, “Modeling the shape of cylindrically focused transducers in three-dimensional optoacoustic tomography,” J. Biomed. Opt. 18(7), 076014 (2013).
[CrossRef] [PubMed]

Desco, M.

Durduran, T.

T. Durduran, R. Choe, W. B. Baker, A. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73(7), 076701 (2010).
[CrossRef]

Ephrat, P.

P. Ephrat, L. Keenliside, A. Seabrook, F. S. Prato, J. J. Carson, “Three-dimensional photoacoustic imaging by sparse-array detection and iterative image reconstruction,” J. Biomed. Opt. 13(5), 054052 (2008).
[CrossRef] [PubMed]

Ermilov, S. A.

K. Wang, S. A. Ermilov, R. Su, H. P. Brecht, A. A. Oraevsky, M. A. Anastasio, “An imaging model incorporating ultrasonic transducer properties for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 30(2), 203–214 (2011).
[CrossRef] [PubMed]

España, S.

J. L. Herraiz, S. España, J. J. Vaquero, M. Desco, J. M. Udías, “FIRST: Fast Iterative Reconstruction Software for (PET) tomography,” Phys. Med. Biol. 51(18), 4547–4565 (2006).
[CrossRef] [PubMed]

Falcón, C.

D. Ros, C. Falcón, I. Juvells, J. Pavía, “The influence of a relaxation parameter on SPECT iterative reconstruction algorithms,” Phys. Med. Biol. 41(5), 925–937 (1996).
[CrossRef] [PubMed]

Fukutani, K.

S. Bu, Z. Liu, T. Shiina, K. Kondo, M. Yamakawa, K. Fukutani, Y. Someda, Y. Asao, “Model-based reconstruction integrated with fluence compensation for photoacoustic tomography,” IEEE Trans. Biomed. Eng. 59(5), 1354–1363 (2012).
[CrossRef] [PubMed]

Gao, L.

J. Yao, C. H. Huang, L. Wang, J. M. Yang, L. Gao, K. I. Maslov, J. Zou, L. V. Wang, “Wide-field fast-scanning photoacoustic microscopy based on a water-immersible MEMS scanning mirror,” J. Biomed. Opt. 17(8), 080505 (2012).
[CrossRef] [PubMed]

Garcia-Allende, P. B.

P. B. Garcia-Allende, J. Glatz, M. Koch, V. Ntziachristos, “Enriching the Interventional Vision of Cancer with Fluorescence and Optoacoustic Imaging,” J. Nucl. Med. 54(5), 664–667 (2013).
[CrossRef] [PubMed]

Garcia-Uribe, A.

L. Wang, K. Maslov, W. Xing, A. Garcia-Uribe, L. V. Wang, “Video-rate functional photoacoustic microscopy at depths,” J. Biomed. Opt. 17(10), 106007 (2012).
[CrossRef] [PubMed]

Gateau, J.

Glatz, J.

P. B. Garcia-Allende, J. Glatz, M. Koch, V. Ntziachristos, “Enriching the Interventional Vision of Cancer with Fluorescence and Optoacoustic Imaging,” J. Nucl. Med. 54(5), 664–667 (2013).
[CrossRef] [PubMed]

Haltmeier, M.

P. Burgholzer, G. J. Matt, M. Haltmeier, 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]

Herman, G. T.

G. T. Herman, L. B. Meyer, “Algebraic reconstruction techniques can be made computationally efficient [positron emission tomography application],” IEEE Trans. Med. Imaging 12(3), 600–609 (1993).
[CrossRef] [PubMed]

Herraiz, J. L.

J. L. Herraiz, S. España, J. J. Vaquero, M. Desco, J. M. Udías, “FIRST: Fast Iterative Reconstruction Software for (PET) tomography,” Phys. Med. Biol. 51(18), 4547–4565 (2006).
[CrossRef] [PubMed]

Hoelen, C. G.

C. G. Hoelen, F. F. de Mul, “A new theoretical approach to photoacoustic signal generation,” J. Acoust. Soc. Am. 106, 11 (1999).

Hu, S.

L. V. Wang, S. Hu, “Photoacoustic tomography: in vivo imaging from organelles to organs,” Science 335(6075), 1458–1462 (2012).
[CrossRef] [PubMed]

Huang, C. H.

J. Yao, C. H. Huang, L. Wang, J. M. Yang, L. Gao, K. I. Maslov, J. Zou, L. V. Wang, “Wide-field fast-scanning photoacoustic microscopy based on a water-immersible MEMS scanning mirror,” J. Biomed. Opt. 17(8), 080505 (2012).
[CrossRef] [PubMed]

Intes, X.

X. Intes, V. Ntziachristos, J. P. Culver, A. Yodh, B. Chance, “Projection access order in algebraic reconstruction technique for diffuse optical tomography,” Phys. Med. Biol. 47(1), N1–N10 (2002).
[CrossRef] [PubMed]

Jacques, S. L.

G. Paltauf, J. A. Viator, S. A. Prahl, S. L. Jacques, “Iterative reconstruction algorithm for optoacoustic imaging,” J. Acoust. Soc. Am. 112(4), 1536–1544 (2002).
[CrossRef] [PubMed]

Jetzfellner, T.

A. Rosenthal, T. Jetzfellner, D. Razansky, V. Ntziachristos, “Efficient framework for model-based tomographic image reconstruction using wavelet packets,” IEEE Trans. Med. Imaging 31(7), 1346–1357 (2012).
[CrossRef] [PubMed]

Johnson, P.

J. Laufer, F. Norris, J. Cleary, E. Zhang, B. Treeby, B. Cox, P. Johnson, P. Scambler, M. Lythgoe, P. Beard, “In vivo photoacoustic imaging of mouse embryos,” J. Biomed. Opt. 17(6), 061220 (2012).
[CrossRef] [PubMed]

Juvells, I.

D. Ros, C. Falcón, I. Juvells, J. Pavía, “The influence of a relaxation parameter on SPECT iterative reconstruction algorithms,” Phys. Med. Biol. 41(5), 925–937 (1996).
[CrossRef] [PubMed]

Keenliside, L.

P. Ephrat, L. Keenliside, A. Seabrook, F. S. Prato, J. J. Carson, “Three-dimensional photoacoustic imaging by sparse-array detection and iterative image reconstruction,” J. Biomed. Opt. 13(5), 054052 (2008).
[CrossRef] [PubMed]

Koch, M.

P. B. Garcia-Allende, J. Glatz, M. Koch, V. Ntziachristos, “Enriching the Interventional Vision of Cancer with Fluorescence and Optoacoustic Imaging,” J. Nucl. Med. 54(5), 664–667 (2013).
[CrossRef] [PubMed]

Kondo, K.

S. Bu, Z. Liu, T. Shiina, K. Kondo, M. Yamakawa, K. Fukutani, Y. Someda, Y. Asao, “Model-based reconstruction integrated with fluence compensation for photoacoustic tomography,” IEEE Trans. Biomed. Eng. 59(5), 1354–1363 (2012).
[CrossRef] [PubMed]

Köstli, K. P.

Laufer, J.

J. Laufer, F. Norris, J. Cleary, E. Zhang, B. Treeby, B. Cox, P. Johnson, P. Scambler, M. Lythgoe, P. Beard, “In vivo photoacoustic imaging of mouse embryos,” J. Biomed. Opt. 17(6), 061220 (2012).
[CrossRef] [PubMed]

Laufer, J. G.

B. E. Treeby, T. K. Varslot, E. Z. Zhang, J. G. Laufer, P. C. Beard, “Automatic sound speed selection in photoacoustic image reconstruction using an autofocus approach,” J. Biomed. Opt. 16(9), 090501 (2011).
[CrossRef] [PubMed]

E. Z. Zhang, J. G. Laufer, R. B. Pedley, P. C. Beard, “In vivo high-resolution 3D photoacoustic imaging of superficial vascular anatomy,” Phys. Med. Biol. 54(4), 1035–1046 (2009).
[CrossRef] [PubMed]

Li, M. L.

Liu, Z.

S. Bu, Z. Liu, T. Shiina, K. Kondo, M. Yamakawa, K. Fukutani, Y. Someda, Y. Asao, “Model-based reconstruction integrated with fluence compensation for photoacoustic tomography,” IEEE Trans. Biomed. Eng. 59(5), 1354–1363 (2012).
[CrossRef] [PubMed]

Lythgoe, M.

J. Laufer, F. Norris, J. Cleary, E. Zhang, B. Treeby, B. Cox, P. Johnson, P. Scambler, M. Lythgoe, P. Beard, “In vivo photoacoustic imaging of mouse embryos,” J. Biomed. Opt. 17(6), 061220 (2012).
[CrossRef] [PubMed]

Ma, R.

R. Ma, S. Söntges, S. Shoham, V. Ntziachristos, D. Razansky, “Fast scanning coaxial optoacoustic microscopy,” Biomed. Opt. Express 3(7), 1724–1731 (2012).
[CrossRef] [PubMed]

X. L. Dean-Ben, R. Ma, D. Razansky, V. Ntziachristos, “Statistical approach for optoacoustic image reconstruction in the presence of strong acoustic heterogeneities,” IEEE Trans. Med. Imaging 30(2), 401–408 (2011).
[CrossRef] [PubMed]

Maslov, K.

Maslov, K. I.

J. Yao, C. H. Huang, L. Wang, J. M. Yang, L. Gao, K. I. Maslov, J. Zou, L. V. Wang, “Wide-field fast-scanning photoacoustic microscopy based on a water-immersible MEMS scanning mirror,” J. Biomed. Opt. 17(8), 080505 (2012).
[CrossRef] [PubMed]

Matt, G. J.

P. Burgholzer, G. J. Matt, M. Haltmeier, 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]

Meyer, L. B.

G. T. Herman, L. B. Meyer, “Algebraic reconstruction techniques can be made computationally efficient [positron emission tomography application],” IEEE Trans. Med. Imaging 12(3), 600–609 (1993).
[CrossRef] [PubMed]

Nayak, K. S.

T. Shin, J. F. Nielsen, K. S. Nayak, “Accelerating dynamic spiral MRI by algebraic reconstruction from undersampled k--t space,” IEEE Trans. Med. Imaging 26(7), 917–924 (2007).
[CrossRef] [PubMed]

Nielsen, J. F.

T. Shin, J. F. Nielsen, K. S. Nayak, “Accelerating dynamic spiral MRI by algebraic reconstruction from undersampled k--t space,” IEEE Trans. Med. Imaging 26(7), 917–924 (2007).
[CrossRef] [PubMed]

Norris, F.

J. Laufer, F. Norris, J. Cleary, E. Zhang, B. Treeby, B. Cox, P. Johnson, P. Scambler, M. Lythgoe, P. Beard, “In vivo photoacoustic imaging of mouse embryos,” J. Biomed. Opt. 17(6), 061220 (2012).
[CrossRef] [PubMed]

Ntziachristos, V.

D. Queirós, X. L. Déan-Ben, A. Buehler, D. Razansky, A. Rosenthal, V. Ntziachristos, “Modeling the shape of cylindrically focused transducers in three-dimensional optoacoustic tomography,” J. Biomed. Opt. 18(7), 076014 (2013).
[CrossRef] [PubMed]

P. B. Garcia-Allende, J. Glatz, M. Koch, V. Ntziachristos, “Enriching the Interventional Vision of Cancer with Fluorescence and Optoacoustic Imaging,” J. Nucl. Med. 54(5), 664–667 (2013).
[CrossRef] [PubMed]

R. Ma, S. Söntges, S. Shoham, V. Ntziachristos, D. Razansky, “Fast scanning coaxial optoacoustic microscopy,” Biomed. Opt. Express 3(7), 1724–1731 (2012).
[CrossRef] [PubMed]

M. A. Araque Caballero, A. Rosenthal, J. Gateau, D. Razansky, V. Ntziachristos, “Model-based optoacoustic imaging using focused detector scanning,” Opt. Lett. 37(19), 4080–4082 (2012).
[CrossRef] [PubMed]

X. L. Deán-Ben, A. Buehler, V. Ntziachristos, D. Razansky, “Accurate model-based reconstruction algorithm for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 31(10), 1922–1928 (2012).
[CrossRef] [PubMed]

A. Rosenthal, T. Jetzfellner, D. Razansky, V. Ntziachristos, “Efficient framework for model-based tomographic image reconstruction using wavelet packets,” IEEE Trans. Med. Imaging 31(7), 1346–1357 (2012).
[CrossRef] [PubMed]

X. L. Deán-Ben, V. Ntziachristos, D. Razansky, “Artefact reduction in optoacoustic tomographic imaging by estimating the distribution of acoustic scatterers,” J. Biomed. Opt. 17(11), 110504 (2012).
[CrossRef] [PubMed]

X. L. Dean-Ben, R. Ma, D. Razansky, V. Ntziachristos, “Statistical approach for optoacoustic image reconstruction in the presence of strong acoustic heterogeneities,” IEEE Trans. Med. Imaging 30(2), 401–408 (2011).
[CrossRef] [PubMed]

A. Rosenthal, V. Ntziachristos, D. Razansky, “Model-based optoacoustic inversion with arbitrary-shape detectors,” Med. Phys. 38(7), 4285–4295 (2011).
[CrossRef] [PubMed]

D. Razansky, A. Buehler, V. Ntziachristos, “Volumetric real-time multispectral optoacoustic tomography of biomarkers,” Nat. Protoc. 6(8), 1121–1129 (2011).
[CrossRef] [PubMed]

V. Ntziachristos, “Clinical translation of optical and optoacoustic imaging,” Philos Trans A Math Phys. Eng. Sci. 369, 4666–4678 (2011).

V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods 7(8), 603–614 (2010).
[CrossRef] [PubMed]

A. Rosenthal, D. Razansky, V. Ntziachristos, “Fast semi-analytical model-based acoustic inversion for quantitative optoacoustic tomography,” IEEE Trans. Med. Imaging 29(6), 1275–1285 (2010).
[CrossRef] [PubMed]

X. Intes, V. Ntziachristos, J. P. Culver, A. Yodh, B. Chance, “Projection access order in algebraic reconstruction technique for diffuse optical tomography,” Phys. Med. Biol. 47(1), N1–N10 (2002).
[CrossRef] [PubMed]

Oraevsky, A. A.

K. Wang, S. A. Ermilov, R. Su, H. P. Brecht, A. A. Oraevsky, M. A. Anastasio, “An imaging model incorporating ultrasonic transducer properties for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 30(2), 203–214 (2011).
[CrossRef] [PubMed]

Paltauf, G.

P. Burgholzer, G. J. Matt, M. Haltmeier, 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]

G. Paltauf, J. A. Viator, S. A. Prahl, S. L. Jacques, “Iterative reconstruction algorithm for optoacoustic imaging,” J. Acoust. Soc. Am. 112(4), 1536–1544 (2002).
[CrossRef] [PubMed]

Pavía, J.

D. Ros, C. Falcón, I. Juvells, J. Pavía, “The influence of a relaxation parameter on SPECT iterative reconstruction algorithms,” Phys. Med. Biol. 41(5), 925–937 (1996).
[CrossRef] [PubMed]

Pedley, R. B.

E. Z. Zhang, J. G. Laufer, R. B. Pedley, P. C. Beard, “In vivo high-resolution 3D photoacoustic imaging of superficial vascular anatomy,” Phys. Med. Biol. 54(4), 1035–1046 (2009).
[CrossRef] [PubMed]

Prahl, S. A.

G. Paltauf, J. A. Viator, S. A. Prahl, S. L. Jacques, “Iterative reconstruction algorithm for optoacoustic imaging,” J. Acoust. Soc. Am. 112(4), 1536–1544 (2002).
[CrossRef] [PubMed]

Prato, F. S.

P. Ephrat, L. Keenliside, A. Seabrook, F. S. Prato, J. J. Carson, “Three-dimensional photoacoustic imaging by sparse-array detection and iterative image reconstruction,” J. Biomed. Opt. 13(5), 054052 (2008).
[CrossRef] [PubMed]

Queirós, D.

D. Queirós, X. L. Déan-Ben, A. Buehler, D. Razansky, A. Rosenthal, V. Ntziachristos, “Modeling the shape of cylindrically focused transducers in three-dimensional optoacoustic tomography,” J. Biomed. Opt. 18(7), 076014 (2013).
[CrossRef] [PubMed]

Razansky, D.

D. Queirós, X. L. Déan-Ben, A. Buehler, D. Razansky, A. Rosenthal, V. Ntziachristos, “Modeling the shape of cylindrically focused transducers in three-dimensional optoacoustic tomography,” J. Biomed. Opt. 18(7), 076014 (2013).
[CrossRef] [PubMed]

R. Ma, S. Söntges, S. Shoham, V. Ntziachristos, D. Razansky, “Fast scanning coaxial optoacoustic microscopy,” Biomed. Opt. Express 3(7), 1724–1731 (2012).
[CrossRef] [PubMed]

X. L. Deán-Ben, A. Buehler, V. Ntziachristos, D. Razansky, “Accurate model-based reconstruction algorithm for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 31(10), 1922–1928 (2012).
[CrossRef] [PubMed]

M. A. Araque Caballero, A. Rosenthal, J. Gateau, D. Razansky, V. Ntziachristos, “Model-based optoacoustic imaging using focused detector scanning,” Opt. Lett. 37(19), 4080–4082 (2012).
[CrossRef] [PubMed]

X. L. Deán-Ben, V. Ntziachristos, D. Razansky, “Artefact reduction in optoacoustic tomographic imaging by estimating the distribution of acoustic scatterers,” J. Biomed. Opt. 17(11), 110504 (2012).
[CrossRef] [PubMed]

A. Rosenthal, T. Jetzfellner, D. Razansky, V. Ntziachristos, “Efficient framework for model-based tomographic image reconstruction using wavelet packets,” IEEE Trans. Med. Imaging 31(7), 1346–1357 (2012).
[CrossRef] [PubMed]

A. Rosenthal, V. Ntziachristos, D. Razansky, “Model-based optoacoustic inversion with arbitrary-shape detectors,” Med. Phys. 38(7), 4285–4295 (2011).
[CrossRef] [PubMed]

X. L. Dean-Ben, R. Ma, D. Razansky, V. Ntziachristos, “Statistical approach for optoacoustic image reconstruction in the presence of strong acoustic heterogeneities,” IEEE Trans. Med. Imaging 30(2), 401–408 (2011).
[CrossRef] [PubMed]

D. Razansky, A. Buehler, V. Ntziachristos, “Volumetric real-time multispectral optoacoustic tomography of biomarkers,” Nat. Protoc. 6(8), 1121–1129 (2011).
[CrossRef] [PubMed]

A. Rosenthal, D. Razansky, V. Ntziachristos, “Fast semi-analytical model-based acoustic inversion for quantitative optoacoustic tomography,” IEEE Trans. Med. Imaging 29(6), 1275–1285 (2010).
[CrossRef] [PubMed]

Ripoll, J.

Ros, D.

D. Ros, C. Falcón, I. Juvells, J. Pavía, “The influence of a relaxation parameter on SPECT iterative reconstruction algorithms,” Phys. Med. Biol. 41(5), 925–937 (1996).
[CrossRef] [PubMed]

Rosenthal, A.

D. Queirós, X. L. Déan-Ben, A. Buehler, D. Razansky, A. Rosenthal, V. Ntziachristos, “Modeling the shape of cylindrically focused transducers in three-dimensional optoacoustic tomography,” J. Biomed. Opt. 18(7), 076014 (2013).
[CrossRef] [PubMed]

A. Rosenthal, T. Jetzfellner, D. Razansky, V. Ntziachristos, “Efficient framework for model-based tomographic image reconstruction using wavelet packets,” IEEE Trans. Med. Imaging 31(7), 1346–1357 (2012).
[CrossRef] [PubMed]

M. A. Araque Caballero, A. Rosenthal, J. Gateau, D. Razansky, V. Ntziachristos, “Model-based optoacoustic imaging using focused detector scanning,” Opt. Lett. 37(19), 4080–4082 (2012).
[CrossRef] [PubMed]

A. Rosenthal, V. Ntziachristos, D. Razansky, “Model-based optoacoustic inversion with arbitrary-shape detectors,” Med. Phys. 38(7), 4285–4295 (2011).
[CrossRef] [PubMed]

A. Rosenthal, D. Razansky, V. Ntziachristos, “Fast semi-analytical model-based acoustic inversion for quantitative optoacoustic tomography,” IEEE Trans. Med. Imaging 29(6), 1275–1285 (2010).
[CrossRef] [PubMed]

Scambler, P.

J. Laufer, F. Norris, J. Cleary, E. Zhang, B. Treeby, B. Cox, P. Johnson, P. Scambler, M. Lythgoe, P. Beard, “In vivo photoacoustic imaging of mouse embryos,” J. Biomed. Opt. 17(6), 061220 (2012).
[CrossRef] [PubMed]

Seabrook, A.

P. Ephrat, L. Keenliside, A. Seabrook, F. S. Prato, J. J. Carson, “Three-dimensional photoacoustic imaging by sparse-array detection and iterative image reconstruction,” J. Biomed. Opt. 13(5), 054052 (2008).
[CrossRef] [PubMed]

Shiina, T.

S. Bu, Z. Liu, T. Shiina, K. Kondo, M. Yamakawa, K. Fukutani, Y. Someda, Y. Asao, “Model-based reconstruction integrated with fluence compensation for photoacoustic tomography,” IEEE Trans. Biomed. Eng. 59(5), 1354–1363 (2012).
[CrossRef] [PubMed]

Shin, T.

T. Shin, J. F. Nielsen, K. S. Nayak, “Accelerating dynamic spiral MRI by algebraic reconstruction from undersampled k--t space,” IEEE Trans. Med. Imaging 26(7), 917–924 (2007).
[CrossRef] [PubMed]

Shoham, S.

Someda, Y.

S. Bu, Z. Liu, T. Shiina, K. Kondo, M. Yamakawa, K. Fukutani, Y. Someda, Y. Asao, “Model-based reconstruction integrated with fluence compensation for photoacoustic tomography,” IEEE Trans. Biomed. Eng. 59(5), 1354–1363 (2012).
[CrossRef] [PubMed]

Söntges, S.

Stoica, G.

Su, R.

K. Wang, S. A. Ermilov, R. Su, H. P. Brecht, A. A. Oraevsky, M. A. Anastasio, “An imaging model incorporating ultrasonic transducer properties for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 30(2), 203–214 (2011).
[CrossRef] [PubMed]

Treeby, B.

J. Laufer, F. Norris, J. Cleary, E. Zhang, B. Treeby, B. Cox, P. Johnson, P. Scambler, M. Lythgoe, P. Beard, “In vivo photoacoustic imaging of mouse embryos,” J. Biomed. Opt. 17(6), 061220 (2012).
[CrossRef] [PubMed]

Treeby, B. E.

B. E. Treeby, T. K. Varslot, E. Z. Zhang, J. G. Laufer, P. C. Beard, “Automatic sound speed selection in photoacoustic image reconstruction using an autofocus approach,” J. Biomed. Opt. 16(9), 090501 (2011).
[CrossRef] [PubMed]

B. E. Treeby, 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]

Udías, J. M.

J. L. Herraiz, S. España, J. J. Vaquero, M. Desco, J. M. Udías, “FIRST: Fast Iterative Reconstruction Software for (PET) tomography,” Phys. Med. Biol. 51(18), 4547–4565 (2006).
[CrossRef] [PubMed]

Vaquero, J. J.

Varslot, T. K.

B. E. Treeby, T. K. Varslot, E. Z. Zhang, J. G. Laufer, P. C. Beard, “Automatic sound speed selection in photoacoustic image reconstruction using an autofocus approach,” J. Biomed. Opt. 16(9), 090501 (2011).
[CrossRef] [PubMed]

Viator, J. A.

G. Paltauf, J. A. Viator, S. A. Prahl, S. L. Jacques, “Iterative reconstruction algorithm for optoacoustic imaging,” J. Acoust. Soc. Am. 112(4), 1536–1544 (2002).
[CrossRef] [PubMed]

Wang, K.

K. Wang, S. A. Ermilov, R. Su, H. P. Brecht, A. A. Oraevsky, M. A. Anastasio, “An imaging model incorporating ultrasonic transducer properties for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 30(2), 203–214 (2011).
[CrossRef] [PubMed]

Wang, L.

L. Wang, K. Maslov, W. Xing, A. Garcia-Uribe, L. V. Wang, “Video-rate functional photoacoustic microscopy at depths,” J. Biomed. Opt. 17(10), 106007 (2012).
[CrossRef] [PubMed]

J. Yao, C. H. Huang, L. Wang, J. M. Yang, L. Gao, K. I. Maslov, J. Zou, L. V. Wang, “Wide-field fast-scanning photoacoustic microscopy based on a water-immersible MEMS scanning mirror,” J. Biomed. Opt. 17(8), 080505 (2012).
[CrossRef] [PubMed]

Wang, L. V.

L. V. Wang, S. Hu, “Photoacoustic tomography: in vivo imaging from organelles to organs,” Science 335(6075), 1458–1462 (2012).
[CrossRef] [PubMed]

J. Yao, C. H. Huang, L. Wang, J. M. Yang, L. Gao, K. I. Maslov, J. Zou, L. V. Wang, “Wide-field fast-scanning photoacoustic microscopy based on a water-immersible MEMS scanning mirror,” J. Biomed. Opt. 17(8), 080505 (2012).
[CrossRef] [PubMed]

L. Wang, K. Maslov, W. Xing, A. Garcia-Uribe, L. V. Wang, “Video-rate functional photoacoustic microscopy at depths,” J. Biomed. Opt. 17(10), 106007 (2012).
[CrossRef] [PubMed]

L. V. Wang, “Multiscale photoacoustic microscopy and computed tomography,” Nat. Photonics 3(9), 503–509 (2009).
[CrossRef] [PubMed]

H. F. Zhang, K. Maslov, L. V. Wang, “In vivo imaging of subcutaneous structures using functional photoacoustic microscopy,” Nat. Protoc. 2(4), 797–804 (2007).
[CrossRef] [PubMed]

H. F. Zhang, K. Maslov, M. L. Li, G. Stoica, L. V. Wang, “In vivo volumetric imaging of subcutaneous microvasculature by photoacoustic microscopy,” Opt. Express 14(20), 9317–9323 (2006).
[CrossRef] [PubMed]

M. L. Li, H. E. Zhang, K. Maslov, G. Stoica, L. V. Wang, “Improved in vivo photoacoustic microscopy based on a virtual-detector concept,” Opt. Lett. 31(4), 474–476 (2006).
[CrossRef] [PubMed]

K. Maslov, G. Stoica, L. V. Wang, “In vivo dark-field reflection-mode photoacoustic microscopy,” Opt. Lett. 30(6), 625–627 (2005).
[CrossRef] [PubMed]

M. Xu, 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]

Xing, W.

L. Wang, K. Maslov, W. Xing, A. Garcia-Uribe, L. V. Wang, “Video-rate functional photoacoustic microscopy at depths,” J. Biomed. Opt. 17(10), 106007 (2012).
[CrossRef] [PubMed]

Xu, M.

M. Xu, 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]

Yamakawa, M.

S. Bu, Z. Liu, T. Shiina, K. Kondo, M. Yamakawa, K. Fukutani, Y. Someda, Y. Asao, “Model-based reconstruction integrated with fluence compensation for photoacoustic tomography,” IEEE Trans. Biomed. Eng. 59(5), 1354–1363 (2012).
[CrossRef] [PubMed]

Yang, J. M.

J. Yao, C. H. Huang, L. Wang, J. M. Yang, L. Gao, K. I. Maslov, J. Zou, L. V. Wang, “Wide-field fast-scanning photoacoustic microscopy based on a water-immersible MEMS scanning mirror,” J. Biomed. Opt. 17(8), 080505 (2012).
[CrossRef] [PubMed]

Yao, J.

J. Yao, C. H. Huang, L. Wang, J. M. Yang, L. Gao, K. I. Maslov, J. Zou, L. V. Wang, “Wide-field fast-scanning photoacoustic microscopy based on a water-immersible MEMS scanning mirror,” J. Biomed. Opt. 17(8), 080505 (2012).
[CrossRef] [PubMed]

Yodh, A.

T. Durduran, R. Choe, W. B. Baker, A. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73(7), 076701 (2010).
[CrossRef]

X. Intes, V. Ntziachristos, J. P. Culver, A. Yodh, B. Chance, “Projection access order in algebraic reconstruction technique for diffuse optical tomography,” Phys. Med. Biol. 47(1), N1–N10 (2002).
[CrossRef] [PubMed]

Zhang, E.

J. Laufer, F. Norris, J. Cleary, E. Zhang, B. Treeby, B. Cox, P. Johnson, P. Scambler, M. Lythgoe, P. Beard, “In vivo photoacoustic imaging of mouse embryos,” J. Biomed. Opt. 17(6), 061220 (2012).
[CrossRef] [PubMed]

Zhang, E. Z.

B. E. Treeby, T. K. Varslot, E. Z. Zhang, J. G. Laufer, P. C. Beard, “Automatic sound speed selection in photoacoustic image reconstruction using an autofocus approach,” J. Biomed. Opt. 16(9), 090501 (2011).
[CrossRef] [PubMed]

E. Z. Zhang, J. G. Laufer, R. B. Pedley, P. C. Beard, “In vivo high-resolution 3D photoacoustic imaging of superficial vascular anatomy,” Phys. Med. Biol. 54(4), 1035–1046 (2009).
[CrossRef] [PubMed]

Zhang, H. E.

Zhang, H. F.

H. F. Zhang, K. Maslov, L. V. Wang, “In vivo imaging of subcutaneous structures using functional photoacoustic microscopy,” Nat. Protoc. 2(4), 797–804 (2007).
[CrossRef] [PubMed]

H. F. Zhang, K. Maslov, M. L. Li, G. Stoica, L. V. Wang, “In vivo volumetric imaging of subcutaneous microvasculature by photoacoustic microscopy,” Opt. Express 14(20), 9317–9323 (2006).
[CrossRef] [PubMed]

Zou, J.

J. Yao, C. H. Huang, L. Wang, J. M. Yang, L. Gao, K. I. Maslov, J. Zou, L. V. Wang, “Wide-field fast-scanning photoacoustic microscopy based on a water-immersible MEMS scanning mirror,” J. Biomed. Opt. 17(8), 080505 (2012).
[CrossRef] [PubMed]

Appl. Opt. (1)

Biomed. Opt. Express (1)

IEEE Trans. Biomed. Eng. (1)

S. Bu, Z. Liu, T. Shiina, K. Kondo, M. Yamakawa, K. Fukutani, Y. Someda, Y. Asao, “Model-based reconstruction integrated with fluence compensation for photoacoustic tomography,” IEEE Trans. Biomed. Eng. 59(5), 1354–1363 (2012).
[CrossRef] [PubMed]

IEEE Trans. Med. Imaging (8)

X. L. Dean-Ben, R. Ma, D. Razansky, V. Ntziachristos, “Statistical approach for optoacoustic image reconstruction in the presence of strong acoustic heterogeneities,” IEEE Trans. Med. Imaging 30(2), 401–408 (2011).
[CrossRef] [PubMed]

G. T. Herman, L. B. Meyer, “Algebraic reconstruction techniques can be made computationally efficient [positron emission tomography application],” IEEE Trans. Med. Imaging 12(3), 600–609 (1993).
[CrossRef] [PubMed]

T. Shin, J. F. Nielsen, K. S. Nayak, “Accelerating dynamic spiral MRI by algebraic reconstruction from undersampled k--t space,” IEEE Trans. Med. Imaging 26(7), 917–924 (2007).
[CrossRef] [PubMed]

A. H. Andersen, “Algebraic reconstruction in CT from limited views,” IEEE Trans. Med. Imaging 8(1), 50–55 (1989).
[CrossRef] [PubMed]

X. L. Deán-Ben, A. Buehler, V. Ntziachristos, D. Razansky, “Accurate model-based reconstruction algorithm for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 31(10), 1922–1928 (2012).
[CrossRef] [PubMed]

A. Rosenthal, D. Razansky, V. Ntziachristos, “Fast semi-analytical model-based acoustic inversion for quantitative optoacoustic tomography,” IEEE Trans. Med. Imaging 29(6), 1275–1285 (2010).
[CrossRef] [PubMed]

K. Wang, S. A. Ermilov, R. Su, H. P. Brecht, A. A. Oraevsky, M. A. Anastasio, “An imaging model incorporating ultrasonic transducer properties for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 30(2), 203–214 (2011).
[CrossRef] [PubMed]

A. Rosenthal, T. Jetzfellner, D. Razansky, V. Ntziachristos, “Efficient framework for model-based tomographic image reconstruction using wavelet packets,” IEEE Trans. Med. Imaging 31(7), 1346–1357 (2012).
[CrossRef] [PubMed]

J. Acoust. Soc. Am. (2)

C. G. Hoelen, F. F. de Mul, “A new theoretical approach to photoacoustic signal generation,” J. Acoust. Soc. Am. 106, 11 (1999).

G. Paltauf, J. A. Viator, S. A. Prahl, S. L. Jacques, “Iterative reconstruction algorithm for optoacoustic imaging,” J. Acoust. Soc. Am. 112(4), 1536–1544 (2002).
[CrossRef] [PubMed]

J. Biomed. Opt. (8)

P. Ephrat, L. Keenliside, A. Seabrook, F. S. Prato, J. J. Carson, “Three-dimensional photoacoustic imaging by sparse-array detection and iterative image reconstruction,” J. Biomed. Opt. 13(5), 054052 (2008).
[CrossRef] [PubMed]

D. Queirós, X. L. Déan-Ben, A. Buehler, D. Razansky, A. Rosenthal, V. Ntziachristos, “Modeling the shape of cylindrically focused transducers in three-dimensional optoacoustic tomography,” J. Biomed. Opt. 18(7), 076014 (2013).
[CrossRef] [PubMed]

B. E. Treeby, 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. Laufer, F. Norris, J. Cleary, E. Zhang, B. Treeby, B. Cox, P. Johnson, P. Scambler, M. Lythgoe, P. Beard, “In vivo photoacoustic imaging of mouse embryos,” J. Biomed. Opt. 17(6), 061220 (2012).
[CrossRef] [PubMed]

L. Wang, K. Maslov, W. Xing, A. Garcia-Uribe, L. V. Wang, “Video-rate functional photoacoustic microscopy at depths,” J. Biomed. Opt. 17(10), 106007 (2012).
[CrossRef] [PubMed]

J. Yao, C. H. Huang, L. Wang, J. M. Yang, L. Gao, K. I. Maslov, J. Zou, L. V. Wang, “Wide-field fast-scanning photoacoustic microscopy based on a water-immersible MEMS scanning mirror,” J. Biomed. Opt. 17(8), 080505 (2012).
[CrossRef] [PubMed]

B. E. Treeby, T. K. Varslot, E. Z. Zhang, J. G. Laufer, P. C. Beard, “Automatic sound speed selection in photoacoustic image reconstruction using an autofocus approach,” J. Biomed. Opt. 16(9), 090501 (2011).
[CrossRef] [PubMed]

X. L. Deán-Ben, V. Ntziachristos, D. Razansky, “Artefact reduction in optoacoustic tomographic imaging by estimating the distribution of acoustic scatterers,” J. Biomed. Opt. 17(11), 110504 (2012).
[CrossRef] [PubMed]

J. Nucl. Med. (1)

P. B. Garcia-Allende, J. Glatz, M. Koch, V. Ntziachristos, “Enriching the Interventional Vision of Cancer with Fluorescence and Optoacoustic Imaging,” J. Nucl. Med. 54(5), 664–667 (2013).
[CrossRef] [PubMed]

Med. Phys. (1)

A. Rosenthal, V. Ntziachristos, D. Razansky, “Model-based optoacoustic inversion with arbitrary-shape detectors,” Med. Phys. 38(7), 4285–4295 (2011).
[CrossRef] [PubMed]

Nat. Methods (1)

V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods 7(8), 603–614 (2010).
[CrossRef] [PubMed]

Nat. Photonics (1)

L. V. Wang, “Multiscale photoacoustic microscopy and computed tomography,” Nat. Photonics 3(9), 503–509 (2009).
[CrossRef] [PubMed]

Nat. Protoc. (2)

H. F. Zhang, K. Maslov, L. V. Wang, “In vivo imaging of subcutaneous structures using functional photoacoustic microscopy,” Nat. Protoc. 2(4), 797–804 (2007).
[CrossRef] [PubMed]

D. Razansky, A. Buehler, V. Ntziachristos, “Volumetric real-time multispectral optoacoustic tomography of biomarkers,” Nat. Protoc. 6(8), 1121–1129 (2011).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (3)

Philos Trans A Math Phys. Eng. Sci. (1)

V. Ntziachristos, “Clinical translation of optical and optoacoustic imaging,” Philos Trans A Math Phys. Eng. Sci. 369, 4666–4678 (2011).

Phys. Med. Biol. (4)

E. Z. Zhang, J. G. Laufer, R. B. Pedley, P. C. Beard, “In vivo high-resolution 3D photoacoustic imaging of superficial vascular anatomy,” Phys. Med. Biol. 54(4), 1035–1046 (2009).
[CrossRef] [PubMed]

D. Ros, C. Falcón, I. Juvells, J. Pavía, “The influence of a relaxation parameter on SPECT iterative reconstruction algorithms,” Phys. Med. Biol. 41(5), 925–937 (1996).
[CrossRef] [PubMed]

X. Intes, V. Ntziachristos, J. P. Culver, A. Yodh, B. Chance, “Projection access order in algebraic reconstruction technique for diffuse optical tomography,” Phys. Med. Biol. 47(1), N1–N10 (2002).
[CrossRef] [PubMed]

J. L. Herraiz, S. España, J. J. Vaquero, M. Desco, J. M. Udías, “FIRST: Fast Iterative Reconstruction Software for (PET) tomography,” Phys. Med. Biol. 51(18), 4547–4565 (2006).
[CrossRef] [PubMed]

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

M. Xu, 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, 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]

Rep. Prog. Phys. (1)

T. Durduran, R. Choe, W. B. Baker, A. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73(7), 076701 (2010).
[CrossRef]

Science (1)

L. V. Wang, S. Hu, “Photoacoustic tomography: in vivo imaging from organelles to organs,” Science 335(6075), 1458–1462 (2012).
[CrossRef] [PubMed]

Other (4)

M. B. Taisuke, A. Pau Giannoula, and T. Durduran, “MBio: a comprehensive Monte-carlo package for Diffuse Correñation Spectroscopy/Tomography,” in European Conferences on iomedical Optics, 2013)

L. H. Wang, Biomedical Optics: Principles and Imaging (Wiley, Hoboken, New Jersey, 2007).

T. Koichi, W. Katsuhiro, F. Kazuhiko, and S. Tsuyoshi, “Advanced model-based reconstruction algorithm for practical three-dimensional photoacoustic imaginbg,” in SPIE, 2011)

B. Shuhui, L. Zhenbao, S. Tsuyoshi, and F. Kazuhiko, “Matrix compression and Compressed sensing reconstruction for photoacoustic tomography,” Elektonika Ir Elektrotechnika, 18 (2012).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

: (Top) Representation of a row of the weight matrix W corresponding to a specific time point and a detector characterized by the position of its focal point rd1. (Bottom) Representation of a row of the weight matrix for the same time point, corresponding to the same detector but now situated at position rd2 (focal point). A large area of the bottom image can be seen as a translation of the top image. The weights correspond to a circular transducer with a radius of 12.7 mm and a numerical aperture of 0.36 that is, situated in the positive part of the z axis.

Fig. 2
Fig. 2

A schematic of the simulated objects for the numerical simulation. Five spheres of 300 μm diameter separated by 500 μm each are shown. In the simulation each sphere is homogeneously heated.

Fig. 3
Fig. 3

The diagram of the ICFO-PAM scanning head.

Fig. 4
Fig. 4

(Left) Raw, simulated PAM data of the imaged objects obtained after the linear scan. (Right) Model based reconstruction after three iterations of the ART algorithm using the low memory cost generator matrix. All five objects (shown in Fig. 1) are clearly resolved in both dimensions. All data are normalized to the maximum.

Fig. 5
Fig. 5

The 3D reconstruction of the thread after three iterations of the ART algorithm using the low memory cost generator matrix. The reconstructed image is represented with 30 equally spaced axial slices. The image is normalized to the maximum.

Fig. 6
Fig. 6

Representation of a slice in the z-y plane of the 3D reconstruction corresponding to x = 2.9 mm.

Fig. 7
Fig. 7

Representation of a slice in the z-x plane of the 3D reconstruction corresponding to y = 4.5 mm

Tables (1)

Tables Icon

Table 1 Reconstruction time and size of the matrix corresponding to the numerical experiment

Equations (13)

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

2 p ( r , t ) t 2 c s 2 2 p ( r , t ) = Γ H ( r ) δ ( t ) t .
p ( r , r j , t ) = p 0 ( r j ) [ U ( R c s t | r r j | ) + | r r i | c s t 2 | r r j | U ( | r r j | | R c s t | ) U ( R + c s t | r r j | ) ]
p ( r , r j , t ) = p 0 ( r j ) p s p ( r , r j , t ) ,
p ( r , t ) j = 1 N p o ( r j ) p s p ( r , r j , t )
p ( r d , t k ) j = 1 N p o ( r j ) p s p ( r d , r j , t k ) , where d = 1... S k = 1... T
b = [ W ˜ ] x
p det ( r d , t ) = p ( r , t ) D ( r ) d r
p det ( r d , t k ) h 3 j = 1 N p o ( r j ) l = 1 B p s p ( r d , l , r j , t k ) = j = 1 N p o ( r j ) w ( r d , r j , t k )
b = [ W ] x .
p det ( r d , t k ) j = 1 N Γ μ ( r j ) ϕ ( r j ) w ( r d , r j , t k ) = j = 1 N p ^ o ( r j ) w ^ ( r d , r j , t k ) .
w ( r d 2 , r j , t k ) = w ( r d 1 , r j ( r d 1 r d 2 ) , t k ) .
w ( r d 2 , r j , t k ) = w ( r d 1 , r j ( r d 1 r d 2 ) , t k ) .
x i ( l + 1 ) = x i ( l ) + λ b i j w i j x j ( l ) j w i j 2 w i .

Metrics